Nuclear Physics B101 (1975) 285-303 © North-Holland Publishing Company PARTIAL-WAVE ANALYSES OF THE (3n)- SYSTEM 1N THE REACTION n-p ~n-n-n+p A T 11.2 GeV/c Bologna-Florence-Genoa-Milan-Oxford-Pavia Collaboration G. THOMPSON l , P. ANTICH 2, A BOLDETTI 3, A. CARTACCI 4, G. COSTA 3, N.W. DAWES 1 , G. DI CAPORIACCO 4, A. FOR1NO s, J.L. LLOYD 1 , L. MAPELLI 2, S.J. OREB1 GANN 6 , A. QUARENI VIGNUDELLI s , D. RADOJIC1C 1 , S. RATTI 2, G. TOMASINI 7 and U. TREVISAN 7 Received 21 July 1975 The results are presented of two partial-wave analyses of the (3~r)- system in 30 000 events of the reaction n-p --* n-~r-~r÷p at 11.2 GeV/c. Both techniques incorporate the assumptions of the isobar model and are (a) the University of Illinois program which fits in terms of the (3n) density matrix elements and (b) an amplitude parametrisation in- cluding possible effects of both spin non-flip and spin flip at the baryon vertex. The re- sults obtained with these independent programs are found to be very close. The proportions of contributing states, their t-dependence and the phases of off- diagonal density matrix elements are discussed for the mass range 0.9 < M(3~r) < 1.9 GeV/c 2. The A 1 phenomenon is investigated in the context of a recent model; values of the mass, width and cross sections for the A1, A2, A 3 states are given, and an interesting variation in the 2+PM=I wave is observed at high masses. 1. Introduction Considerable interest [1 ] has recently been aroused in three-body partial-wave analyses and already much important information has been gained. Most of these analyses employ the program written at the University of Illinois [2] whilst others analyse in terms of amplitudes [3]. This paper contains a comparison of results from what has become the standard density matrix program with those from an amplitude parametrisation. I Nuclear Physics Laboratory, Oxford University. 2 Istituto di Fisica Nucleare and Sez. I.N.F.N., Pavia. 3 lstituto di Scienze Fisiche and Sez. I.N.F.N., Milano. 4 lstituto di Fisica dell Universita Firenze and Sez. I.N.F.N., Firenze. s Istituto di Fisica dell Universita Bologna and Sez. I.N.F.N., Bologna. 6 As 1, now at Imperial College, London. 7 Istituto di Scienze Fisiche and Sez. 1.N.F.N., Genova. 285 286 G, Thompson et al. / n-p ~ rr-n-Tr*p Although there are now a number of three-pion analyses a considerable degree of controversy still surrounds the results. The A 2 has been confirmed as a bona fide resonance both in intensity and phase variation. The A 1 phenomenon has a phase change which is too small to be regarded as due to a simple resonance alone, but a recent paper [4] attempts to save the 1+ SU(3) octet by claiming that interaction with a Deck-like effect [5] will reduce the expected phase variation. In the high mass region this experiment confirms recent observations of a phase variation in the 2-S (fir) wave in the (3rr) + system [6, 7] which at first seemed to contradict the results in the (370- system [8], whilst interesting variations of the 2+PM~I (fTr) wave are noted. 2. Experimental data The source of the data for this analysis is an 11.2 GeV/c 7r-p experiment per- ~brmed in the CERN 2 m chamber by the Universities of Bologna, Florence, Genoa, Milan, Oxford and Pavia. 500 000 pictures were taken in April 1971 and 350 000 in June 1972. The sample used in this study derives from the 29 611 events which had a fit to the hypothesis 7r-p ~ rr-rr-Tr+p, with an acceptable kinematic ×2 probability and consistent with ionisation require- ments. The beam momentum bite taken for the analysis was 11.19 + 0.20 GeV/c. Some 40% of the film has been measured on the Oxford University PEPR system and reconstructed using the RHEL geometry and kinematics programs. The rest of the film was measured on HPD's at the CNAF in Bologna and was processed through the THRESH-GRIND program chain. Technical details of the experimental proce- dures can be found in ref. [9] *. The resolution on the 37r mass is between 10 and 12 MeV/c 2 in the mass region of interest, and that on 2n mass is between 6 and 10 MeV/c 2. The three-pion mass spectrum can be seen in fig. 1, the shaded region correspond- ing to events with 1.12 < M(pn +) < 1.32 GeV/c 2 that is reflection of A++ production. It can be seen that contamination from this sotrrce is only serious at higher (3n) masses but for use in the Illinois program, events in this region were anti-selected throughout, the corresponding phase-space normalization integrals being corrected accordingly. The possible reflection of 4 ° and N*'s was also tested and cuts of varying severity were tried on the (prr-) and (p;r +) spectra. It may be asserted that none of the results quoted would shift by more than a small fraction of a standard deviation with bigger cuts than those used, and for the final analysis no (p~r-) cuts * For details of the experimental procedures and the amplitude analysis, see ref. [9a] ; for details of data compatibility, contamination checks and the use of the Illinois program, see ref. [9b]. G. Thompson et al. / n-p ~ n-n-Tr÷p 287 5ft. T 1£ 2oo c" 1130 00.9 1.1 1.3 1-5 1.7 1.9 M( 3'tr ) C-¢V/c 2 • Fig. 1. The effective mass spectrum of Or-rr-n÷). The shaded region corresponds to events with 1.12 <M(wr ÷) < 1.32 GeV/c 2. at all were found to be necessary. Spectra for the (pzrn) systems are reproduced in Monte-Carlo event generation using the fitted (3n) density matrix elements, indicat- ing that three-body decays of N*'s or A's are not important. 3. The isobar model Both methods in the analysis use a Bose-symmetrised isobar model (the terminol- TheIsobar Model "~,/~s Ir~ ,it.- P p Fig. 2. The terminology of the isobar model used. A (3rt) mass m is produced with momentum transfer t' = t - tmin with spin-parity JP z-component M. It decays via an/-wave into an isobar of spin s (J = I + s) and an odd 7r-. 288 G. Thompson et al. / 7r-p -~ n-n-n*p 20OO 4OO -F Ca) (b) 300 m 1000 ..1- ~ IO0 %';" e:7 01.0 010 1.0 M( 'rr"rr -) GeVIc 2 Cos 0j 500 3O (c) (d) 400 I 300; 200 f- uJ 100 i 0 ~12 (J~j (rad) (rad) ---~ Fig. 3. Distributions from the interval 1.2 < M(37r) < 1.4 GeV/c 2 and 0 < It'l < 0.5 (GeV/c) 2 with a fit to the data; (a) mass Or÷n-), two entries per event; (b) cos 0j in the Jackson frame; (c) Oj in the Jackson frame; (d) % the third Euler angle defining the (3~r) system, is the rotation angle of the n-n" plane about the ~r÷ direction in the (3n) rest frame. ogy of which is illustrated in fig. 2), with a maximum likelihood optimization in which the 3n system is fully represented by the required 3n - 4 = 5 kinematic variables. Two of these are the neutral dipion masses squared, but to make the ap- proaches as different as possible within these constraints, the usual Gottfried- Jackson frame cos 0, q~ of the 7r÷, and the ~r-Tr- plane rotation angle 3' were replaced in the amplitude analysis by the momentum vectors of the final state particles. In fig. 3 is shown typical distributions in the density matrix analysis variables for the 3rr mass interval 1.2 to 1.4 GeV/c 2 and 0.0 ~< It'l <<- 0.5 (GeV/c) 2. The G. Thompson et al. / rr-p -~ rr-rr-Tr+p 289 Table 1 Masses and widths of isobars Dipion spin Mass (GeV/c 2) Width (GeV/c 2) +O.O9O 0 (e) 0.747 -+ 0.035 0.360 -0.081 1 (p) 0.766 ± 0.005 0.137 ± 0.012 2 (f) 1.272 _+ 0.010 0.152 ± 0.020 smooth curves here represent the results of one fit, using the Illinois program. A full account of the Illinois method can be found in ref. [2] and of the ampli- tude parametrisation in ref. [9a] where there is also a detailed comparison of the two. Both programs use as decay states those combinations of (37r) spin states which have a well-defined Y-parity (r/); states oft/= +1(-1) can be shown to correspond to natural (unnatural) parity exchange in a t-channel model in the limit of small l/s [10]. It can be shown that states of different r/do not interfere in the absence of polarisation information. In practice it was found that production of the 7r-n-Tr÷ system is dominantly in the r/= +1 and M = 0 states. For this reason these quantum numbers are assumed in the naming of states in this paper, unless noted otherwise. The dominant (n÷n -) states are those of the e 0, p0 and f0 and were included in each decay amplitude by the relevant relativistic Breit-Wigner propagator. No at- tempt has yet been made to include dipion spin/>3.