Coo0-1112-3 THE U N I V E R S I T Y OF M I C H I G A. N COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS Department of Physics Technical Report FOUR- AND FIVE-PARTICLE PRODUCTION IN 3.7 BeV/c V-p COLLISIONS William D. C, Moebs, III ORA Project 04938 under contract with: U. S. ATOMIC ENERGY COMMISSION CHICAGO OPERATIONS OFFICE CONTRACT NO. AT(11-1)-1112 ARGONNE, I LLINOIS administered through: OFFICE OF RESEARCH ADMINISTRA.TION ANN ARBOR September 1965

This report was also a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1965.

TABLE OF CONTENTS Page LIST OF TABLES V LIST OF FIGURES vi ABSTRACT x CHAPTER I. INTRODUCTION 1 1. Introductory Remarks 1 2. Area of Investigation 6 II. THE EXPERIMENT AND THE DATA 10 1. The Beam 10 2. The Chamber 10 3. The Scanning 11 4. The Measuring 13 5. Geometry, Kinematics, and Event Identification 14 III. DEFINITIONS, NOTATION, AND PHASE SPACE 27 1. Introduction 27 2. Mass 27 3. Phase Space and Dalitz Plots 28 4. Resonances 30 5. The Method for Treating "Dolble-Resonance Events" 35 6. More Definitions 36 IV. THE REACTION T'+p-+-i+rtc+s ++p 39 1. The Mass Spectra 39 2. The p~-N,3(1238) Separation and their Cross Sections 41 3. The Two-Pion Decay of the co~ 49 4. The p~ Meson 52 4.1 Introduction 52 4.2 Isobar Production in Association with the p~ Meson 53 4.3 The p~ and the One-Pion-Exchange Model 55 4.4 The p0 Decay 58 4.5 The A1 and A2 Mesons 63 iii

TABLE OF CONTENTS (Concluded) Chapter Page 5. The N* (1238) Channel 72 5.1 '~ntroduction. 72 5.2 The (-,,c-,N3,3(1238)) Masses 73 5.3 A Study of the (x-,x-) ElasticScattering Cross Section 73 5.4 The (C-,x-) Scattering Angle Distribution 80 6. Production Angles 84 V. THE REACTION x- + p + +- + + + p + gx 86 1. Introduction 86 2. The Mass Plots 86 3. The cu~ Peak 87 3.1 The w~o Cross Section 87 3.2 The Spin and Parity of the wc~ 89 3.3 The Mass Spectra for the (w~ 0,-,p) State 91 3.4 The B Peak 94 4. The p- Peak 98 4.1 Introduction 98 4.2 (N*,xt) Decay Modes of the Higher Nucleon Isobars 98 4.3 The Production Mechanism for the p- 104 5. cp Meson Production 108 6. The Production Angles 109 VI. THE REACTION + p + + + ++ + n 111 VII. RESONANCE CROSS SECTIONS 112 APPENDIX A. LORENTZ INVARIANT PHASE SPACE AND THE DALiTZ PLOT 114 APPENDIX B. THE RELATIVE DECAY RATES FOR THE T = 1/2 AND T = 3/2 ISOBARS 120 APPENDIX C. p AND po PRODUCTION IN THE ONE-PION-EXCHNGE MODEL 121 REFERENCES 124

LIST OF TABLES Tab le Page I. Event Classification After the Bubble Density Check 22 II. The Final Disposition of Events Along with Cross Sections 26 III. The Estimated Division of the p~ - N, 3(1238) Overlap Events 44 IV. The p~ and N,3 (1238) Cross Sections for the Reaction x- + p + x- + ir + + p 48 V. The Results of X2 Fits to (IV.1) for the p~ Region with Various Momentum Transfer Cutoffs 62 VI. The Results of X2 Fits to (IV.8) for Various M -~- Regions 83 VII. The Cross Sections for the Resonances Found in This Experiment 113

LIST OF FIGURES Figure Page 1. One-meson-exchange diagrams for (a) Tr- + p + + + N>3,3 and (b) g+ + n + p + c~. 3 3+ 2. A schematic representation of the J = 2 decuplet. 4 3. One-pion-exchange diagrams for (a) reaction (1.11) and (b) reaction (1.12). 7 4. A simplified sketch of the bubble chamber and its cameras. 15 5. A. given track as seen by the cameras C1 and C2. 17 6. An example of a track fitted to its measured points. 18 2 7. The X distributions for the good events. 23 8. The g~ kinetic energy for the events ambiguous between (r-,:T-,gr+,p,y~c) and (-, ',:+,p). 25 9. The X2 distributions for the events ambiguous between (:K, -,+,p,~ ) and (:,K,+,:,n).25 10. Two-body masses for the final state (+r-,C-,i,p). 32 11. Three-body masses for the final state (rr,r,c-+,p). 33 12. Diagram for an arbitrary single-pion-exchange process with all momenta given in the beam rest frame. 38 13. The momentum vectors for a typical reaction of type (4.2). 40 14. Mg+p for the p~ events and M _g+ for the N,3 (1238) events. 42 15. Various stages of the p~-N3 (1238) overlap estimates. 45 vi

LIST OF FIGURES (Continued) Figure Page 16. Mx_x+ for various momentum transfer regions. 51 17. Mr-p for the p~ events. 54 18. Possible pion-exchange diagrams for the (c-,-,xc+,p) final state. 56 19. The A2 o distribution. 57 20. The production angle for the p~ events. 57 21. The Trieman-Yang angle for the pO events. 57 22. The scattering angle for the X- in the p~ center of mass. 60 23.. The scattering angle for the X- in the p~ center of mass with various A2 0po cutoffs imposed on the data. 61 24. The M o distribution. 64 p 25. The M distributions when the A1 and A2 mesons are produced. 66 26. Dalitz plot for the (p~,x-,p) final state. 69 27. The M distribution for low momentum transfer to the A mesons. 70 28, The M_ and MN 3 distributions for the (i -,i,N33 (1238)) final state. 74 29. The A distribution for the (-r,N- 3(1238)) final state. 75 30. The Trieman-Yang angle for the negative pions in the (rc-,-,N* (1238)) final state. 75 3,3 31. The (X-,7r) cross section as a function of the center-of-mass energy. 79 vii

LIST OF FIGURES (Continued) Figure Page 32. The c- scattering angle in the (K-,xE) center of mass for various M regions. 82 33. The particle production angles for the reaction - + p -)-; J + Jr ++ p. 85 345 The particle production angles for the reaction Tr + p -+ 7r + gC + N,3 (1238). 8 35. The particle production angles for the reaction + + p -p + +o + p. 85 36. Mit-o and M+p for the final state (x,-, +,p, )o 88 537 Mg-t+go and M-,,+p for the final state (n-,+v-,+,p,~ )o 88 38. Dalitz plot for the three-pion decay of the co. 90 39. Dalitz plot and its projections for the final state (w0~,~,p). 92 40~. M-n+To for (a) the inside and (b) the outside events. 95 41. MG _x+ o for the events satisfying 760 < M -,+,~ < 820 MeV. (a) the inside and (b) the outside events. 95 2 42. M for those events which satisfy Tc + p ~ B- + p. 96 '-p 435 M-+p for the reaction o- + p - p- + gt + T + po 99 44. M,, o for the reaction x- + p + Ac + + co + N3* (1238). 99 45. M *N for the reaction x- + p + p- + 353 + N (1238). 101 53.13 46~ M~+h~3 for the reaction x- + p + pi + x+ + N3,(12358). 101 viii

LIST OF FIGURES (Concluded) Figure Page 47. Dalitz plots for (a) 1600 < M_-.+p < 1760 MeV and (b) 1800 < M Kr +p < 2040 MeV. 103 48. Possible meson-exchange diagrams for p- production in reaction (5-10). 105 49. Ma+N* for the reaction -c + p - "po o + 3, -3 + N, (1238). 107 50. The xr- scattering angle in the p- center of mass. 107 51. The particle production angles for the reaction +- +-+ p + + p + 110 52. One-pion-exchange diagrams for reactions (1) and (2). 121 ix

ABSTRACT In an exposure of the BNL 20-inch hydrogen bubble chamber to a 3.7 'r beam, 805, 1025, and 489 events of the reaction type: (1) K- + p + x- + x- + + + p, (2) '- + p -+ - + i- + + p + p + and (3) - + p- + T+ + it + + + n~ respectively, have been observed. The two-three- and four-body mass spectra have been studied in a search for short-lived resonant states involving the various particle combinations. In reaction (1) there are peaks corresponding to the p~, the 1238 and 1512 MeV isobars, and the Al and A2 mesons. It is found that both the p~ and the 1238 MeV isobar channels can be analyzed by means of the one-pion-exchange model, and consequently, the pionpion interaction is studied for both. Reaction (2) is found to be dominated by p' and c~ production. It is observed that both of these mesons are produced in conjunction with nucleon isobars. The p- channel furnishes examples of the higher nucleon isobars decaying into a pion and the 1238 MeV (jr+,p) resonance, which in turn breaks up into a A-+ and a p. A. peak is also found in the (x_,uo) mass spectrum at 1250 MeV, but serious questions are raised about its interpretation as a (Jr,r ) resonance. Cross sections for the three reactions and the various resonance channels are also presented. xi

CHAPTER I INTRODUCTION 1. INTRODUCTORY REMARKS During the past four years a vast amount of high-energy physics research has been devoted to the search for and the investigation of resonant states existing between the elementary particles. In this short period of time experimenters have discovered approximately thirty resonances, many of which have more than one charge state. The first elementary particle resonance was discovered in 1952 when it was found that the pion-proton elastic scattering cross section goes through a broad maximum centered at a beam momentum of approximately 200 MeV.1 This resonance, which is called the N*(1238), has since been found in multiparticle production by examining the invariant mass plots of the pion-proton system. In the years from 1952 to 1960, with the exception of pionnucleon elastic scattering studies, there was virtually no work done in the field of resonance production. Then in 1960, while analyzing the reaction K + p - A~ + Tir + t+~ (1.1) A.lston et al. 2 found that the (T,A) system forms a resonant state at 1385 MeV. A. short time later two meson resonances, the p~ and V0, 35-6 were discovered by many different groups. The search for both of

these was inspired by their predicted existence in order to explain the charge structure of the nucleon.7-9 Since these initial discoveries many additional resonant states have been found. These include the o0, various pion-nucleon states, the A. and B mesons, and many others. For a complete list of all elementary particles and resonant states known at this time, the reader is referred to a recent article in Reviews of Modern Physics. Along with the ever-increasing list of new particles, many theoretical models have been brought forth in an attempt to explain resonance production. These have been somewhat confined to elastic scattering and single-pion production processes such as + p + pr + a + n, (1.2) and no decent explanation of multiple-particle processes has been formulated. It is of interest, therefore, to attempt to relate the many-particle states to simpler two- and three-body states. If this simplification can be made, it is then possible to apply the existing theoretical models to these higher multiplicities. This has been done with some success by J. Alitti et al., and N. Schmitz15 who were able to study the (Oi,y-) interaction by applying the one-pion-exchange model (see the Feynam diagram of Figure l(a)) to the reaction K- + P + K- + - + 3,3 + (1.3) + t + p~ Also, a recent refinement of the meson-exchange models to include

absorptive effects arising from coupling between different channelsl6'17 is now being tested in various experiments. This version of the p —exchange model (see Figure l(b)) has been applied to w~ production in the reaction + + n +p + ~ + Tr + NO (1.4) and gives good estimates of the production cross section and decay properties of the '~. ~~(oh4a~~~~ ~(b' + oT Figure 1. One-meson-exchange diagrams for (a) - + p-* g- + K+ N3 and (b) X1 + n t p + o. In addition to the dynamical models for particle production, many mass schemes and formulas have been proposed which attempt to 19,20 place the particles in some systematic pattern. Since there is no real understanding of the strong interaction, a basic assumption that nature choses her mass states in some well-ordered manner underlies all of these classification methods. At the present time the most 21,22 promising of these is the "eightfold way" (SU3) which is based on the mathematical properties of Lie algebras and Lie groups. This system places particles of the same spin and parity into a group and then

conjectures a mass formula connecting the members of the group. So far, multiplets consisting of one, eight, and ten members have been described quite accurately by SU3. Undoubtedly, the theory's most striking success is the experimental confirmation of the baryon decuplet with the spin-parity assignment JP= 3/2+. At the time that SU3 was introduced, only the quartet (the 1238 MeV N* ) and the Z triplet 303 (the 1385 MeV(~A) resonance of Alston et al. 2) had been seen. Since the mass rule predicts approximately equal mass intervals between the members of the group, there should be a doublet at 1530 MeV and an Q- singlet, which is stable under strong and electromagnetic interactions, at 1676 MeV (see Figure 2). These have both been found23'24 and furnish striking evidence of the eightfold way's validity-even though the spin and parity of the Q2- have not yet been measured. MA.SS(MeV):X &I- 1676 x x-~ 153 o x Z- x Z xZ+ 1385 x-15/2+ I-1/2I +X-1/2 +5/2x 1238 -3/2 -1/2 +1/2 +3/2 Figure 2. The J=3/2+ decuplet with mass represented by the vertical axis and the Z component of isotopic spin represented by the horizontal axis. The formalism of the eightfold way satisfies the rules of a Lie algebra which has eight independent quantum numbers. These eight

quantities are the hypercharge Y, the three components of isotopic spin I, and four other symmetries which have not yet been identified with known observables. The basic assumption of SU3 is that the strong interaction can be divided into two parts-one preserves all eight symmetries, and the other violates the symmetries associated with the four new quantum numbers while preserving Y and I. If there weren't this symmetry breaking, all strongly interacting particles of a spin —parity multiplet would have the same mass; a given group just represents different states of the same particle. A. simple but instructive analogue to SU3 is furnished by the properties of the spinless hydrogen atom. The rotational invariance of this system is characterized by the conservation of angular momentum L and can be expressed mathematically by the rules of the Lie algebra for the group called SU2. When the atom is placed in a Z-directed magnetic field Bz, only the symmetries associated with the Z direction are preserved ([HLi] f 0, unless Li = Lz), and additionally, the energy degeneracy associated with a given angular momentum state- is broken. The similarity with SU3 is quite clear if one associates the unperturbed Hamiltonian with the particle mass operator, the perturbing term Bz with the mass splitting, L with the set of new quantum numbers, and Lz with the set [Y,I). Just as the magnetic field destroys most of the rotational symmetry and causes energy splitting in the atom, some part of the strong interaction executes an analogous influence on the symmetries and mass states of the SU3 system.

2. AREA OF INVESTIGATION The purpose of this report is to discuss the results of a detailed study of certain pion-pion and pion-nucleon resonances found in a hydrogen bubble chamber experiment. Sixty-thousand pictures were taken in the Schutt 20-inch chamber using a 3.7 BeV/c separated K- beam. The reactions:- + p - + - + + + p, (15) I p+ + + +p (1.5) + +~ p +,(6 and 4+~ + -+:t++ + % + n (1.7) are considered here. The complete results on the reactions t- + p + -c +T c + n, (1.8) _~ + to +p (1.9) ~+ ~ + ), (1.10) 25 -31 plus preliminary results on both types have been reported elsewhere.5 Reaction (1.5) is found to be dominated by resonance production, with only 22% of the events not having at least one mass value in either the N* (1238)- or p~ peak. The production of these two 3,3 resonances is represented by the reactions ~ - + p + ~- + X- + N* (1238) (1.11) 3.,3 T+% + p *The notation N. (1238) will be used throughout the text and represents a nucleon isobar of mass 1238 MeV with total isotopic spin i/2 and Z component j/2.

and ~ _ + p + P + po +p(1.12) - X- + %+ Both (1.11) and (1.12) are found to occur by means of a single-pionexchange processll and therefore, a detailed analysis of the upper verticies in Figures 3(a) and 3(b) is undertaken. (a,) (b) Figure 3. One-pion-exchange diagrams for (a) reaction (1.11) and (b) reaction (1.12). The pion-pion vertex is analyzed by means of a partial wave expansion for both, and with the aid of the Chew-Low method and reaction (1.11), the ((-,i-) cross section is determined as a function of center-ofmass energy. It is also found that the p0 is frequently produced in two-body final states via the modes 7- + p p + N (1238) (1.13) + t- +p, + po + N, 1(1512) (1.14) (1.14) +- +p, + pO +.and p + A2 (1.16) + po + r1_.

In reaction (1.6) a large fraction of the events involve the production of the wO and p mesons through the processes + _ + p + Do (1.17) +C+ 3 + + 7C and + ~- + X + + p + p- (1.18) (1.18) -* Xrt~ + 7T. Again two-body final states are prominent, with a significant number of events belonging to the channels r- + p + i~ + N* _1(1238) (1.19) + t + P + C + N *1(1512) (1.20) + CD~ + N1,1(1688) (1.21) +-.I +p, + p + N1 j(1512) (1.22) +, + N, (1238) + P + p + N* (1688) (1.23) + A + N;,5(1238) nt + P, and + p + N3,1(1920) (1.24) + r + N3,3(1238) + P. In the (0~,7() mass plot an enhancement appears at approximately 1250 MeV which corresponds to the B meson. It will be seen, however, that there are very serious questions about this peak which make its inter

pretation very indefinite. The analysis of (1,7) does not show the prolific resonance production that characterizes the other two reactions. There is a strong peak in the (r-,n) system due to the reaction - + p r T + ++ + N* (1238) (1.25) 5,-3 t -~ + n, but this is the only resonant state found. Other pion-proton experiments33-39 of this type have been performed at various beam momenta in the range 2-5 BeV/c. All of these see the strong p~ and N (12388) production in (1.5), the w~ peak in (1. 6), and the N3 (1238) in (1.7). There is also general agreement on the existence of the two peaks in the (g-,p0) mass plots at 1090 and 1310 MeV. The p peak in (1.6) is one serious source of disagreement between this and other experiments. All other results indicate virtually no evidence of charged p production in the multipion final states. Because the production and decay processes represented by reactions (1,22-1o. 24) are heretofore unseen, there is a definite necessity for further data, either to confirm or to destroy this result.

CHAPTER II THE EXPERIMENT AND THE DATA 1. THE BEAM The beam used in this experiment was obtained in a parasitic run at the Brookhaven Alternating Gradient Synchrotron. A. small fraction of the internal proton beam was deflected onto an aluminum target which was 0.1 inch in height, 0.25 inch wide, and 2.0 inches long. Before reaching the bubble chamber, the beam travelled 270 feet through a beam transport section, two separation stages, and a beam shaping section. At the target the beam was composed of mostly pions with less 39 than 10% contamination due to K- and T. After the two beam separation stages all but a negligible amount of the K- and p had been eliminated, and the only contamination, the result of i- produced in 4o the decays of the beam pions, was less than 4%. A. detailed descrip41 tion of the beam can be found in the reference. 2. THE CHAMBER The Schutt 20-inch hydrogen bubble chamber was used as the source of data for this experiment. The chamber is rectangular with 10 inch sides and 20 inches long, the beam entrance being on one of the 10 x 10 inch sides. There are windows on both 20 x 10 inch sides, with four fiducial marks on the front window and seven on the back window. For illumination there is a mercury arc placed behind the rear window which 10

11 flashes a short time (140 Ctsec for this experiment) after expansion. The light from the mercury arc is scattered off the bubbles into four cameras which are placed in front of the chamber and focused on a plane in the center of the chamber. The optical axes of the cameras arb perpendicular to the front window and intersect it at the four corners of a- 9 inch square. For momentummeasurements and charge identification:there is a 17.2 kilogauss field whose direction is perpendicular to the chamber windows. More complete descriptions of 42,43 the chamber can be found elsewhere. 3. THE SCANNING The scanning machines project the film images directly onto a green translucent screen. Two of the three machines furnish images approximately 1,3 times life size for the hydrogen film, and the third projects an image about equal to actual size. All three machines are able to project simultaneously two views onto the screen and then superimpose one view on the other. With this device it is very easy to distinguish tracks which stop in the chamber from those which leave through either of the windows. The scanning of the film was accomplished in the following manner: a) All interactions within a defined fiducial volume were recorded on scan sheets. This included events with zero, two, four, and six prongs, plus one eight-prong event. If there were defining characteristics such as decaying tracks, stopping tracks, "V particles"

12 pointing to the interaction, gamma rays, etc., these facts were also noted on the scan sheets. b) If the picture had more than 20 but less than 30 beam tracks, this was noted by the scanners. If the picture had more than 30 beam tracks, it was not used in order to eliminate scanning and measuring difficulties that occur because of overcrowded pictures. c) The film was then rescanned independently by a second scanner. d) The two scan sheets were then compared and all disagreements were recorded. The frames in which a track count had been noted by the scanners were also considered for placement on the disagreement sheets with the following set of rules: 1) If both scanners counted less than 23 tracks, the picture was considered to be acceptable. 2) If both Scanners counted more than 27 tracks, the picture was considered too crowded and the events on that -picture were discarded. 3) If one or both scanners had between 23 and 27 tracks, that frame was recorded on the disagreement sheet. e) The disagreement sheets were then looked at by a physicist who decided on the proper disposal of this set of events. For the frames with a track count disagreement the physicist accepted those with 25 or less tracks, and he discarded those with more than 25 tracks. f) Measurement sheets were then prepared for all acceptable twoand four-prong events.

13 The fiducial volume was defined so that an appreciable length of track could be measured. This was necessary to keep the measuring errors as small as possible. Because of the relative ease in finding four-prong events, scanning biases were not important. 4. THE MEASURING The machines used to measure the events also project the picture image onto a green translucent screen. These machines have the same film superposition device as the scanning machines. The picture projection is more complicated, however, as the film is loaded in a horizontal plane approximately perpendicular to the screen. This requires the employment of a series of mirrors to reflect the image onto the green screen. The measuring machines have both a high and low magnification, with the high magnification furnishing an image approximately 2.6 times life size for the hydrogen film. High magnification is used for the measuring. The measuring is accomplished by moving the stage on which the film is loaded. This causes the film image to move on the green screen, and the measurer sets on points of the film with a cross hair. The coordinates of these points are then recorded by means of a Moire fringe counting device or a disc encoder. These coordinates are then automatically punched on IBM cards. The machines can measure to an accuracy of a few microns on the filmo

After two views for each track were.measured, the punched cards 44 were then fed into an IBM program called CHECK. Besides coordinate points, the cards also contained the frame number, view number, charges of the tracks, and whether the tracks stopped or not. The program did some simple checks on the data which caught and corrected many format errorso CHECK then punched out new cards in the proper format for the 'track reconstruction program. 5. GEOMETRY, KINEMATICS, AND EVENT IDENTIFICATION The track reconstruction was furnished by the computer program 45 TRED. This program uses the coordinates furnished by the measurement to find the momentum and direction of each track at its point of origin. As a first step in understanding the program, it. is necessary to acquaint oneself with the physical arrangement of the chamber and cameras. Figure 4 shows a simplified version of the chamber, with just its main body, front window, and two of the four cameras depicted. A. point in 'the chamber, e.g., a bubble, is represented by B, fiducial marks on the inside of the front window are given by F1 and F2, R1 and R2 represent light rays from B to the cameras C1 and C2, and I, and I2 give the points of intersection of the light rays with the inside of the front window. Since the positions of C1, C2, F1, and F2 are known, it is possible to find the coordinates of B by measuring the positions of I1 and 12 relative to the two fiducial marks and then re

tracing the light rays back from C1 and C2 until they intersect. This point of intersection is B. i/S Figure 4. A simplified sketch of the bubble chamber and its cameras. Fl and F2 represent fiducial marks on the inside of the front glass, Cl and C2 represent two cameras outside the chamber, and B represents a point in the chamber. Light rays Rl and R2, emanating from B. enter the front glass at IL and 12. With this rather rudimentary knowledge of the optical system's physical properties, ore is now able to understand the basic operations of TREDO First let the discussion be restricted to one view, e.g., that corresponding to camera C1. By measuring the positions of F1

16 and F2 on the film, the orientation of a given coordinate system on the inside of the front glass is defined relative to the planar coordinate system of the measuring machine. This in turn defines the proper transformation for changing the machine coordinates of any measured point to the coordinates of the front glass. If the projection of point B on the film of camera Cl is measured, this gives the coordinates of the point Ii, which can then be transformed to the chamber's frontwindow system. This then defines the point B as lying somewhere in the chamber along the ray Rl. To get the actual position in the chamber of the point B, the same procedure is repeated for another view such as that of camera C2. This defines the ray R2. The intersection of the rays R1 and R2 now defines the bubble chamber coordinates of B. So far, the problem has been restricted to a point in the chamber which can be identified on the two measured views. In an actual measurement this is very seldom the case —only when a point can be identified by some characteristic such as the end point of a stopping track. Ordinarily, there are points measured along the track on two views, none of which are corresponding. To find the momentum and direction of the track at its origin, the following steps are executed: a) First a given track is measured in two views. With a knowledge of the fiducial-mark coordinates, these measurements define the intersections of the light rays with the front glass for both cameras (see Figure 5 ),

17 Ct Figure 5. A. given track as seen by the two cameras C1 and C2. The cross marks represent measured points on the tracks. b) Circles are fit through all sets of three consecutive points on C2. c) A measured point on C1 (Pc1) is then projected parallel to the line between the cameras C1 and C2 onto the appropriate circle of C2. Call this point Pclc2. This point is a first approximation to the corresponding point of Pc1. d) Pc1 and Pclc2 are then projected back into the chamber along light rays which are constructed by using the coordinates of the cameras and the points Pcl and Pclc2. e) The point of closest approach is then found for the two rays. Call this point P. f) Using the computed coordinates of P and the given coordinates of the cameras, light rays are constructed for the two measured views. Next the intersections of these rays with the front window are computed. If these intersections are found to be sufficiently close to both Pcl and Pclc2, then P is chosen to be a point in space for the

track. If they do not agree a new value for Pclc2 is tried, and this is continued until a suitable fit for the point P is found. g) This same procedure is applied to all points on C1. This gives a sequence of points in space corresponding to the path of the particle (see Figure 6). A parabola is then fit to these points, and errors for the fitted variables are computed. Figure 6. An example of a track fitted to the measured points in space. The deviations of the points from the fitted track define the errors in the momentum and direction. h) For a stopping track range-energy relationships are used to compute momentum. For a particle which leaves the chamber, TRED finds momentum from curvature at the midpoint of the measured portion of the track and then computes the momentum at the track's origin by using the range-energy relationships. Since these are mass dependent, a different momentum is computed for each particle assignment. The kinematical analysis for this experiment was handled by the Brookhaven modification of the program KICK. 5' This program takes the momentum and direction assignments plus their errors, assumes a mass assignment for each track, and then adjusts the track variables so that energy and momentum conservation are satisfed. The modification

is restricted to rather limited changes in the variables by requiring a small X — This quantity is given by: 2 (xi-Xim)G (xjXj), (II.1) i.,j=l where Gij = 3Xi5Xj, a product of the errors in Xi and Xj, Xi the fitted value of the i'th variable, Xim = the measured value of the i'th variable, and n = the number of measured variables. From the definitions it is seen that the requirement of minimal changes in the track variables is equivalent to requiring a small value for X2 Also, because of the inverse square influence of the errors, it is clear that larger adjustments are possible for the poorly measured variables than for the well-measured variableso Using the method of Lagrange multipliers, the fitting process can be formulated mathematically by searching for the minimum of the function K M(Xl. ooXn, lo. ak) = X + jCF(Xl...xn), (II. 2) j=l where K = the number of constraints, Fj(Xi ooXn) = 0 are the constraint equations, and Ogj = Lagrange multipliers. For each track assignment of interest KICK finds the minimum X by means of an iterative procedure. The iteration is either stopped by

20 the inability to find the minimum after many steps or by a successful fit. There are, of course, many other criteria, e.g., an inconsistent missing mass, which cause an hypothesis rejection, often before the X2 fit is even attempted. In this experiment all of the four-prong data was tested with the hypotheses ~-+ p +T + Jr + + p (2o1) + y T+r+ -,+ J 0 (2.2) + r +~ +t+ + + n, (2.3) and a large percentage of the data was also tested with the hypothesis - + p K + K+ K- + T + p. (2.4) Because of energy and momentum conservation X for reactions (2.1) and (2.4) was minimized subject to four constraint equations (4C fit). For reactions (2.2) and (2.3), since three of the four equations were used to compute the neutral particle's momentum and direction, X was minimized subject to one constraint equation (1C fit). The maximum X allowed for the 1C and 4C fits was 5.4 and 11.7, respectively. Both of these values correspond to a X2 probability of 2%. Most of the 2 failures were due to interactions with two or more neutral particles leaving the vertex. Typical examples of this type are - + p + - + - + i-+ + n+ n + itO (256) ~~~" ~. p -+ os ( 2sd f 6l + ) 0 ~

21 These could not be fitted because of an insufficient number of constraint equations. Those events which satisfied the X2 test for one or more of the above hypotheses (reactions 2.1-2.4) were studied by physicists in order to make the final decision on the event type. The decision, was made on the basis of bubble density. Bubble density is defined as the number of bubbles formed per unit length by a charged track and is approximately proportional to the inverse square47' 48 of the particle's velocity. It is defined relative to the 357 BeV/c beam track which is arbitrarily given the value 1.0. The value used is actually the true density divided by the cosine of the track's dip angle. This corrects for the fact that bubble chamber pictures are two-dimensional and in the plane of the front window. After the bubble density check each event was placed in one of the following categories: 2 a) The X test and bubble density check satisfied only one of the hypotheses (unambiguous event). b) The X2 test and bubble density check satisfied two or more of the hypotheses (ambiguous event). c) The event failed either the X test or the bubble density check (rejected event). d) The event was self-ambiguous; i.e., the two positive tracks were acceptable as either (Tc+,p) or (p,f+). Table I summarizes the event classification. The X distributions for the unambiguous events of reactions (2.1), (2.2), and (2.3) are shown

22 49 in Figures 7(a-c) along with the theoretical curves. The distribution for reaction (2.1) also includes the ambiguous events for reasons which will be explained below. TA.BLE I EVENT CLASSIFICATION AFTER THE BUBBLE DENSITY CHECK. THE K+K-i-p FIT WAS TRIED FOR ONLY TWO-THIRDS OF THE DATA CATEGORY NUMBER 520 air-tpnC To 1021 xc -it+i +n 489 K"K K +-p 20 ~J + Xt s s Amb. 277 ir it 7 paTJ -r-+Pff+p} Amb. 5 it -t -P+P Ambo. 121 it -c+p Self-amb. 3 t i + pto Self-amb. 4 Rejected 1020 Those events which are ambiguous between the 4C and the 1C fits will all be considered as belonging to the 4C case in the following analysis. The reasoning behind this selection is based on the following results:

23 105- 475 90 ' (a) 450 z 425 w 75 W 225 o0 60 45 -:::) ujE~~~~~~~~~> 175 Z z 5 ~~~~~~~~~~w 15 150 - T 2 3 4 5 6 z ~~~ ~ ~ r 125 -C w ~~I0 ~~25~~~~~ ~25 1I2503 150-()/ 1 2 3 4 5 6 ~125 ~x2 (a) ~J-1-~+p, (b):~u _ c+pn"o and (c) ~~~~n

24 2 a) Only a very few of the events that passed the X test for the 4C fit alone were rejected because of the wrong bubble density. b) All ambiguities between the 4C and 1C cases that could be resolved on the basis of bubble density belonged to the 4C category. c) As is seen from Table I, most of the 4C ambiguities are with reaction (2.2). Figure 8, which shows the Tc~ kinetic energy distribution along with phase space, clearly favors the assumption. The ambiguities between (2.2) and (2.3) could not be resolved (see Figure 9). Consequently, any graphs drawn for these reactions will have the ambiguous events plotted separately so that the reader can observe their effect on the data. It will be seen, however, that there are no results which in any way depend on the treatment of this set of events. For the few self-ambiguous events one of the two fits has been eliminated in a random manner. After making the above changes the total number of events for the four reactions along with their cross sections are as given in Table II. The total cross section for the four-prong events was found by counting tracks on eavery twenty-fifth picture and then computing the total track length scanned. There were corrections made and errors estimated due to beam attenuation, tracks coming in and going out the side of the fiducial volume, the varying depth of the beam in the chamber, and the purity of the beam (.97 + O02). For the beam attenuation the total cross section of Diddens et al.o, was used, and the density of hydrogen was assumed to be.0637+.0020 gm/cm.o3

25 120 z 90 W I.U 0 i, 60 z 30 I00 300 500 700 900 T (MEV) Figure 8. The irX kinetic energy for events ambiguous between (r,,+, p,~)o) and (-,i-i p) 45 40 35 35 z 30 30 I w C,) (a) 25 z 25 0 W W Cr20 20 w o 15 15 z r010 z 5 1 2 3 4 56 X2 Figure 9. The X distributions for events ambiguous between (*,~,~,p,~ and (n-,r-.,+,-+,n). (a) if (n,i,,p,~ is assumed, and (b) if (n,~,,+,n) is assumed.

26 TABLE II TEE FINAL DISPOSITION OF EVENTS ALONG WITH THE PARTIA.L CROSS SECTIONS (The column labelled "'Number" represents the actual number found in each category, while the column labelled "Adjusted Number" gives the corrected number of events after the two-percent addition is made. Note the comment in Table I for the K+K- -p fit) Evaent Type Number mAdjb. Cross Section Number in mb.o ~r Jt p 805 821 1l68~.o09 ~_~+p~ o 1025 1046 2.14~.lo0 Tc- rr+r +cn 489 499.1o 02- 0o6 K+K-TC.p 20 20 o6 o o3 ~ - p'P~ Amb. 121 124.25- 03 Rejected 1020 970 1.99+~10 Total 3 480 3 480 713+~.26 The partial cross sections were found by multiplying the total cross section by the fraction of events for the appropriate channelso The numbers in all fitted categories were increased by 2% to correct for the X2 rejection level, and the total number in the unfitted category was reduced by the corresponding amount.

CHAPTER III DEFINITIONS, NOTATION, AND PHASE SPACE 1. INTRODUJCTION In the following chapters, wherein this report focuses on the results of the data analysis, certain quantities and their notation will be used repeatedly, Although most of these are quite familiar to the reader, the multiple particle states to be considered here furnish numerous notational pitfalls which must be eliminated. Therefore, all commonly used quantities will now be defined precisely, and a standard method for representing them will be explained. 2o MASS The effective mass, a Lorentz invariant, of a group of particles is given by Effective Mass Eij P (IIIo1) i i where El is the energy and Pi the -vector momentum of the itth particle> The mass of any combination of particles can be identified by the symbol "M", with the names of the constituents written as subscriptso For example, the mass of the (E-,+) system is represented by MT- + and the mass of the (e-,-,p) system by M-,-po 27

28 3. PHASE SPACE AND DALITZ PLOTS Suppose there exists an initial quantum state Ii> which consists of a set of particles so far apart that they do not interact, e.g., the A- beam and target proton before interaction. Now let these initial-state particles collide and form a new state which will be called If> when all particles are sufficiently separated so that they do not interact. It is believed that the probability of forming If> from li> can be represented by a unitary operator S. p(i+f) = I<flsli>2 (TIIo2) In order to describe completely the quantum states If> and li>, it is necessary to specify momenta, spin, isotopic spin, etc. All of these are fixed values for any one state. If a specific reaction such as '- + P + ~a + b + K+ + P (31) is considered, then Formula IIIo2 can be written = 2 P(J P +p a 1 + Jr + P) = IGglrL-frp S|3r P.>| (IIIo2a) where all variables necessary to specify the states are fixed. The transition probability which is usually desired is that from an initial fixed-momentum state-e.g,, a beam of fixed momentum on a stationary target-to all final states of a given typee-eog., all possible states of the type (0T-_(,,~+,p). To compute this transition a b probability, a sum has to be made over all final states and an average taken ovrer all possible initial states, Let this be written as

29 p(i +~p-t~X-cp) = E E dp1<xT (>rT+pIS1yTrp>I, (III.3) a b L Lba b li> f> where o(jr-p+a-Trb+p) represents the total transition probability, Z represents an average over the initial states, li> Z, represents a sum over all final states except for the momentum sum, If> and fdp represents the sum over all possible final-state momenta which satisfy energy and momentum conservation. A sum over initial momenta is not needed since these are assumed to be constant. Because very little is known about the form of S for strong interactions, its functional dependence is often assumed to be such that it can be pulled outside the integral and summations and given some average value S. Although it might be argued that this is a good approximation because of the large number of states involved in the summation, probably the most convincing argument for this assumption is simply that it works for many cases. The transition probability can now be written P(i f) of dp. (iIi.4) The differential dp is called the phase space distribution and can be shown to be given by

30.3'*. 3-0~ d Pl d Pn 4 2 ' ~ ' 2 En (fp) (III) where Pree.~ n are the vector momenta of the n particles in the final state, E1...En are the energies of these particles, Pf and Pi are the final and initial four-momenta of the system, and 54(Pf-Pi) is the Dirac delta function which here expresses conservation of energy and momentum. In Appendix A. the methods for evaluation of this integral are discussed, with emphasis placed on the phase-space mass distributions. It is also shown that for a three-body state (Call it A, B, and C) obeying phase space, a scattergram of MB vs. MkC should be uniformly AB populated within the calculable kinematic limits. 4. RESONANCES The distinguishing feature of resonant particles is their very short lifetimes, most of which are on the order of 1023 seconds. Because of this the resonance doesn't travel much farther than a nuclear diameter before it decays, and consequently, only its decay products can be seen with the detection devices available to the experimenter. By far the most common method of resonance detection is to plot the effective mass of a given combination of particles and then to examine the histogram for a; surplus of events above phase space. This is illustrated in the next chapter where reaction (3.1) is discussed.

31 The M,-x+ plot of Figure 10(a) shows a strong enhancement in the region from 660 to 820 MeV and is a consequence of p~ production. Contrast this with the Mx-x- distribution of Figure 10(c) where there is no evidence of a resonant state. Another useful tool for resonance study is the Dalitz plot. This is only applicable to three-body final states such as x- + P + PO + x- + P, (3.2) and its utility is therefore more limited than the mass histogram. Since phase space implies a uniform population of points inside the boundaries of the Dalitz plot, a resonance appears as an overpopulated band perpendicular to one of the axes of constant mass-squared. It must be emphasized that every deviation from phase space cannot be immediately interpreted as a consequence of resonance production. Indeed, one of the major tasks of the experimenter is to decide whether such deviations are due to real particles, or instead, whether they are caused by some kinematical or dynamical effect. Examples of this type will be encountered later for the M p distribution (see Figure ll(a)) of reaction (3.1) and the Dalitz plot (Figure 38) representing the three-pion decay of the co. It will be seen that the peak in the Ma-s-p histogram is caused by the kinematics of reaction (3.2), and the density of points for the Dalitz plot will be shown to depend on the co, spin-parity assignmernt. Because of angular momentum barriers this assignment affects the dynamics of the decay in such a way that the matrix element <no(|S| K (Y>~ cannot be ignored.

32 70' 60 (a) 50 50 40 40 (b) 30 I n~ ~~ ~U~ ~ ~30 20- I 20 10 1i 11,i/SXA0 ~300 S~,YLLLL00 700 900 1 n100r 13~00 1500 1150 1350 1550 1750 1950 2150 2350 M 11+p CMEV) M -,+ (M ev) 70 - 60 r 40- C (d) the p or 3(238)peak50 " 30 - nil l 40 I0 O 30 0. 20. mW z 20 260 440 620 800 980 1160 1340 1520 1700 1050 1230 1410 1590 1770 1950 2130 2310 2490 ME-E- (MEV) Ma-p (MEV) Figure 10. The two-body masses for the final state (~ p). The shaded area represents the 176 events which have no mass value in either the po or N* (1238) peaks. 3,~3

70 -70 -60 -f60 C) z(b) z W I 50 - 50 5 (a) U- 0~~~~~~~~~~~ u- 40 - 40 -LU W ~3030 zU z 20 20 to 0 _ 10 1300 1600 1900 2200 2500 1300 1600 1900 2200 2500 Mff7-p (MEV) M-ff+p (MEV) f2 50- Figure 11. The three-body masses for the final 40 (c) state (it,,,+,p). The shaded area represents L 40 the 176 events which have no mass value in either LL_ the p0 or N*,5(l238) peaks. W. 30 W 7E20 -z 10 500 650 800 950 1100 1250 1400 1550 1700 1850 M y-;7-W (MEV)

34 In the above discussion the resonances are referred to in terms of mass intervals rather than specific values. This spread in mass arises from two independent effects: a) The Heisenberg uncertainty principle states that the accuracy of an energy measurement for a system is limited by the time that the system exists. This limitation is given by A E A t > —~, (II.6) where A E is the energy uncertainty, A t is the lifetime of the system, and =i = 6.58 x 10-2 MeV.Seco, Planck's constants Since the lifetime of a particle is given in the center-of-momentumn frame (. Pi = 0), Formula III.6 can be rewritten as A M A t > (III.7) This can be seen immediately upon inspection of Formula IIo.lo Because -23 the lifetime of a strongly decaying particle is typically 10 second, Formula III7 requires it to have an experimentally detectable mass spread of approximately 100 MeVo There can, of course, be decayinrhibiting effects due to angular momentum barriers and phase-space factors which increase a particle s lifetime and thereby decrease its wid-th. b) Because of errors in the momentum and direction measurements, there are errors in the mass computations of the partiscle icombi nationse These errors are large enough so that the c& (see Figure 37(a)), whose

35 inherent width due to Formula III.7 is less than 10 MeV, is spread out over a 60 MeV mass range in this experiment. 5o THE METHOD FOR TREATING "DOUBLE-RESONANCE EVENTS" It has already been mentioned that there is a strong peak in the MX+ distribution of reaction (3.1). It is also found that the channel P + 0 (3) a b shows an w~ in the (a~-,3r+,o~) system, and this same reaction also furnishes a significant p- peak in the My _, o plot. All three of these have one property in common-they all include the Am, a particle which appears twice in both reactions (3a1) and (3 3). Since these reasonances are defined in a mass interval, both M ac+ and M -b+ can fall in the a Trb p~ peak of reaction (3.1), Ma,+,~o and M - + o can both be associated with the r~ of (33), and the same is also true for Ma- o and MC- o in the pa peak of (353). This "double-resonance" situation introduces the problem of which mass combination is to be chosen as the actual resonance. Whenever any one of these peaks is studied, it is necessary to use consistently the same combination throughout the analysis. It is not wise to choose, for example, (ra, +) to calculate one quantity and then for the same evTent, to choose (ibe+ ) to make another calculation. For this report, since all results were printed so that those associated with Va were listed first, the choice is simple. Whenever both mass

36 combinations fall in a given peak, the one which includes ia is used. Thus the production angles, scattering angles, momentum transfer, etc., will always be associated with the Ta resonance and never with the ib resonance, This is equivalent to arbitrarily choosing one of the two combinations. Also, when cross sections are computed by counting events above phase space, a correction for the above situation has to be made. Since this problem is not handled the same way in every case, its solution will be explained at the appropriate places in the report. 6. MORE DEFINITIONS a) The Scattering Angle-Given the elastic scattering process A. + B + A' + B?, the scattering angle is defined by cos =: (PAoPA )/IPAIIPA PI (IIi 8) where PA and PA, are the vector momenta of particle A, before and after the interaction in the center-of-momentum reference frame of the particles A. and B. b) The Production Angle-The production angle of a particle A is defined by cos:,P (IIIog9) IP IPBI- I where A and PB are the vector momenta of the particle A and the beam B, respectively, in the overall center-of-momentumn system0

37 c) The Trieman-Yang Angle —Consider a final state consisting of three or more particles, two of which are A. and C. Assume these are produced by a beam B incident on a target T. Now define the following variables in the rest system of the beam particle: PA. momentum of A.. PC momentum of C. P vector sum of all final-state particle momenta except A. and Co PT momentum of the target. The Trieman-Yang angle53 is defined by (PTXPR) (PAXPC) (I10) cos (TY) = - (II.lo) PTXPR I PAXPCI If the interaction producing this final state procedes via unmodified one-pion exchange, then the distribution of this angle (not the cosine) should be flat. This is made intuitively obvious by an examination of Figure l12. Since the pion is spinless, it cannot carry any directional information between the verticies, except along its momentum vector. Thus the planes defined by the momentum vectors at each vertex are completely uncorrelatedo d) Momentum Transfer —Consider a beam B interacting with a target T and producing two or more particles. Divide the final-state particles into two groups A. and C. Now define the following variables in any reference frame:

38 p,PA APE Figure 12. Diagram for an arbitrary single-pion-exchange process with all momenta given in the beam rest frame. The line representing the beam is dashed to emphasize that ~B=0. P:B beam four-momentum PT target four-momentum PA sum of the particle four-momenta for group A. PC sum of the particle four-momenta for group C. The momentum transfer from B to A is defined by B-A (B PA) = (P -P) (EB- EA). (III.11) B-+A Since momentum transfer is a Lorentz invariant, the coordinate system in which it is computed does not affect its value. Also, it follows from conservation of energy and momentum that 2A 2 A2 (III.12) B-=A. T-C

CHAPTER IV THE REACTION Tr +purs+c-+-+++p 1. THE MA-SS SPECTRA The various two- and three-body mass spectra for the reaction _- + p -C+ - + t+ + p (4.1) are shown in Figures 10 and 11. The M~ _+ plot shows a strong peak in the region from 660 to 820 MeV which can be attributed to the wellknown po meson. From the M.+p histogram it is seen that the N3,3(1238) resonance is also produced for a large fraction of the events which satisfy (4o1). Of the 805 events which belong to this channel, only 176 of them cannot be associated with at least one of the following two reactions: r- +p + + + p O - (4.2) r- + p Tr + x + N3 ( 1238) (4.3) + T+ pP The mass spectra for these 176 events are represented by the shaded areas at the bottoms of the histograms. The other two-body mass combinations show no evidence for additional resonances. However, it will be seen later that there is some (dr,p) isobar production associated with the p~. In the three-body plots involving the proton, MI-t p deviates from phase space at the high mass values, and M- +p shows an excessive 39

40 number of events at the low end of the spectrum. Both of these phase-space deviations are found to be primarily a reflection of reaction (4.2). The reasons for this are made quite clear when the production process for the p~ is studied. In the overall center-ofmass reference frame it is found that the p0 is produced chiefly in the beam direction, and the (x-,p) state, in order to conserve momentum, goes opposite to the beam. Furthermore, the p~ decay is characterized by a fast 7- almost parallel to the direction of motion and a much slower x+ with a fairly random decay angle. A typical example of such a process is shown in Figure 13. Figure 13. The momentum vectors for a typical reaction of type (4.2). = ppo and P_p + po = O. Because the momenta of the x-' and the (xr-,p) system are large, their corresponding energies are large, and the same is also true of the scalar sum Ex- + E -p which represents the energy of the ( -,,X-,p) state. Since PT- and P,-p are almost in opposite directions, their vector sum, which is tsr-P) is small. Thus by Formula III.1, the resultant mass of the (7-,7-,p) system is concentrated at the high end of the spectrum for the p~ events. On the other hand, for the (c+,i-,p)

41 state, since most of its energy and momentum contribution comes from the (urp) combination, Formula III.1 gives an unusually large number of low values for M + -p. In the MT_( + histogram there is some evidence for the A.1 and A2 mesons, but the number of events above phase space is within two standard deviations for both peaks. It will be seen later that these peaks are significant, and that they are associated specifically with the (pO,x ) combination in reaction (4.2) rather than the three-body state. 2. THE p~-N, 3 (1238) SEPARATION AND THEIR CROSS SECTIONS If a resonant state is considered to be a distinct particle, as will be done in this section, then for reaction (4.l) only one pO or one N* 3 (1238) can be produced in a given event because of the single 3, I+o Thus some separation procedure has to be developed for those events which can be interpreted as belonging to either reaction (4.2) or reaction (4.3). In order to estimate production cross sections above phase space and to get certain angular distributions, the following method for the p~-N3* (1238) overlap is used. 3,5 Figure 14(a) gives the M++p spectrum for those events in which a po is produced. Phase space is computed by assuming reaction (4o2), letting the po decay into a x- and a a+, then computing Mu+ps and finally, normalizing to that portion of the histogram where ML+p > 1340 MeVo This is accomplished by means of a Monte Carlo calculation, using

42 25' 20 15 I0 I 10 13'00 1500 1700 1900 2100 2200 Mn+p (MEV) (b) NORMALIZED TO EVENTS WITH M<660 MEV NORMALIZED TO EVENTS 20 300 5'00 7'00 90 1100 1300 15 00 M n- n+(MEV) Figure 14. (a) M~+p for the po events, and (b) M,-,,+ for the N,3 (1238) events.

two- and three-body programs which generate events according to phase space. The p~ is assumed to have the mass values 670, 690, 710... 810 MeV, and the results for each mass are then weighted according to the bin 'sizes in Figure 10(a). Figure 14(b) represents the Ma-x+ spectrum for those events which satisfy reaction (4.3). Phase-space curve (1) is normalized to the events where M-a+ < 660 MeV, and curve (2) is normalized to that portion of the histogram where M-_,+ > 820 MeV. Phase space is computed in the same manner as was done for the p~, only the initial threebody state (T-, rc-, N3 (1238)) is assumed. From Figure 14(a) it is estimated that the p~ sample contains 85~9 more N* (1238) events than there should be according to phase space. From Figure 14(b) it is estimated that there is an excess of 45~9 p~ events in the N,3 (1238) sample. Finally, since there are 162 events belonging to both the p0 and N* (1238) peaks, there must be 32~13 phase-space events of this type. Of these 162 p~ -N3 (1238) overlap events, a total of 25 of 5,3 them have both (-,7T+) combinations falling in the po region. From the Monte Carlo calculations it is estimated that there should be 21 double- p~ events in this sample. It is seen that the calculated and experimental numbers are in good agreement. The assumed division of these 162 events is summarized below in Table II-Io

44 TABLE III THE ESTIMATED DIVISION OF THE p~-N* (1238) OVERLAP EVENTS 3,3 Calculated NumType Number ber of Double-p~'s * -+p-r-+rc-+N3 3(1238) 85+9 I+t-+P-+P+O 45+9 6 -+p-'+- +i++p 3 2+ 13 4 With these numbers it is now possible to find the proper normalization for phase space along with the p~ and N 3(1238) cross sections. The large 41% error in the number of p~-N5 (1238) phase-space events will be implied in the normalization calculation but will be considered explicitly when the p0 and N353(1238) cross sections are computed. The method used to find these quantities is best explained in the following step-by-step summary: a) From the M +p histogram (Figure 10(b)) all po events are subtracted. This result is the unshaded area in Figure 15(a). The unshaded area in Figure 15(b) shows the Ma-_+ plot of Figure 10(a) with all N* (1238) events subtracted. 5,5 b) Out of 6,000 Monte Carlo events for the final state (lr-,t-,N;,3(1238)), 2583 p0 mesons are generated. Therefore, if there are 3 2 p-N3 ( 1258) events in phase space, there are (600> x 36 84 \2583/

45 40 30 (a) 20 1150 1350 1550 1750 1950 2150 2350 M -r+p (MEV) 60 50 40 (c) 30 20' 10 300 5O00 7000 900 110o 1300 1500 Mu- n+(MEV) 303 10 300 500 700 900 1100 1300 1500 Figure 15. Various stages of po-N5~(1258) overlap estimates.

46 phase-space events satisfying reaction (4.3). The number 36 is used in this calculation because there are 4 double -p~'s in 32 po-N5* (1238) 3,3 events. c) In the (p~,x-,p) final state 6,000 Monte Carlo calculations generate 1490 events satisfying reaction (4.3). With this same final state 1090 p~'s are generated with the T' from the po decay and the Ad not involved in the decay. Therefore, *there are 000) x32 129 1i49o phase-space events satisfying reaction (4.2)o This corresponds to 1+.090/ x 129 152 6oo mass points in the p0 region of phase space. d) Now the proper normalizations for the M-_t+ and M.+p phasespace distributions can be found. This is accomplished by taking the phase-space distributions calculated for the (c-7E+p) final state and normalizing M,,-+ to 152 events between 660 and 820 MeV and MV+p to 84 events between 1130 and 1330 MeV. The two phase-space curves are drawn on the appropriate histograms in Figures 15(a) and 15(b). Although only one of the two normalizations is necessary to get the phase-space curves for the two histograms, both are used in order to check the numbers found in the Monte Carlo calculations. This is accomplished by finding the ratio of the area under the My<+ curvre to

that under the M+p curve. A. numerical integration gives the result 760/377 which is very close to the correct value of 2/1. e) Since many events have been incorrectly subtracted from the two mas-s. distributions, these now have to be put back into the proper histograms. These additions, all of which are made to the unshaded portions of Figure 15(a) and 15(b) and represented by the shaded areas in these figures, are listed below: 1) From Table III it is seen that 85 events of the p~ -N3 (1238) overlap have to be added to the Mr+p distribution. 2) Also from Table III, it is seen that 45 events of this same type have to be added to the Ma-_+ histogram. Since there are two (r-,T+) combinations per event, this addition totals 90 points, fifty-one of which are in the p0 region. 3) Since there are 84 phase-space events satisfying reaction (4.3), 2 x 84 = 168 points of this type have to be added to the M- + distribution. As a result of the division summarized in Table III, thirty-two of these have to be of the p~-N,3 (1238) overlap variety. 4) Because there are 129 phase-space events satisfying reaction (4.2), the M,,+p histogram has to be increased by 129 points, with thirty-two of these belonging to the p~-N3 (1238) overlap sample. f) In Figure 15(b), with the shaded area now included, there are 244 events above phase space. For every one of these there is another (eo,r+) mass value which is not part of phase space and should therefore be subtracted from the histogram. Because of the double-p0

48 possibility this peak actually corresponds to (; 6ooo ) x 244 = 206 000+1090 p0 events above -phase space. Therefore, in order to represent the Mt-,+ distribution correctly, 206 events have to be subtracted from Figure 15(b), and thirty-eight of these must come from the p~ region. After this subtraction is made, the M _ + distribution shown in Figure 15(c) is obtained. g) The M,+p and M._-,+ distributions represented by Figures 15(a) and 15(c) can now be used to calculate the N3 3(1238) and p~ cross sectionso This is accomplished by simply counting the number of events above phase space. These cross sections along with their errors are given in Table IV. The large uncertainties are primarily due to the 41% error in the phase-space normalization. TABLE IV THE p0 AND N;,3(1238) CROSS SECTIONS FOR THE REACTION ++p-*+rf+f++p Number Above Cross Section Type Type Phase Space in mb. Ts +p r-+Tr-+N* '(1238) 243+39.51~.09 r-+p —' +p+p 206+65. 43+. 14 +-p +p-hc —'+~-+ ~++p *.74+~.30

49 In the Monte Carlo calculations described above, the production angles for the p0 and N3 (1238) are distributed according to phase space. This is not found to be true for the real events, as the p~ is produced primarily in the forward direction and the N (1238) is produced primarily in the backward direction. In order to evaluate the influence of this effect on the above estimates, the phase-space mass distributions have also been computed for just those events in which the production angle of the p0 is small (cos @>.9) and the production angle of the N33(1238) is large (cos Q@<-9). It is found that these restrictions have virtually no effect on the phase-space estimates and can therefore be ignored. 3. THE TWO-PION DECAY OF THE co Since the cw has a negative G-parity, it cannot decay into two pions through the strong interaction. However, a two-pion electromagnetic decay, for which G-parity is not a good quantum number, is allowed for the w~o Since phase space and angular momentum barriers favor this over the three-pion decay, it is possible that the twoand three-pion rates may be comparable in spite of the different decay mechanisms There have been many experiments with widely varying results which have attempted to detect this decay mode of the co. In a compilation of the data from several experiments, LUtjens and Steinberger6 conclude that "there is no statistically significant indication for the

decay of the c~ into two pions." This is contrary to the results of some of the subsamples of their data, and it is in strong disagreement with the results of Fickinger, Robinson, and Salant.57 In this experiment a strong c~ peak is found in the reaction (see Chapter V) + r + p + u + o (4~4) + o + M Since wo production for the (Cr-,C,+,p) state also has to occur through the channel + p +~ + p + 0o (4[5) + X + Jr + the branching ratio R = can be computedo ( - +p ->t +p * o~+v + p+ p + t+ o ) This experimental number, however, is only valid if there is no interference between the (r-,J+) states produced in the ~0 and p~ decayso Durand and Chiu58 have pointed out that a very small R can lead to a fairly large change in the M + spectrum at the LuO mass if interference is assumed. Thus the branching ratio computed here is only an upper limit on the true valueo In Figure 16(a) M_ + is shown in 10 MeV bins for the region 600-840 MeVo The 770-800 MeV region shows a surplus of approximately 8~ 10 events above a smooth background. Assuming 18 events above phase space, this corresponds to a branching ratio of R <.18 and is consistent with R = O0

W09 < +~- -V (p) pu 099 > +_- >V > oZ (3) (a9W) +L -WA 00t1 OOzI 0001 008 009 00O 01 JL 09 zV (P) 0 0~ ZS Z m L 0 0> V (q) Z 0001 006 008 OOL 009 00S Otv liv (~~~~0)

My-t+ is presented in Figures 16(b), 16(c), and 16(d) for the three regions: (1) A2 < 20M2, (2) 2M2 < A < 6 2 p.*I-p it PI - - OMT (3) 60M2 < Ap-p. In Figure 16(b) there is some structure to the p0 region of the histogram which one might want to attribute to the c~, but it is statistically no more significant than the two peaks of Figure 16(d) which cannot be associated with w0 production because of their masses. Finally, it should be noted that the apparent structure in the mass plot of Figure 15(c) cannot be considered seriously because of the many additions and subtractions which were made to arrive at this histogram. 4, THE p0~ MESON 4.1 Introduction Once the existence of a new particle has been established, an understanding of the mechanism responsible for its production then becomes desirable. This requires a study of quantities such as production angles, momentum transfer, etc., in order to compare their distributions against those predicted by the theoretical models. The purpose of this section is to discuss the results of such a study for the p0 meson produced in reaction (4.1). The mass range chosen for the p~ is from 660 to 820 MeV, and the method of Chapter III, Section 5 is used for picking one of the two possible (em,I+) combina. tions when both of them fall in the p~ region~

It will be found that the p0 can be associated with many different production processes. Some are produced in the reactions r_ + p + p0 + N, 1(1238) (4.6) +- 7 +p and + p + N1 _l(12) (47) + I- +p, others are produced via the modes K + p + p + A1 (4.8) + p0 + Xand + p + A2 (49) + po + _ and some can only be associated with reaction (4.2). 402 ISOBAR PRODUCTION IN ASSOCIATION WITH THE p~ MESON The first thing that should be examined is the distribution of M for reaction (4.2). This is shown in Figure 17(a) with phase space normalized to the total number of events. The shaded histogram corresponds to the 162 evrents which belong to both the p0 and N353 (1238) peaks Since it was concluded in Section (3) that 85 events of the p~N3 *(1238) overlap should be placed in the N3 3(1238) category, a more accurate representation of M,_p is obtained by subtracting approximately one-half (85/162) of these. The result of a random subtraction of 85 N3 (1238) events is shown in Figure 17(b). Since the high-mass distribution follows phase space quite accurately, the normalization

54 30 35 Cn H t~~~~~~~~~~~~~~~~~~~/)2 w 30 {n 25 > (a) Z (b) "' w u. 25 > 0 W 20 w 20 m:/M xIIRc 15 D ~~~~~~~~~~~W ~~~~~~~~~~z 15 z 10 5 - s 5 10 12 14 16 18 20 22 I0 12 14 16 18 20 22 M/-p(100 MEV) M7r-p(100 MEV) Co 20 20 20 Z Co -~ (c) Z Co > ~~~~~~z W w Hw 15 > 15 z Li > (e) cr LL~~~~~~~~~~~L 0 w10 a: I0 (d) o 10 rn W~:m: r W Z ~ m z 5 z 5- 2 5 z 10 12 14 16 1- 2 -0 10 12 14 16 18 110 12 14 16 18 20 0 2 4 6 20 22 Mnr-p (100 MEV) M'-p (100 MEV) Mr-p (100 MEV) Figure 17. Ny-p for the reaction - r + p po + r- + p. (a) all events. with the shaded area representing the N*,3(1238) overlap; (b) the distribution of (a) with 8 N3,3(1238) events subtracted and phase space normalized to ~ > 1700 MeV; (c) b2 < 2oM; (d ~oL < A_+~o < )4o; 2 2 and (e) A,-+p0 > )4OMJrf.

is made for the region where Mc-_p> 1700 MeV. If this normalization is assumed to be correct, it is then concluded that a fairly large number of the p~ mesons are produced by means of reactions (4.6) and (4.7). In Figures 17(c), 17(d), and 17(e) the Mr_p distribution is given for three different ranges of A2 (1) for A2 < 20M2, (2) for Ap3 +~ _p-*7tp _p 2CM2 0< A+< 6CM2, (3) for A2 - > 60 M2. From these histograms it 2_M < Tp-p C, P+1t P is quite clear that reactions (4.6) and (4.7) dominate the production of po mesons at low momentum transfer. Although it is not shown here, 2 the N3,3(1238) contamination is just as large for these low Ap2-p events as it is for the entire sample of reaction (4.2). 4.3 THE p AND THE ONE-PION-EXCHANGE MODEL In the last few years many pion production processes have been found to be consistent with the one-pion-exchange model.ll This is based on the diagram shown in Figure 18(a), where the exchanged particle is the relatively light ET meson. Since G-parity is conserved in strong interactions, only an even number of pions can come from the upper vertex. For reaction (4.1) this limits the number of possible cases to the two shown in Figures 18(b) and 18(c). Because p0 and N3, (1238) production require that the Tr+ be associated with different verticies, the entire sample of 805 events cannot be explained by one diagram. Figure 18(b) is needed for the p0 meson, while N* (1238) production, if it occurs by means of pion exchange, 353 requires the mechanism of Figure 18(c).

(a,) (b) (c) i state T Figure 18. Pion-exchange diagrams for (a) an arbitrary process and Figure 18. Pion-exchange diagrams for (a) an arbitrary process and (b and c) the possible cases of reaction (4.1). The purpose of this section is to determine whether or not the p0 can be analyzed in terms of a one-pion-exchange process; that is, the validity of the diagram of Figure 18(b) will now be investigated with the upper vertex restricted to the region 660 < y-,+ < 820 MeV (see Figure 3). In a peripheral interaction such as that represented by the exchange of a low-mass particle, the net momentum at either vertex should not have a large transverse component. This property can be tested by examining the momentum transfer and production angle distributions for the resultant particle at either vertex. These distributions are shown in Figures 19 and 20 for the p~ region, and they are both clearly consistent with the one-pion-exchange model. The Trieman-Yang angle is shown in Figure 21(a). Ignoring absorptive effects, the distribution of this angle should be flat if reaction (4.2) is governed by one-pion exchange. It is apparent that this is not true for the entire p~ sample. However, this plot cannot

5.7 136 124 80 70' 84 z O w50 w 7 Z " 60- 1260 > L U-i~~vf "I1 w 0 40' 48' 0o. 0 302 z 36 z 20Figure 1. The F e 2 Pou4-t al f th10 N ( ov12elp st te N (.4 1.6 2.8 4.0 5.2 -1. -.~8 -.~6 -.4 -.2 6.'2.4.'6.8 I. 30~~ A{BEV) CO0 S 0,, Figure~~6 120 60e A20 isriu Figure 21. The Tr2edisn-Yang angle Figure 20. Production angle for tion. The shaded area represents tep.Tesae rarpe sents the N~,(28*oelp th he N,3(1238) overlap. o l s d n ) t oneofa (a). 03 3O0 60o 120 6'0 120 T-Y ANGLE. (DEGREES) Figure 21. The Trieman-Yang angle for the po events. (a) all events

be considered as representative of reaction (4.2) until the N,33(1238) overlap is subtracted properly. After randomly subtracting 85 N* 3(1238) events, the result shown in Figure 21(b) is obtained. This shows a fairly uniform distribution with perhaps a slight overpopulation at the low and high angles. Since a straightline fit to this plot yields a X2 probability of 744%, the TriemanYang test agrees very well with the one-pion-exchange assumptiono 4.4 THE p~ DECAY Since the p~ data is rendered so complex by the N (1238) 3,15 events and the multitude of reactions responsible for the meson's production, and furthermore, since a fairly pure po sample is available in other final states, anything more than a rather qualitative investigation of its decay would be quite fruitless. A. thorough analysis of this problem can be found in studies of the reaction29 i- + p + n + p~ (4.10) If the one-pion-exchange model is assumed to be valid, and further, if the exchanged lt+ is assumed to be real, then the peak can be analyzed by means of a partial wave analysis for (J-,Tr+) scattering. Since Bose statistics require two pions to be in a symmetric state, even angular momentum corresponds to even isotopic spin and odd angular momentum to odd isotopic spin.

If Q is defined as the scattering angle for the t- in the p0 center of mass, and if all angular momenta above L = 1 are ignored, then d c )- Je+sin _ 2+ eio sin 1o + s e1 d(cosQ0 k2 = A + B cos Q + C cos 2, (IV.1) where k is the propagation number of the pions in their center of mass, and 5o and 61 are the phase shifts of the s- and p- waves, respectively. The coefficients A, B, and C are given in terms of the phase shifts and the propagation number by A = 2 A 2 Sin 6, 123t B 2 sin 5o sin bl cos (6o-'l), (IV.2) k2 and 18jr 2 C 2 r~ sin 21' k2 In Figure 22(a) the cos Q distribution is shown for all A 2_po After subtracting 85 N 13(l258) events in the same manner as was done for the Trieman-Yang angle, the distribution shown in Figure 22(b) is obtained. Both of these plots display the familiar forward-backward 29,37 asymmetry that has been observed in many other experiments. In Figures 23(a-c) the scattering angle is given for three 2 2 2 2 2 ranges of momentum transfer: A-o < 20M 2) 20M2 < A (3) 40M2 < A2 +oo Here it is seen quite clearly that the assymmetry is associated entirely with the low A2 events It should be noted, 0 o

40 (a) cn 30- 30 -5~~~~~~~~~~~~~3 (b) z wJ (/)W z i, Z IC bcJ u_ 20- > 20 -0 b.0~~~ 0~~~~LL0 0 ~ ~ ~ ~ ~ ~ o 0_ z z 10- 10 --1.o -.5 0.5 1 1.0;.5 5 0 i~~~~o- -:s06:5 1.0 C0 S 8 COS a Figure 22. The scattering angle for the a- in the p0 center of mass. (a) all events with the N5,5(l238) overlap shaded, and (b) after a subtraction of 85 N,(1238) events. the N,3(l N,

w of < 0_ (D) pue wzX 08 > UV > Oa ( O > ~ -V ss-U,O JuaGO d aGq; uT _; a; lo GTo BUe 3aG;E, GT aGn G1, 9 0 gO- 1- II 0 9- 1 -z 0 01 m mrr -Iz C') 0 01 "-n -9 < (I)

however, that this is not because the p~ peak vanishes at higher momentum transfer (see Figures 16(b-d)). This change is probably due to the fact that the treatment of the dipion vertex as a scattering problem is only valid for low A 2- po. In concluding the p~ scattering discussion, the results of a 2 X fit to IV.1 for the various distributions are summarized in Table V. TABLE V THE RESULTS OF X2 FITS TO (IV.1) FOR THE p0 REGION WITH VA.RIOUS MOMENTUM TRANSFER CUTOFFS Comments A B C X All events (Fig. 24(a)) 15.72 7.09 135.18 23% + + + 1.43 1.90 3.59 All events with 12.98 3.32 8.61 85 Nw,3(1238) subtrac- + + + 38% tions (Fig. 24(b)) 1.30 1.68 3.22 2 A^ < 20 (Fig. 25(a)) 2.32 5.63 10.01 + + + 7.65 1.14 1.97 2 20 < At+p < 40(Fig. 25(b)) 2.39.90 2.00 + - + 23%.65.83 1.60 A flop > 40 (Fig. 25(c)) 8.91 -.44 2.44 + + + 48% 1.07 1.31 2.49

4.5 THE A1 AND A 2 MESONS 5 9-61 In the past year many different experimental groups have presented evidence for two peaks in the (p~,+- ) mass distribution. Their masses are centered at 1090 and 1310 MeV and they are called the A1 and A2, respectively. At this time the A2 is believed to be a true particle state, but there is still some doubt concerning the A1. The results to be presented here further confuse the status of the A1,. and in addition, introduce some serious questions about the A2. It will be shown that almost all of the events of reaction (4.2) which satisfy - +p p A.1 + p (4.8) and A2 + P (4.9) can also be assumed to belong to one of the modes + p + p +p + N _1(1238) (46) P+ N,1(1512), (4.7) + p + N,_1(1688), (4.11) and + po + N 1(1920). (4.12) In Figure 24(a) Mpo _ is shown for all events which satisfy reaction (4~2). Phase space is normalized to the total number of events. In this plot there is some evidence for A2 production, but the peaking in the A1 region is not statistically significant. However, when the mass is examined s a function of momentum transfer to the proton, the A. mesons become quite prominent. A. scattergram of

64 40- (a) " 20 -0 0 900 1200 1500 1800 M po T(MEV) (c) 30o (b) l) z 20" 20 -Z 0 w w 0 LL 0- Iz0 -0 0 z 900 1200 1500 1800 900 1200 1500 1800 M po r ( MEV) M po '- (MEV) Figure 24. The Mp~'-,istribution for (a) all ap2P (b) AP and (c) Ap2p <.8(BeV). The shaded area represents the N (1238) overlap in all histograms.

Ap2p vs. Mpo - has been studied, and the projections for the regions 2 2 2 s A2p <.40(BeV)2 and Ap2 < A80(BeV) are shown in Figures 24(b) and 24(c). Here a definite enhancement is noticed in the regions corresponding to the two mesons. This is especially evident in Figure 24(c) where A <.80(BeV)2. Since the A mesons cannot be produced p+p by a one-pion-exchange mechanism, it is not too surprising that they appear in large number at higher momentum transfer than do the positive-G- parity particles such as the pO. In addition to the pO events, M+-,+,- has also been investigated for the rest of the data in reaction (4.1). It is found that neither of the A. peaks exist except for the p~ sample. Thus both of these resonances can be associated with a (ia,po) combination rather than a three-pion state. 2 2 Of the 129 events in which A- pO < 20M, sixty-six of these also satisfy 1000 < MpoT- < 1350 MeV. If it is now recalled that the po mesons produced at low momentum transfer appear to be made with (c-,p) resonances (see Figure 17(c)), it becomes clear that the A. peaks may be drastically affected by these isobars. In Figure 25(a) M Tp is plotted for all events in which Mpo,- is in the range 1000 -1350 MeV with no momentum transfer cutoffo Here one sees strong evidence for the N3 1(1238) and also the possibility of an Nl _1(1512) peak. The M distribution is shown in Figure 25(b) for the A1 region (1000 < Mpof- < 1150 MeV) and in Figure 25(c) for the A2 region

a) I000 < MpoT- < 1350 15 10 - Cn -5 -S 10- b b 1000 M - < 1150 c 1200 < M < 1350 10 5L 1100 1500 1900 Mar- p (Mev) Figure 25. The Mr-p distribution when the Al and A2 mesons are produced. (a) 1000 < Mp~^- < 1350 MeV, (b) 1000 < Mp~o- < 1150 MeV, and (c) 1200 < Mp~ - < 1350 MeV. The shaded areas in (b) and (c) represent M,-p after acomplete 3,3(1238) subtraction.

(1200 < Mpo _ < 1350 MeV). Again there is no momentum transfer cutoff. In these two plots there are obvious peaks at many different mass values. Besides the existence of these peaks, the very striking feature of them is their position on the mass axis. All of these are centered close to known pion-nucleon resonances-the 1238 and 1688 MeV isobars in Figure 25(b) and the 1238, 1512, and 1920 MeV isobars in Figure 25(c). Furthermore, these two histograms keep their general shapes when all N* (1238) events are subtracted (shaded areas*). x2 fits to the distributions of Figures 25(b) and 25(c) have been made for various hypotheses. These are summarized below: a) Figure 25(b) 1) Assuming the phase-space distribution of reaction (4.8), the X2 probability is much less than 1%. 2) Assuming the phase space of reaction (4.8) plus some NZ,_1(1238) with a Breit-Wigner distribution, the maximum X2 probability is 3% when there are 28 phase-space and 39 NT,_1(1238) events, respectively. 3) Assuming just N *,_1(1238) and NI, _1(1688), both with Breit-Wigner distributions, the maximum X probability is 68%. This is obtained assuming 33 events of type (4.6) and 34 events of type (4.11). b) Figure 25(c) 1) Assuming the phase-space distribution of reaction (4.9), the X probability is slightly less than 1%. *The shaded areas in Figures 25(b) and 25(c) represent those events which do not have a mass value in the N, 3(1238) peak. This is different than most of the histograms where the shaded area represents those events in the N~,3(1238) peak.

68 2) Assuming the phase space of (4.9) plus some N~,_1(1238) and N~1,_1(1512) with Breit-Wigner distributions, the maximum X2 probability is 9%. This is obtained with 30, 28, and 37 events of type (4.9), (4.6), and (4,7), respectively. 3) Assuming just N,_1(1238), N1,_1(1512), and N, _1(1920), all with Breit-Wigner distributions, the maximum X2 probability is 84%. This is obtained assuming 28, 34, and 33 events of type (4.6), (4.7), and (4.12), respectively. In Figure 26 a Dalitz plot is shown for the (p~,c-,p) final state. Due to the width of the p~ there are two boundaries for this plot. These have been fitted together to form a smooth curve which encloses all of the points. Upon close observation it appears that the density of points is unusually high where A meson and isobar bands overlap. This overlap contains so many of the points in the A. bands that the regions between the isobars are almost empty (see Figures 25(a) and 25(b)). Both of the A. peaks can be attributed entirely to the overlap regions, and additionally, the evidence for isobars is very, very meager outside the A bands. This is not what one would expect from independent (A-,p) and (ic,p~) resonances. So far, there is one important point which has been ignored-the 2 A1 peak just appears when a A cutoff is imposed. If it is assumed p-*p that only these low momentum transfer events should be considered, then the N1 _1(1688) can be disregarded. M4-p is plotted in Figure 2 2 27(a) for just those events in which: (1) A <.80(BeV) and (2) 1000 < Mpo 1350 MeV. Although the other three (~-,p) peaks

69 4.4 3.6-.>~~ ~ ~2.8-* * 2. 0 - ~ e~ ~ ~ * 0 0 2.0 -*.-.... -. -.. i.2t I I I 0.2 1.0 1.8 2 6 3.4 2 2 M.-o (Bev) Figure 26. The Dalitz plot for the final state (p~,r-,p). 2o8- 0 0 0 0 0 ~~~ I I ~ ~ ~~~~~~~~~~~~~~~0 a 0, 0 a 2.0- A l e ~ ~~0.I 182. m e o Figue 2. Te Dlit plt fr th fial tat (P~jTP)

(a) 15 -10 U) z 5 u_ 1200 1600 2000 0 10; (b) 1200 1600 2000 M7-p (MEV) Figure 27. The Mr-p distribution for low momentum transfer (A-~+po <.8 (BeV)2) to the A mesons (1000 < MpoK- < 1350 MeV). (a) all events of this type, with the shaded area representing the N3 3(1238) overlap, and (b) the distribution of (a) with all N3,3(1238) events subtracted.

71 are still evident, it is quite apparent that the i688 MeV isobar has been completely eliminated by the cutoff. How the above observations should be interpreted is not at all 62 clear. R. Deck has tried to explain the A1 as a kinematical consequence of a one-pion-exchange mechanism in reaction (4.2), but in his model the A.2 is considered to be a real particle. The data from this experiment suggests the possibility that both A. peaks may be kinematical reflections of reactions (4.6), (4.7), (4.11), and (4.12). But if this is so, why should one isobar produce an M,,-po enhancement around 1090 MeV while another causes the (i-,p~) mass to peak at 1310 MeV? There is no obvious correlation between the isobar and A. meson masses. The N,_ 1(1512) is associated with the A2, the heavier N*_(1688) is connected with the Al, the still heavier N* (1920) can be related to the A2, and the N,_1(1238) can be associated with both A. peaks. Furthermore, if this hypothesis is valid, why are A. mesons found in the final state (po,g+,p)? Here the isobar contamination is not bothersome, as the A. mesons are still seen after all events of the type + + p p~ + N 3(1238) (4.13) It+ p are subtracted, while the 1512 and 1688 MeV resonances do not exist in the (O+,p) state. Another possible interpretation is that the A. mesons cannot be experimentally separated from the (i-,p) resonances for the simple

72 reason that.they are not produced independently of the isobars. It could be that the Tr is somehow shared by the p0 and p in such a way that both the (K-,p) and (:-,po) combinations form resonant states in the same physical event. The N3 (1238), N1 1(1512), and N3 1(1920) 3,-1 1, - are produced in conjunction with the A2, while the N* 1(1258) and possibly the N1,_(1688) share a rr- with the A.1 Finally, because of the small number of events involved, one cannot eliminate the possibility that the entire N* effect is no more than a statistical fluctuation. This is especially true for the A.2 It is seen from Figure 25(c) that very few events would be required to change the apparently isobar-dominated distribution to one which follows phase space. 5. THE N; (1238) CHA.NNEL 5 1. Introduction In this section the analysis will be devoted to the reaction +- +P n + + N3 (1238) (4-3) + Using the one-pion-exchange model, 11 the (TC,iC) scattering cross section -._ will be calculated as a function of center-of-mass energy by means of the Salzman-Salzman approximation to the Chew-Lo~w2 formula. The differential cross section will also be investigated, but because of a statistically insufficient sample, no attempt will be made to extrapolate this to the pole at A2. =* M2o P+I~B. B

73 5.2 The (12-,-,N5,3(1238)) Masses For this reaction there are only two mass combinations to be studied. Mi-~- and M *_N are shown in Figures 28(a) and 28(b),,3 respectively. It is obvious that both distributions follow phase space quite closely. This is also true when momentum transfer cutoffs are imposed. The shaded areas in both plots correspond to the p~ overlap. Since only forty-five of these actually belong to the p~ channel (see Section 2.), it is clear that this contamination does not affect the conclusions derived from either histogram. 5.3 A Study of the (r-,r-) Elastic-Scattering Cross Section As a first step in this study, it is necessary to examine the validity of the one-pion-exchange model of Figure 3 (a) as the proper tool for analyzing reaction (4.3). In Figure 29 the A distribup 13,3 tion is presented. This shows a strong accumulation of events at low momentum transfer and is therefore consistent with the model. The Trieman-Yang angle for the dipion system is plotted in Figures 30(a) 2 and 30(b) as a function of A * and M a_, respectively. Both of these indicate a definite sparseness of points in the region of 90~, an effect which is found to be independent of A2 N* and dependent on M~_Mo At mass values above approximately 900 MeV the Trieman-Yang distribution is quite isotropic, while for the mass region M. — < 900 MeV it is peaked at 0~ and 180~, a result which still persists when only the low momentum transfer events are considered. Finally,

30 (a) Iz w 20 -LL. 0 -0 400 700 1000 1300 1600 M 7r- - (MEV) 401 (b) 30 cn I-. z u. 20 0 10 1400 1700 2000 2300 2600 M'- N (MEV) 33 Figure 28. Me-g- and *-N3 3 for the final state (r-,r-,N3,3(1238)). The shaded areas correspond to the p0 overlap.

73 60 co, 50j 50 -z > 40 w.IL o 30 0 8 Z 20 I0 -50 100 50 200 250 A2 (PION MASSES)2 Figure 29. A2 * for the ( -,N;3, (1238)) final state. p+~N 3,3 3, 3.6 (a) (b 1800 3.0 500 ~ 2.4 ~ ~ o ~o.~,....o 1200 cncn ~ ~.~ ~ ' ~ ~ '1 3E 12 0.'.. ~.~~..~.... ~ o*. ~900. ~ 0.9 ~ ~ ~~ ~ 1 ~ ~~~~~~~~~~~~. ~.~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~ '..~ '. *~~ ~~ 600! 0.6 * *.::. ~. '~~ ~~ ' ' '9~300 ~~~~~~~~~~~.,~ ' C~ state N(*,,,,N(1238)). (a) A2 3vs. TY angle, and (b) M, -~vs. TY angle.

76 a subtraction of the p0 contamination does not change the above conclusions significantly, because these show almost the same Trieman-Yang distribution as do the non- p0 events~ Because of the relatively poor Trieman-Yang test the following calculations, which are based on the unmodified one-pion-exchange model, must be regarded with considerable suspicion at low dipion masses~ It is worth noting, however, that identical experiments ' 5 at different beam momenta have found a more isotropic distribution, and the poor result found here could, therefore, be more statistical than physical. The method which will be used to compute a - was first pro32 posed by Chew and Low. Their procedure uses information obtained from a beam interaction on an unstable target particle to analyze the scattering properties of the target's "decay products." Thus it is possible to study the scattering processes a + ' -~ ( 4~14) and + + N >(1238) + + p (4o 15) in terms of reaction (4.3), provided the one-pion-exchange diagram of Figure 3(a) can be assumed. According to Chew and Low, the total cross section for reaction (4.5) is given in terms of +p (A2W) and cros (A, V) by

77 AaVov - A=,W l26rak2M2 2k-V) 2 x +p (A,W)kwW, where V is M,-,-, W is M~1+p, is the pion mass, k is the momentum of the incident pion in the laboratory, kv is the momentum of one of the pions in the (K',y-) rest frame, kw is the momentum of the proton in the (c+,p) rest frame, M is the mass of the target nucleon, and A2 is A2+. * In the limit A2+-_2, a-_- (A2 V) and a+p (A2,W) approach the values of__ (V) and ca+p (W) which are the real total elastic cross sections at the energies V and W. With the aid of the experimentally determined value for a,+p (W) and a careful measurement of the quantity (A2+L2).(63a-_-N*/6A2%V2aM2) for given values of V and M, it is possible to find a -3- (V) by means of an extrapolation to the pole at A2 = _ 2 However, in order to do this a prohibitively large number of events is required, and it is therefore necessary to resort to certain approximations which make Formula IV.3 applicable in the physical region without the limit. One such approximation is furnished by Salzman and Salzman.63 They suggest that Formula IV.3 can be applied at low A2 when the substitutions c-(-(vA 2,v) = — (V)

78 are made and the limit is ignored. These approximations are made in an attempt to correct for the fact that the exchanged pion is virtual 2 2 and does not behave as a real particle except at A2 = -. With these assumptions the Chew-Low formula can now be written ~A2 W2~ V( 1 i).v( 2 / 2F 22M222 2 1/2 aA 3 W2bv2 16,r M 2W (Iv.5) 22 r.W-)~a a-~~waL\ 2 W -2 xQ2+) [(W:M) 2+] To find a_ (V) all that is needed is to integrate the right-hand side of IV.5 over A2 and W2. The W range of integration is 1130 < 2 W < 1330 MeV, and the A region extends from a lower limit dependent 2 on W to an upper limit which is determined by the A cutoff. For 64 a4+p(W) a Breit-Wigner fit to the experimental cross section is used. After performing the double integration the expression d K a1-r-(V2) (IV.6) d V2 is obtained, where K is just a number. From the experimental values for (dao__N*(VV2)/dV2) it is now possible to determine at-,-(2)-. The results of this determination are shown in Figure 31(a) for two upper 2 2 2 2 2 limits on A A < 2qL2 and A < 4L2. The corresponding histograms for (d~axN*(V2)/dV2) are shown in Figure 31(b). These results are 15 in good agreement with those obtained by N. Schmitz and a Saclay14 Orsay-Bari-Bologna collaboration. Both of these experiments used the same final state considered here with Am beam momenta of 4.00 BeV/c

79 12 2 2 A <20 MT 10 2 2 x < 40 M 8 E b I o, I -.'... ' '.10 0.50.70.90 1.10 1.30 (b) 2 2 c' 15~" A < 20 M* 2 2 2 z 0 20 M <5A<40 M Figure 31. The (t',J ) cross section as a function of center-ofwma 8 energy. 0 5 0 z.10.30.50.70.90 1.10 1.30 1.50 1.70 1.90 2.10 2 2 M ww'- (Bev) Figure 351. The (I —) cross section as a function of center-of-mass energy.

8o and 2.75 BeV/c, respectively. The calculations of Schmitz were also based on the Salzman-Salzman formula, and the other group used the expression given by Ferrari and Selleri 5 for the nucleon-vertex approximat ion. 5.4 The (ar-, c) Scattering Angle Distribution Let it be assumed that reaction (403) is governed by the one-pionexchange model and that the exchanged r- is real. Then, since the generalized Pauli Principle requires that even isotopic spin be accompanied by even angular momentum, the differential cross section for (W-,) scattering can be written da 2 7~....." 2 d(cos~) k =eve n 2 2 Although this expression is valid only in the limit Ap+N* -=M c it 353 will be applied in the physical region at low momentum transfier, The statistical sample is just too small to attempt a more refined calm culation based on an extrapolation to the pole. Also, all angular momenta greater than L - 2 will be ignored. This allows (IVo7) to be written in the form da = A + B cos2G + C cos4, (iv.8) d(cosG) where A = sin2 5 + 25/4'sin2525 ~ Cos( 2o )isinbsln5 n B = 75/2 sin22 -+ 15 cos(52-50)sin2sinS o, and

C = 225/4 sin2 2. In Figures 32(a-e) the cos @ distribution is shown for five Mk-,- regions: (1). 280-500 MeV, (2) 500-700 MeV, (3) 700-900 MeV, (4) 900-1200 MeV, (5) MT-7- > 1200 MeV. These regions are chosen simply to agree with those picked by the European collaborationl4 at a beam momentum of 2.75 BeV/c. The first two distributions are isotropic, and the next two show an increasing dependence on the cos Q terms. This indicates that higher angular momentum states reach significant proportions at approximately 800 MeVo The last mass region shows a drop in the cos Q dependence, but this is probably a consequence of poor statistics rather than a physical effect. These results agree very well with other experiments ' which have studied T=2 scattering in this reaction and also in the reaction Tr+ p + T + + no (4o16) The summary of a X fit to the data for the curve represented by (IV.8) is given in Table VI. From the table below it is seen that the errors in the fitted coefficients are very large. This, coupled with the fact that the coefficients cannot be evaluated at A2 -M2, makes it impossible to compute the phase shifts 50 and F2o It is probably safe to conclude that 62 does become significant at approximately 800 MeV, but nothing can be said with any certainty about its sign or magnitude.

82 2 2 2 2 2 -] A < 20 Mr 0 20 M r <_A<40 Mr c) H -- [ (a) (b) (cl z 15 280-500 500-700 700-900 w 10E 10 5 0 L 0.5. 0.5. 0.5 COS 8 (d) (e) 25 900-1200 - 1200 -U) 20 > 15 w 0 5 0.5 I. 0.5 I. COS 8 Figure 32. The ~- scattering angle in the (7-,t-) center of mass for (a) 280 < Mlr-~- < 500, (b) 500 < M~-,r- < 700, (c) 700 < M,-J:- < 900. (d) 900 _<M-~- < 1200, and (e) 1200 < M~-~- < 1670.

TABLE VI THE RESULTS OF X FITS TO (IV.8) FOR VARIOUS M - REGIONS 2 * 20 ) 2p < 40 M Mass (MeV) A P-N.,. 3 2P`... 2 2 A B C X A B C X 280-500 1.7~1.0 -1.8+6.2 2.4+ 7.1 97% 2.2+1.1 -3.7~6.4 4.1~ 7.2 98% 500-700 1.2~.9 1.153.8 3.1~ 7.1 2% 2.9~1.2 1.8~7.4 -0o.1 8.5 12 700-900 2.9~1.2 -5.3+7.9 11.3~ 9.2 40% 2.8~1.3 6.9+9.0 -2.8~10.3 32% 900-1200 1.2~0.9 -4.3+8.1 23.8+11.1 65o 1.7~1.1 0. 1~9.5 25.7+12.9 93% 1200-1670 0.5+0.7 -3.8~4.9 5.7+6.2 88% 1.7+1.0 -6.8~7.6 15.2~10.0 26o

84 6. PRODUCTION ANGLES With the knowledge that both the p~ and N3,3(1238) are produced in peripheral interactions, the distributions of the production angles for the individual particles of reaction (4.1) are exactly what one would expect. These are shown in Figures 33-35 in the following order: 1) Figure 33 —This corresponds to all events. (a) the rt, (b) the p, (c) the T+. 2) Figure 34-This corresponds to just those events in which an N*- (1238) is- produced. The shaded area represents the p overlap. (a) the r-, (b) the p, (c) the c+o 3) Figure 35 —This corresponds to just those events in which a p0 is produced. The shaded area represents the N;* 3(1238) overlap. (a) the i- associated with the p~, (b) tAe Xr not associated with the p~, (c) the p, (d) the it+ Since both p0 and N3,3(1238) production involve an incident act at the upper vertex and a proton at the lower vertex in the onepion-exchange model, the en has a strong forward preference and the proton likes the backward direction. The x- is not peaked as strongly as the proton because of the extra ~T whose production angle is fairly random in both the p~ and N, (1238) channels. The r + distribution is quite flat, because the Tr+ is produced slightly in the forward direction for the p~ channel and slightly backward for the N3* (1238) reaction reaction.

275 250-. _ 15 0 (a) u_ 125 a 100 75 50 25.8-404.8 8 -4 0. 4.8 -8 -4 0 A.8 ces (PRODUCTION ANGLE) Figure 33. Particle production angles for the 7- + p + x- + x- + + + p reaction. 120 110 I00 90 80 > 70 (a).8b).C):> 70 LL60 50 E40 30 20 IO _8 -4 0 4.8 -.8 -4 0 4.8 -8 -.4 0 4.8 COS (PRODUCTION ANGLE) Figure 3. 5 Particle production angles for the 7- + p + ~- + C- + N3,3(1238) reaction. 120 I10 100 Z 90 (0) b J c > 60 o 50 '~ 40 Z 30 20 I0:8 -4 0 4.8 _8 -.4 0.4.8 -.8 -4 0 4.8 _8 -.4 0 4.8 COS (PRODUCTION ANGLE) Figure 35. Particle production angles for the x- + p + x- + p + p0.

CHAPTER V THE REACTION tr- + p + + - + + + p + Co 1. INTRODUCTION Here the report will be almost entirely devoted to the coo and pmesons There will be strong evidence presented which indicates that both of these resonances are produced in quasi two - body reactions via the modes + p + p + N (5.1) and + C~ + *o (5.2) These initial two - body states -then decay through various channels to the final five - particle state. There will also be some discussion of the B meson which is produced in the reaction cJ- + p + p + Be + X- + ~o (5~3) 26 THE MASS PLOTS From the five particles produced in the reaction _ + p + +c + Jr - + p + t0, (5.4) eighteen different mass combinations can be constructed. The mass spectra for all of these have been investigated for the following cases: (1) all. events, (2) low momentum transfer, (3) all co events subtracted, (4) all cwo and p- events subtracted, (5) with and without the 121 events ambiguous with the neutron final state. In addition to the four to be

87 discussed below, only the (. —,p) and (ro,p) combinations show any evidence for resonance production. In both of these cases there is a slight peaking in the region of the 1238 MeV isobar, while all other plots follow phase space quite closely. M~ -~, + Mi+, M +, and M+-,+p are shown in Figures 36 and 37 with the ambiguous events plotted separately. The shaded areas in each histogram. correspond to the wo events, and therefore, the unshaded areas represent the various distributions after a complete &o subtract tiorn MMr+ o shows a very strong W~ peak centered at 790 MeV, Mr-,~ peaks in the region (750 MeV) of the p- meson, and M..+p shows a definite enhancement corresponding to the 1238 MeV isobar. Although M -a+p seems to follow phase space, it will be seen later that there is a definite structure associated with this distribution when the analysis is restricted to just the p- events. 3. THE c~0 PEAK 3.1 The w~ Cross Section All events in which at least one (T,n',Jr) mass value falls in the range 760-820 MeV are defined to belong to the co sample. In those cases where both (>-, n, ) mass combinations satisfy the wo definition, the methood of Chapter III, Section 5 is used to choose one of the two as the coo Upon fitting the c~ peak to a Breit-Wigner distribution, the central mass is found to be Mob D 789~2 MeV, which is about 6 MeV

88 24 (b) an 96 101 ~~~~~~~~~~~~~~~~~~I-z > 84 5 w LU. (0) 0 72 80-,= z m 60 > 70 Ww~~~~~~~~ z U-LL~~~~~~~~~~ 60 -1 m ~~7E~~48 0 =r 50 5 536 40 z30 24 20 12 10 30)0 400 560 600 700 800 900 I100 1100 1200 300 5 1800 2100 2400 M r-f~ (Mev) Mv'p.+ (MEV) Figure 56. M~-* o and M+p for the final state (_,jT_ +,p, O). The shaded areas represent the cw events. The upper histograms represent those events ambiguous with the final state (Tr-,ic-,c,c+,n). 120- (a) 96 Ito10-~~~~~ z I1~~~~~10;~~~~ "' 84 (n 100 w LL -72 - Z 90 U7 )~~~~~~~~~~~~~~~~~ W 80o U- W 60 -0 70 60- z 48, 60 50 40 36 40 30 24 204 12 10 500 600 700 800 900 1000 1200 1300 1400 1500 1600 1700 1800 1200 1500 1800 2100 1200 1500 1800 2100 M7r-'+vr~ (MEV) Mr+p (Mev) 7Zr-r x I - - -:3 I A' 4.1 — -P4~ --,+ o - Figure 57. M-~+ and M~-,+p for the final state (~cnr,,p,rco). The shaded areas represent the i~ events. The upper histograms represent those events ambiguous with the final state (-, -,,+ +

89 higher than the accepted value.10 The fitted full width at half maximum is r = 36+4 MeV. This, of course, is larger than the f~'s true width because of experimental errors in the mass computations (see Chapter III, Section 4). The cross section for co production through this reaction is estimated to be a =.28~.04 mb. This is found by counting the number of events above a smooth background (unshaded area) of Figure 37(a) and then correcting for the double - c& events. This correction is made by simply taking the total number (142) of co0s above phase space and then determining experimentally the number (7) of double - ~ s in this sample. This cross section, of course, is just for the three - pion decay and is not corrected for neutral modes which are responsible for approximately 10% of the co decays. 3.2 The Spin and Parity of the c~ Since the spin and parity of the wo are well-known (JP = i1), and since the results from this experiment confirm these assignments, only a brief description of the spin-parity analysis will be presented here. The spin-parity determination is based on the method used by MoLo Ste-venson et al 67 This involves a study of the distribution of points inside the Dalitz plot shown in Figure 38. If the c& isotopic spin is asesumped to be zero and the decay matrix elements are restricted to the simplest ones possible-that is, low internal angular momentum

9o.7-.6'.s~~~~~~~~~~~~ ~. ~ ~ ~ `W(~ ~.3~~~~~~~~~~~~~~~~~~~~~~e...44.... I '~~~~~~ 41 ~.3.2 -.1 0.1 ~ ~ / ~ 4 t~ Figurej8. Daitz plt for he cu"events X=(T~ - Tt) J~ ~:: -- "/, eed ~ ~ ~-+T

91 states for the decay pions-then for the assignments JP = 0O, 1i, 1+, 2 2+, only JP = 1- requires a nonzero density at the center of the Dalitz plot. The JP = 0+ possibility can be ignored because decay into three pions is impossible for such a state if parity is to be conserved. In Figure 38 a finite population near the center of the plot is seen, and the data is therefore only consistent with JP = 1% This is further confirmed upon investigation of the density distribution versus the distance from the center of the Dalitz plot. This has been compared with the predictions for the various assignments and clearly favors JP 1 o Although there are approximately 115 phase-space events in the a~ sample, they do not introduce any serious problems. Because the JTP 1 distribution is so much different than that for any other assignmnent tested, the background could not possibly influence the data to the extent that an incorrect spin-parity determination would result. If the wo were, for example, a J- = I particle, the background would probably make it impossible to distinguish between the 1' and 0O assiginments, but fortunately, that is not the case. 3.3 The Mass Spectra for the (0~,V-,p) State The Dalitz plot for the reaction ier + p is rps p + r (5i o) is presented in Figure 39(a) M2 is represented by the horizontal o ~-p

92 3.6 3.2 2.8 2.4 W 2.0 la 1.6 1.2.8.4.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 M2"-p (BEV)2 30 - (C) 25 > 20 15 (b) z 10 I5 1.2 1.6 2.0 24 2.8 3.2 3.6 4.0 900 00 0 1500 1700 900 M2rP (BEV)2 M 7r- (MEV) Figure 39. (a) Dalitz plot for the final state (u~,r-.p). Those events ambiguous with the (i -,-,i+,1+,n) state are represented by (x). (b) for the same final state with A-o < 1.5(BeV). (c) M)- for all events belonging to the (c~n,~-,p) state. The events ambiguous with (~-,r,-~+,~+n) are added to both (b) and (c) and then represented separately by the shaded areas.

93 axis and M2_ o by the vertical axis. Here the evidence for resonance production does not seem to be at all favorable. However, both the (ir,p) and the (r-,wo) systems do display very definite mass peaks when the two projections are plotted in the appropriate manner. When the horizontal projection is restricted to just those points for which 2_o K < io(BeV2 (see Figure 39(b)), the higher nucleon isobars appear. There is strong evidence for wo production through the channels - + p _+ ( + N,l(1238) (5.6) + Tr + P + O + N1.1(l1512) (5e7) and + ~ + N1, 1(1688) (5.8) + - + p. In the (C-,a~) system there are also clear signs of a mass enhancement. This is seen in Figure 39(c) where Mg- ~ is plotted. The distribution peaks quite strongly in the region from 1200-1300 MeV and can be 37,68,69 associated with the B enhancement seen in other experiments. The (e-,,+,+,o ) mass distribution has also been investigated for the events not satisfying 760 < Ma:+:o < 820 MeV. It is found that there is no evidence whatsoever for a peak in the 1250 MeV region. Thus the B can be associated with the (,c) ~) state rather than a pure follr-pion combination.

94 3o4 The B Peak If it is assumed that the c~ is a JP = 1 particle, then the ratio of true c~'s to background should be much larger near the center of the Dalitz plot of Figure 38 than at the edge. For the inner boundary of this plot, assuming a JP = 1- distribution, the calculated number of cMOs inside and outside are approximately equal. In Figures 40(a) and 40(b) the M+~ distribution is shown for all events, with Figure 40(a) restricted to those inside and Figure 40(b) to those outside the inner boundary. By counting the number of events above and below phase space, the w~-to-background ratio is found to be 65/30 and 70/85 for the inner and outer areas, respectively. Now, as the data seems to suggest, if the B peak is a consequence of an (wu0,~K-) resonant state, then the larger c~-to-background ratio for the center of the Dalitz plot should result in a more pronounced M.,-,peak for the events on the inside compared with those on the outside. This, however, is not the case. A.s was first observed by Go Goldhaber et alo,69 the B peak is obtained almost entirely from the events whose points are situated in the outer area. This is seen very clearly in Figures 41(a) and 41(b) where M 0o is plotted separately for the inside and outside events. Another disturbing fact about the B enhancement is that every point 2 2 2 in the peak (1.4(BeV)2 < M~-,~ K 1.7(BeV) ) also falls in one of the N* bands~ This is shown in Figure 42 where M2f-p is plotted for just

95 60 60 (bI - 50 50 z z w w > > w 40 w 40 0 0 30 30 0 0 z z 20 20 t- 10L, 10 400 500 600 7OO 800 900 1000 1100 1200 1300 1400 1500 1600 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 Mr-,-+ (Mev) M,.- +,o (Mev) Figure 40. Mg-g+ ~ for (a) the inside and (b) the outside events. 20 20 20 (a) 20 (b) C/) 15 z 15 z 15 w w w w U- 0~~~~~~~~~~~~~~~~~~~~~~~. 0a 00 0 0 0 0 O z Z - 5 - 900 1200 1500 1800 900 1200 1500 1800 Mw.-.-T.+ 7.o (Mev) MT7.- T.+7.o (Mev) Figure 41. M —+o for the events satisfying 760 < M~-,+~~ < 820 MeV. (a) the inside and (b) the outside events.

IC') z O0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~O 1.4 1.8 2.2 2.6 3.0 34 3.8 M i-rp (BEV)2 Figure 42. MY-p for those events which satisfy t- + p + B- + p. The events ambiguous with (1-,7-,i,+t+,n) are added and then represented separately by the shaded area.

97 the B events. It is seen that the isobars all appear, while the mass intervals outside the peaks are completely empty. At this point one must ask how the B peak is to be interpreted. Could it just be a four-pion resonance? This is ruled out because the B only appears when Me,+,~ is restricted to the interval 760-820 MeV. This is definitely not the result of the phase-space mass distribution for three of four pions produced in the decay of a 1250 MeV particle. But if it is a (-,cw~) resonance, why do the B mesons seem to be associated with the sample whose relative wo enrichment is smaller? Maybe there is another T = 0 three-pion resonance with a mass close to that of the co but with a different spin-parity assignment. The same analysis has been applied to the region 820 < M,-,+,o < 900 MeV, and there is no evidence of a B peak for either the inner or outer areas. Therefore, if there is such a particle, its upper mass, limit must be approximately 820 MeV. Also, it is very improbable that its lower mass limit could be much less than 760 MeV because of the small number of events with M-g+,r~ < 760 MeV (see Figure 37(a)). Thus, if there is a T = 0 three-pion resonance with JP t 1-, its width must be such that its mass limits are either inside or equal to 760-820 MeV. And finally, is it possible that the B peak is somehow related to the isobars? Maybe, with increased statistics, the B peak will be explained in terms of reactions (5.6), (5o7), and (5.8). It is remembered that this same possibility also exists for the A mesons.

98 4. THE p- PEAK 4.1 Introduction The investigation of the p- will be restricted to the reactions a- + p + p- + N3,3(1238) + t+ (5.10) -and + p + N _1(1238))+,+, (. 11) where the p- and N* regions are 660-820 MeV and 1140-1340 MeV, respectively. It will be seen that the entire enhancement in the p- region can be associated with these two channels. Since there are possible biases in the data due to the 121 ambiguous events and co production, the effects of these will be shown separately whenever necessary. However, it is clear from Figure 36(a) that neither can influence the results greatly because of the small number of events involved. 4.2 (N*, r) Decay Modes of the Higher Nucleon Isobars It has already been noted that a significant number of the p- and N3, (1238) states seem to be produced concurrently. This is quite evident when the M,+p spectrum (Figure 43) for the reaction K- + p + p- + + + +(512) and Mggo (Figure 44) for the reaction Ar + p + + _e + go + N3,3(1238) (5-13) are examined. These plots show a definite preference for the simultaneous production of the two resonances. In fact, upon examination of the MIvo and M,+p distributions for reaction (5.4) with all events

99 30 Cn - 25 z, 20 0 i 15 z QL 1000 1100 1200 1300 1400 1500 1600 1700 1800 MrM+p (MEV) Figure 43. M+p i'or the reaction c- + p - p- + +- + + P. The ambiguous events are added and then represented separately by the shaded areas. 60 f250 z w L> 40 U30 co 220 10 -300 500 700 900 1100 1300 M irr' (MEV) Figure 44. M ~ for the reasction iC + p ~. +?r + i( + N( (15) shaded areas.

100 from (5.10) subtracted (not shown), it is seen that both the p- and the N~,(1238) peaks are no longer prominent. Furthermore, the slight remaining enhancement in the p- region can be associated with reaction (5.11). This is verified by examining the M-_,~ spectrum (not shown) for the reaction Tr + p *(+ tr + To +N +N 1(1238). (5.14) From this point on, in light of the evidence just presented, the investigation of the p- will be restricted to reactions (5.10) and 1 5 e11)a The M-,,t and M. 1 distributions for these reactions.1). h M-nlN~,3 and Mn~ -3 1 are shown in Figures 45 and 46. In order to determine the effect of the uo overlap on the data, the two mass distributions are plotted in three different ways: (1) all events, (2) all w~ events subtracted, (3) an Lo subtraction based on a Monte Carlo calculation. The Monte Carlo subtraction is accomplished by assuming the final state (, )0~T,p) and then counting the number of fake events of the type (Tc,N*,p-) that are produced by the wc decay. For the 135 ~O's above phase space it is estimated that fifteen of the type (5o10) or (5.11) are formed. This number is used to arrive at the plots in Figures 45(c) and 46(c), In the MEr-N* histograms there are three obvious deviations from 5,3 phase space. These are all located close to known nucleon-resonance mass values at 1512, 1688, and 1920 MeV. In the M<+N% 1 plots the peaking again appears at 1512 MeV but there is nothing in the 1688 MeV region. There is also an enhancement in the 1920 MeV region, but its central value is 50 MeV on the low side.

101 25- (a) 25 25 (b) (C) n 20 18 20 20 z z W 15 W 15 W Is 0 o a w 10 1 I0 r 10 z 5 z 5 1240 1440 1640 1840 2040 1240 1440 1640 1840 2040 2240 1240 1440 1640 1840 2040 M(N',3,-) MEV M(N3,, n-) MEV M(N,, a ]) MEV Figure 45. M-N;N for the reaction t- + p p- + N;3(128) + x+. (a) all events; (b) all wo events subtracted; and (c) an w& subtraction based on a Monte Carlo calculation. The shaded area in (a) represents the ambiguous events. (0) (b) (C) 20 20 20 () C03 or) z z z w 15 W 15, 15 CO U- U0 l-O~~ 0 10 O loJ w W a- w Li D 5 = 5 5 z:D: z z 1240 1440 1640 1840 2040 1240 1440 1640 1840 2040 1240 1440 1640 1840 2040 M(N,- If+) MEV M(N;_1+l) MEV M(N,_1f+) MEV Figure 46. M+,- for the reaction r- + p- p + N3,_ 1(1238) + 7r+ (a) all events; (b) all 03 events subtracted; (c) an wo subtraction based on a Monte Carlo calculation. The shaded area in (a) represents the ambiguous events.

102 If one now hypothesizes the processes + +p -*p- +N* 1(1512) +- X+ N*( 1238) (5~15) + Tr + P) +- p +,- + 1(1688) + + N*(1238) (5o16) + 7 + P+ and,C + p + p- + N3,1(1920) + + N + (l238) (5.17) + t + Pv then isotopic spin conservation demands that (see Appendix B) o ([Nll +, + N3, 3 ++ T + p ) - 9/1 vAL _(N, +. + N1 + P) and At 1688 MeV there is a peak in the Ma.=N plot which does not appear in the M~+N* histogram~ Also, a Dalitz plot (Figure 47'(a)) of Mp versus M (N for all (,+,p) rmasses of reaction (5 12) in the nterval 1600881.76 MeV shows that the N, p(1238) is ch d favore d ovaer the N 1(1238)P There are 44 points in the N3(1238) region

1o03 2.6- (a) Nr.+P — p ~T ' — r'+ P 2.2 AMB. EVENTS INCLUDED w, 1600 MEV ~ M(7r-r'"P) < 1760 MEV co 1.8 a. + N Z 14 4 0' 1.0 1.4 1.8 2.2 2.6 Mrt(-p) BEV3.8 (b) (b). -: p -.+- 7 ++ -7+P N3 -1 3.4 - AMB. EVENTS INCLUDED 4~~~~~~~~ 1800 MEV < M(r-rr+P) <2040 MEV 3.0 -. off lb ~ ~-~~~~ -2.6 > w 0 a 2.2 '. ~. W \..- ~=Z.. 1.8 1.4 0.~ 108 ~~~~~~~~~~5 I I....t~.8 1.2 1.6 2.0 2.41 2.8 3.2 3.6 M'(7r P) BEVt Figure 117. Dalitz plots for (a) i6oo~~-+ < ly'60 MeV, and (b) 1800 < M~~h< 20110 MeV. These are just for the reaction ~- + p p~ + Irt + + p and also include the ambiguous events.

104 with no N, 1(1238), 24 points in the N,_1(1238) region with no N33 (1238), and 19 points in the overlap between the two isobars. Since the difference between the number of points in the two bands is approximately equal to the number of events above phase space in the MEN*E distribution, the data agrees very well with the 9/1 35, ratio. At 1512 MeV the branching ratio cannot be checked because the available kinetic energy for the decay products is too small. When the Dalitz plot limits are drawn, it is found that most of the area is in the overlap region of the two (u,p) resonances. This is also responsible for the 1512 MeV peak in the MJ+NA 1~ histogram. If this enhancement were real -instead it is a reflection of the (a,N* ) decay mode-the ratio given by V.1 would not be satisfied. The Dalitz plot for 1800 < M-,rc+p < 2040 MeV is shown in Figure 47(b). Here there are two bands, one corresponding to the N3 3(1238) and one for the N* (1238). The ratio of points in these two intervals is very close to 3/2. Considering the large amount of background, this is in good agreement with the predicted value of 9/4. 4.3 The Production Mechanism for the pIt has just been demonstrated that almost the entire p- peak can be associated with reaction (5.10), and furthermore, a significant number of these events can be placed with (5915), (5.16), and (5.17). These results lead one to suspect that the pD may be produced by means

105 of a Tr~- or ~0-exchange mechanism (see Figure 48). (Qf) (b) TT rr_ rr Figure 48...Possible meson-exchange diagrams for p- production in reaction (5.10). It will now be shown that neither diagram can be singled out as the primary contributor to p production in (5.10). This is based on the following results: a) The Trieman-Yang distribution (not shown) is not favorable for pure pion exchange, as the X2 test for isotropy yields a probability of less than 3%. This nonisotropy could be due to absorption, however, so this test alone does not rule out the Xo~ possibility. b) It is shown in Appendix C that if one-pion exchange is assumed, the cross section for X-+ pp o + N ~ + N3, _3 (5.18) - r- + n should be twice that of reactions (5.15) and (5.16), and for the T = 3/2 isobar at 1920 MeV, the cross section in the neutron case should be one-half as large as that of (5.17).

In the reaction + p - + x- + +r ++ + + n t-T ~~ (5 19) a strong N3_, (1238) peak is found in the (r-,n) state, but there is no evidence at all for p~ production. In spite of the fact that the p~ does not appear, the (7+,N* (1238)) mass is plotted in Figure 49 3,-3 for all events that satisfy X- + p pO + t 1 + + (5.20) ),-3' The p~ region is chosen to be 660-820 MeV, and the notation "po", is used in (5.20) to emphasize that there is no evidence for the particle. The histogram does show small peaks in the regions of the heavier isobars, but they are definitely not large enough to agree with the ratios predicted by pion exchange. One might say that there is some contribution from the diagram of Figure 48(a), but it definitely does not dominate the production process. c) The scattering angle distribution for the it in the p- center of mass is shown in Figure 50. If c~ exchange with no absorption is assumed, this plot should behave as sin2Q, the possibility of which is nil. If a small amount of T = 2 amplitude is assumed, this actually agrees quite well with 3~ exchange. However, absorptive effects are known to change angular distributions drastically, so w~ exchange cannot be excluded by this one result; only wo exchange with no absorption is eliminated.

107 25 () F-20 z LU. W 10 -1400 1700 2000 M r +_ ( Mev Figure 49. M,r+N5 for the reaction <Tr + p "pO"t + + + N3;,(1238). 30 Cn i-20 z Li ", t -.8 -.4 0.4.8 COS 9 Figure 50. The scattering angle of the < in the p' center of mass for the events satisfying iC + p -, p + m-i + N5(1238).

1o8 d) If the clo diagram is assumed, then reaction (5.20) is not allowed via this mechanism. This is so because the o~ is an isotopic singlet and does not exist in the charged state. However, neither can (5.17) occur through wo exchange, as this would violate isotopic spin conservation at the lower vertex. So, at most, only the i[L 1(1512) and N* 1(1688) peaks plus the T = 1/2 background in (5.10) can be explained by the w~ diagram. But even this is unlikely, as one would not expect (5.10) to proceed by the c~-exchange process except for that small part satisfying (5.17). Thus it seems quite certain that neither ~c' nor -O~ exchange completely dominate reaction (5.10). The considerations in (b) make the Eto possibility very remote, and the cwo is definitely ruled out for the T = 3/2 channel by isotopic spin conversation. 5. q MESON PRODUCTION In addition to the co there is also another vector meson, the cp, whose quantum numbers are = 1. Except for its mass (MT = 1020 MeV), this particle is identical to the cu, and one might expect its principal decay mode to be 0p + + - + t o. Experimentally, however, - 70,71 the 35 rate of the cp is much less than that for cp-* K +K, implying that the physical coupling constant Gpp, is small compared to G 0Tr 72 As suggested by Glashow, this can also lead to a small production rate for Ts as compared to cL~'s in pion-proton interactions.,

109 The rat io R - b(ng + P + + P + (P) a(g- + p + P + -O) has been determined from the data of this experiment, and it is found that R <.012, indicating that c~'s are, indeed, produced much more abundantly than cps in (cr,p) collisions. A more thorough discussion of this can be found in Reference 27. 6. THE PRODUCTION ANGLES The production angles for the cr-, m p, and 7o are shown in Figures 51(a.d). The pion and proton distributions are peaked forward and backward, respectively, with the negative pion and proton showing the more pronounced asymmetry. Most of this asymmetry can be associated with the a~ and p- reactions, although the distributions are still peaked slightly when only events outside these peaks are considered.

110 192 (a) n |(b) 168 144 > 120 0 96 ~ 72 48 24.8 -.4 O 4.8 -8 -.4 O 4.8 ces (PRODUCTION ANGLE) 192 (C) cd) 168 144 72 48 24 -8 -4 0.4.8 -8 -4 0 4.8 ces (PRODUCTION ANGLE) Figure 51. The particle production angles for the reaction ~- + pK- + K- + K+ + p + C~. (a) the r-. (b) the +. (c) the p, and (d) the o.

CHAPTER VI THE REACTION xc + p + x- +t - + r+ + + n In this reaction there is nothing of interest to report. All possible mass combinations have been studied with various subtractions and momentum transfer cutoffs imposed on the data. The only resonant state to appear is the N, 3 (1238) in the reaction g - p -* t + + + T + N,(1238) (6.1) T-+ + n At first sight, one might consider (6.1) as an ideal reaction to search for three-pion resonances such as the A mesons; however, none are found. This may be due to the fact that the production of such a resonance requires the exchange of a doubly charged particle in any simple meson-exchange process. The production angles for the particles have also been investigated With the exception of the neutron whose distribution is peaked in the backward direction, it is found that the particles are produced isotropically. t111

CHAPTER VII RESONANCE CROSS SECTIONS The cross sections for all resonant states discussed in this report are summarized in Table VII. These were obtained by simply counting the number of events above phase space in the given figure. There are no corrections made for other decay modes of the resonances, and these values, therefore, just represent a specific particle combination. For example, the cross section for the reaction rc + p + p0 + N3*1(1238) (7.1) does not include the contribution from the (i~r,n) decay of the N3,_1(1238); specifically, it is just the cross section for A~+p+ po + N,._1(1238) + p. (7.2) 112

113 TABLE VII THE CROSS SECTIONS FOR THE RESONANCES FOUND IN THIS EXPERIMENT (The column labelled "Mass Interval" represents the mass width assumed for the given particle combination) CHAINEL Mass Interval Figure |(mb. ) + p + po + + p 660 < MP0 < 820 15(c).43 + p0 + N*(1238) 1140 < MN* < 13 40 17(c).0o69 + A1 + p 1000 < MAl < 1150 24(c).050 + A2 + p 1200 < MA2 < 1350 24(c).056 + N*(1238) + c- + ~c 1130 < MN* < 1330 15(a).51 + ~f + r- +p 760 < o < 820 37(a).28 c&o + N*(1238) 1.3 < MN* < 1.8 39(b).031 2 >+ ~o + N*(1512) 2.1 < MN* < 2.5 39(b).o019 + t~ + N*(1688) 2.6 < MN* < 32 39(b).069 + B - + p 1200 < MB- < 1300 39(c).o56 + p + + N*(1238) 66 M - 43.8203 1140 < MN* < 1340 p + N+*(1512) 1480 < MN* < 1600oo 45(a) o061 + p + N*(1688) 1680 < MN* < 1840 45 (a).040 + p- + N*(1920) 1880 < MN* < 1960 45(a).033 + N*(1238)+ T- + g++j+| 1140 < MN* 1140 Not Shown.50

APPENDIX A LORENTZ INVARIANT PHASE SPA.CE AND THE DALITZ PLOT Consider an n-body final state in the center-of-momentum frame (CM frame) and let the following variables be defined: mi, qi, Pi, Ei the rest mass, four-momentum, vector momentum, and the energy of the i'th particle. QT, PT, ET the four-momentum, vector momentum, and the energy of the system. PT vanishes in the reference frame considered. Mij the effective mass of particles i and j. Rm(PTET) the number of states (integrated density of states) for a system with total momentum PT and total energy ET. Ignoring multiplicative constants, Rn(PT,ET) is defined as follows: n Rn(PT,ET) * n 4(QT ) (A) i=l It is easy to show that A.1 is equivalent to n n Rn(O,ET) (I d qi(q -Mi))((ET- Ei) ( Pi), (A.2) i=l i=l where the condition PT = O in the CM reference frame is inserted in the equation Rewriting Formula A.2 in the form n-l Rn(O,E) n d qi(qi-Mi)5 ( qi+qn-Q)) (A ) 2En i= e i=l and using PT = O, Rn (O,E) can be written

115 Rn(O,E) O dd Rnd (Pn5E-En)( Since Rn is constructed to be a Lorentz invariant, it can be expressed in any reference frame. Upon making a transformation to the Pn = 0 system and in addition, using the relationship 2 -*2 2 (E-En) _ (-Pn) = 2, (A.5) then Rn(OE) a dn Rnl(OC), (A.6) 2En a recurrence relation which allows one to calculate the n-dimensional phase-space integral from the (n-l)-dimensional value. Since R2 can be evaluated quite easily, it is possible to find Rn for any n. R2(0,C) is evaluated as follows:,2(oC) a d Pl d3 P2 (Ei +.2-) +p2 (A+7) 2E1 2E2 d3Pl 4 PI2 F (Es+E2-C)Y (A.8) where in A.8 it is assumed IP1l IP21K Now, using El(Pl) = lPl + M1 =I - 2 \ (A..9) E2(P1) = -P12 + M1 R2 can be written R2(0,E) EI Pl)dl( l ( 1P &2>( + 1P22+M2 2-c' (A. o10)

116 This is integrated. quite easily and finally, R2(o, c) t P1 (A. 11) a relationship which allows any Rn to be computed by repeated use of Formulas A.5 and A.6. Now let the effective-mass distribution of m out of n particles be considered. Assume an ordering so that the m particles are numbered 1, 2... m, and the other (n - m) are numbered m + 1... n. Denote the four-momenta of the two groups by Qm and Qn_m and their center-of-momentum energies (or effective masses) by Mm and Mnm. Also make the notational change Rn(P,E) + Rn(Qvml...mn), where Q is the total four-momentum and ml...mn represent the masses of a system of n particles. The phase space distribution of Mm is given by P(yMm)dM -: n-m+l( QTMm(mm+l mn)Rm(m ml' mm) ~ (A..12) Rn(QT,mlo..mn) The derivation of this can be found in RELATIVISTIC KINEMATICS by R. Hagedorn. He starts with Rn(QT;ml...mn) in the form of A.2, makes the substitution n n m,Jd4Qm4(QT-Qm- E q)j)4 (Qm- j)' (A. 1) j=l j=m+l j=l multiplies the resulting expression for Rn by

117 1 = (-Mm)dM, (A.14) and is then able to obtain (A.12) quite easily. The computation of the phase-space distributions for four or more 74 particles was handled in this experiment by the computer program LIMS. This program evaluates the necessary Rn's and then by using relationships similar to A. 12, it calculates the mass distributions for the various particle combinations. Since Rn cannot be put in functional form for n > 3, LIMS has to set up numerical tables to represent the Rn's, which, of course, requires that the integrals of these functions be done numerically. For the three-body final state the phase-space computations were handled by the program DALPS.75 In addition to the mass distributions, this program also calculates the kinematical limits for the Dalitz plot, 2 2 a scattergram of M 12 vs. M 23. As will now be shown, this plot should be uniformly populated for a phase-space distribution. For a three-body final state with center-of-momentum energy M, dPld P2d5P3 ( - R3(M;ml,m2,m3) a E(Pi+P2+P3 )b (M-E1E2-E3) By performing the integration over P3, the result R3 3 a lEd3 (M-E1-E2-E3) (A.16) E1E2E3 is obtained, where ~32 _ fl + P2 + 2j1wt2 (A.17)

If the integration over the direction of P2 is carried out first and then followed by the integration over the direction of P1, then d3P1 = 4 P12dP1 and (A.. 18) d3P2 = 2 P22dP2d(cos@), where + + cosQ = P IP2 (A.19) IP11 IP21 Thus, 2tSE3 Using the energy-omentut i rfOr'tu1as E12 = P + m (A. 21) E22 = p22 + m22 E3 2 = 32+ m35 = P2+P22+21P2cosQ+m3 2 it is readily seen that dddo - E1E2HE dPldP2d(cos~) 2 2 dEldE2dE3, (A.22) P1 P2 and therefore, R3 a dEldE2dE35 (M-E1-E2-E3) (A.23) ol dEldE2 where E3 = M-E1-E2. (A.24)

119 By using M22 = (X-23 ) - 2M( 3+E3) M12 - (M-~)2 _ 2M(~+~,3 ) and (A. 25) 2 3 (M-ml) - 2M(ml+E1), R3 can also be written R3~d~ 2 2 dM12dM23 (A.26) Therefore, assuming a phase-space distribution, a scattergram of M12 vs. M23 is uniformly populated within the prescribed kinematical limit s The limits can be found by squaring A.24 and substituting A.17 for 2 P3 This gives 2 2 2 f72 22 M2-2M(Ei+E2)+(EL+E2)2 = EL-m1+E2-22 NE l-m1. (A.27) x E2-m2 cos Q ' By setting cosG = 1 and then solving for the two solutions of E2 in terms of El, the kinematical limits are obtained.

APPENDIX B THE RELATIVE DECAY RATES FOR THE T = 1/2 AND T = 3/2 ISOBARS The N1 state is given in terms of the pion and T = 3/2 isobar by |N;,1> =W|E N3,3> it No 1 N3, | N 1 (B.1) Thus the decay rate for N 1+N* t (+) is three times that for N-* N*1 + (2) N1,1 But, since the N* state can be decomposed into IN,l> = rJ -p> + Ii con>, (B.2) only one-third of the N* decays are observed wh'en the (Tco,n) state is not considered. Therefore, ur(N*,L N-,5 + At + p + Tr N '9/1. ().3) c(N,1 + N,, + p + + +) For the N3, using B.2 and 3,113,3 A15 1E N3,y1 41 IJ N3,1>, the ratio C(Ny3 + + T + P +-) *+ =N, ++ 9/4 (B.5) I(N13+ N3,1 + c + + P +) is obtained very easily. 120

APPENDIX C o- AND- p PRODUCTION IN THE ONE-PION-EXCHANGE MODEL Let it be assumed that the reactions _- + p po + N* + N +,-3 + ( and t + p + +N* 3+ 7'- (2) are governed by the one-pion-exzhange diagrams of Figure 52, where N* represents any one of the T = 1/2 or 3/2 nucleon resonances. (CX) (b) Figure 52. One-pion-exchange diagrams for reactions (1) and (2). Tz = -1/2 for the N* of (a) and Tz +1/2 for the N* of (b). T = 1/2 or 3/2 for the N*'s in both (a) and (b). At the upper verticies, since I7-> = I-,- 1 (Itop-> - I=-,po>), (C.1),12 the cross sections for p~ and p- production are equal. Thus the ratio of the cross sections for reactions (1) and (2) is solely dependent on the relative rates of the processes at the lower verticies. 121

122 For the combination of a T = 1/2 N* and a pion, the proton state is given by IP> =!~> I I 1> |P> = 2' 2>= /5T I+N* > - 17t Nl,l> (C.2) 2 N -1 3 which immediately gives the ratio (P~ ++l N*1,1) = 2. (c.3) a(P + to + N*1 1) Furthermore, since the rates for 1, -1 3,-3 i+ - + n (3) and N*,1+ - + 3,3 -+ +p (4) are equal because of charge symmetry, the cross section for '- + p + p~ + N* ++ *() is twice that for r" +p + p - + * -+ K- + N3, (6) In terms of a T = 3/2 N* and a pion, the proton state is given by Ip> = = I > I1 J tN,> +,N>(c.4) This furnishes the ratio = 1/2. o(p + t0+ N1) 5,1

And finally, since the rates for NJ _1 + X+ + N 3 5,-3 + - +n (7) and * -,1 +,3 + E + p (8) are equal because of charge s ymmetry, the cross section for T- + p + p0 + N+ 1 + + -3 (9) r rt + n is one-half that for + + p +N + 5,1 + 4C + N5,5 (10) T+ + p.

REFERENCES 1.: H.L. Anderson, E. Fermi, E.A. Long, R. Martin, and D.E. Nagle, Phys. Rev. 85, 934 (1952). 2. M. A.lston, L.W. A.lvarez, P. Eberhard, M.L. Good, W. Graziano, H.K. Ticho, and S.G. Wojcicki, Phys. Rev. Letters 5, 520 (1960). 3. A.R. Erwin, R. March, W.D. Walker, and E. West, Phys. Rev. Letters 6 628 (1961). 4. E. Pickup, D.K. Robinson, and E. 0. Salant, Phys. Rev. Letters 7, 192 (1961). 5. B.C. Maglic, L.W. Alvarez, A.H. Rosenfeld, and M.L. Stevenson, Phys. Rev. Letters 7, 178 (1961). 6. N.-h. Xuong and G.R. Lynch, Phys. Rev. Letters 7, 327 (1961). 7. W.R. Frazer and J.R. Fulco, Phys. Rev. 117, 1609 (1960). 8. Y. Nambu, Phys. Rev. 106, 1366 (1957). 9. G.F. Chew, Phys. Rev. Letters 4, 142 (1960). 10. A.H. Rosenfeld, A. Barbaro-Galtieri, W.H. Barkas, P.L. Bastien, J. Kirz, and M. Roos, Revs. Modern Phys. 36, 977 (1964). 11. E. Ferrari and F. Selleri, Suppl. Nuovo Cimento 24, 453 (1962). 12. F. Selleri, Phys. Letters 3, 76 (1962). 13. L. Stodolsky and J.Jo Sakurai, Phys. Rev. Letters, 11, 90 (1963). 14. J. Alitti, J.P. Buton, A. Berthelot, B. Deler, W.J. Fickinger, M. Neveu-Rene, V. Alles-Borelli, R. Gessaroli, A. Romano, and P. Waloschek, Nuovo Cimento 35, 1 (1965). 15. N. Schmitz, Nuovo Cimento 31, 255 (1964). 16. K. Gottfried and J.D. Jackson, Nuovo Cimento 33, 309 (1964), 17. K. Gottfried and J.D. Jackson, Nuovo Cimento 34, 735 (1964). 124

125 REFERENCES (Continued) 18. J.D. Jackson, J.T. Donohue, K. Gottfried, R. Keyser, and B.E.Y. Svensson, Phys. Rev. 139, B428 (1965). 19. E.E.H. Shin, Phys. Rev. Letters 10, 196 (1963). 20. L.M.Brown, Phys. Rev. Letters 13, 42 (1964). 21. M. GelL-Mann and Y.Neteman, The Eightfold Way (W.A. Benjamin, Inc., New York and Amsterdam, 1964). 22. R.E. Behrends, J. Dreitlein, C. Fronsdal, and W. Lee, Revs. Modern Phys. 34, 1 (1962). 23. G.M. Pjerrou, D.J. Prowse, P. Schlein, WoE. Slater, D.H. Stork, and H.K. Ticho, Phys. Rev. Letters 9, 114 (1962). 24. V.E. Barnes, P.L. Connolly, D.J. Crennell, B.B. Culwick, W.C. Delaney, W.B. Fowler, P.E. Hagerty, E.L. Hart, N. Horwitz, P.V.C. Hough, J.E. Jensen, J.K. Kopp, K.W. Lai, J. Leitner, J.L. Lloyd, G.W. London, T.W. Morris, Y. Oren, R.B. Palmer, A.G. Prodell, D. Radojicic, D.C. Rahm, C.R. Richardson, N.P. Samios, J.R. Sanford, R.P. Shutt, J.R. Smith, D.L. Stonehill, R.C. Strand, A.M. Thorndike, M.S. Webster, W.J. Willis, and S.S. Yamamoto, Phys. Rev. Letters 12, 204 (1964). 25. Y.Y. Lee, W.D.C. Moebs, B.P. Roe, D. Sinclair, and J.C. Vander Velde, Bull. Am. Phys. Soc. 8, 325 (1963). 26. Y.Y. Lee, WoD.C. Moebs, B.P.. Roe, D. Sinclair, and J.C. Vander Velde, Bull. Am. Phys. Soc. 8, 325 (1963). 27. Y.Y. Lee, W.D.C. Moebs, B.P. Roe, Do Sinclair, and J.C. Vander Velde, Phys. Rev. Letters 11, 508 (1963). 28. Y.Y. Lee, B.P. Roe, D. Sinclair, and JoC. Vander Velde, Phys. Rev. Letters 12, 342 (1964). 29. Y.Y. Lee, Investigation of Di-Pion Resonances in 3.7 BeV/c Z-p Collisions (University of Michigan, Dissertation, 1964). 30. W.D.C. Moebs, B.P. Roe, D. Sinclair, and J.C. Vander Velde, "Proceedings of the International Conference on High Energy Physics,," Dubna, 1964 (to be published). 31. M.L. Perl, Y.Y. Lee, and E. Marquit, Phys. Rev. 138, B707 (1965).

126 REFERENCES (Continued) 32. G.F. Chew and F.E. Low, Phys. Rev. 113, 1640 (1959). 33. N.P. Samios, A.H. Bachman, R.M. Lea, T.E. Kalogeropoulos, and W.D. Shephard, Phys. Rev. Letters 9, 139 (1962). 34. C. A.sff, Do Berley, D. Colley, N. Gelfand, U. Nauenberg., D. Miller, J. Schultz, J. Steinberger, T.H. Tan, H* Bruggerr,P. Kramer,, and R. Plano, Phys6. Rev. Letters 9, 322 (1962). 35. P.H. Satterblom, W.D. Walker, and A.R. Erwin, Phys. Rev. 134, B207 (1964). 36. Aachen-Birmingham-Bonn-Hamburg-London (I.C.)-Munchen Collaboration, Nuovo Cimento 31, 485 (1964). 37. Aachen-Berlin-Birmingham-Bonn-Hamburg-London(I.C.)-Munchen Collaboration, Phys. Rev. 138, B897 (1965). 38. R.L. Lander, W. Mehlhop, N.-h. Xuong, and P.M. Yager, "Production of Nucleon Isobar and Multipion Resonances by 3.5 BeV/c T+ in Hydrogen," Report to the Ohio University Topical Conference on Recently Discovered Resonance Particles, April 26-27, 1963. 39. W.F. Baker, R.L. Cool, E.W. Jenkins, T.F. Kycia, S.S. Lindenbaum, W.A. Love, D. Luers, J.A. Niederer, S. Ozaki, A.L. Read, J.J. Russell, and C.L. Yuan, Phys. Rev. Letters 7, 101 (1961). 40. G. Benson (Private Communication). 41. J.R. Sanford, "The Separated Beam to the 20-Inch Bubble Chamber at the AGS" (BNL Internal Report, 1962). 42. E. Hart, BNL-BCG Interhal Report J-22 (i96 ). 43. R. Rau., BNL-BCG Internil Report J-18 (19611) 44. J.C. Vander Velde, University of Michigan Bubble Chamber Group Research Notes HI-1 and HI-3 (1963). 45. W.E. Humphrey and A.H. Rosenfeld, "Analysis of Bubble Chamber Data," UCRL-10812 (1963). 46. J. Berge, F. Solmnitz, and H. Taft, Rev, of Sci. Instr. 32, 538 (1961).

127 REFERENCES (Continued) 47. W.J. Willis, E.C. Fowler, and D.C. Rahm, Phys. Rev. 108, 1046 (1957). 48. D.M. Ritson, Techniques of High Energy Physics (Interscience Publishers, Inc., New York, 1961), p. 1089 49. J. Orear, "Notes on Statistics for Physicists," UCRL 8417 (1958). 50. A. Diddens, E. Jenkins, To Kycia, and Ko Riley, Phys. Rev. Letters 10, 262 (1962). 51. R.P. Feynam., Theory of Fundamental Processes (W.A.. Benjamin, Inc., New York, 1962) p. 73. 52. N.-h. Xuong, R.L. Lander, W.A.W. Mehlhop, and P.M. Yager, Phys. Rev. Letters 11, 227 (1963). 53. So.B Trieman and C.N. Yang, Phys. Rev. Letters 8, 140 (1962). 54. Po Pennock, Tuborg Subprogram (ANL Internal Report). 55. P. Pennock, Tribod Subprogram (ANL Internal Report). 56. G. L'ttjens and J. Steinberger, Phys. Revo Letters 12, 517 (1964). 57. W.J. Fickinger, D.K. Robinson, and E.O. Salant, Phys. Rev. Letters _10, 4_5'7 (:.963)o 58. L. Durand, IiI, and Y.T. Chiu, Phys. Rev. Letters 14, 1039 (1965). 59. Go Goldhaber, J.L. Brown, So Goldhaber, J.A. Kadyk, B.C. Shen, and Go.H Trilling, Phys. Rev. Letters 12, 336 (1964). 60. S.Uo Chung, OoI. Dahl, L.M. Hardy, RoIo Hess, G.R. Kalbfleisch, J. Kirz, DoH Miller, and G.oA Smith, Phys. Revo Letters 12, 621 (1964). / 61 J.. Alitti, JoBo Buton, B. Delei, M. Neveu-Rene, Jo Crussard, J. Gineset, A.H. Tran, Ro Gessaroli, and A.o Romano, Phys. Letters 15, 69 (1965). 62. R.To Deck, Phys. Rev. Letters 1_3, 169 (1964)o 63o Fo Salzman and G. Salzman, Physo Rev. 120, 599 (1960). 64. Mo Gell-Mann and KoMo Watson, Ann. Rev. Nuclo Sci. 4, 219 (1954).

UNIVERSITY OF MICHIGAN 3 9015 03483 7396 128 REFERENCES (Concluded) 65. E. Ferrari and F. Selleri, Nuovo Cimento 27, l450 (1963). 66. D.D. Carmony, D.N. Hoa, R.L. Lander, P.M. Yager, and N.-h. Xuong, "The T = 2 Pion-Pion Interaction" (Physics Dept., University of California at San Diego, April 24, 1964). 67. M.L. Stevenson, L.W. Alvarez, B.C. Maglic, and A.H. Rosenfeld, Phys. Rev. 125, 687 (1962). 68. M. Abolins, R.L. Lander, W.W. Mehlhop, N.-h. Xuong, and P.M. Yager, Phys. Rev. Letters 11, 381 (1963). 69. G. Goldhaber, S. Goldhaber, J.A. Kadyk, and B.C. Shen, Phys. Rev. Letters 15, 118 (1965). 70. P. Schlein, W.E. Slater, L.T. Smith, D.H. Stork, and H.K. Ticho, Phys. Rev. Letters 10, 368 (1963). 71. P.L. Connolly, E.L. Hart, K.W. Lai, G. London, G.C. Moneti, R.R. Rau, N.P. Samios, I.0. Skillicorn, S.S. Yamamoto, M. Goldberg, M. Gundzik, J. Leitner, and S. Lichtman, Phys. Rev. Letters 10, 371 (1963). 72. S.L. Glashow, Phys. Rev. Letters 11, 48 (1963). 73. R. Hagedorn, Relativistic Kinematics (W.A. Benjamin, Inc., New York, 1962) p. 93. 74. T.E. Kalogeropoulos, LIMS (BNL Internal Report F. 89). 75. G. Moneti, DALPS (BNL Internal Report F. 96).