Isobar Model Analysis of Single Pion Production in Pion-Nucleon Collisions Below 1 BeV

Abstract

The following procedure is recommended for analysis of process 0: (1) Define a region AB on the Dalitz plot where the resonance A may distort the analysis. (2) Check that AB does not include any point corresponding to COSA 23 * = 0 [see Fig. 1(c)].(3) Define a C region large enough to contain the A'B f region. (4) For each event included in C, go to the c.m.s. of particles 2 and 3, interchange their direction, and make thereby a fictitious conjugate event. (5) Ignore the fictitious conjugate events which do not fall into AB.(6) Remove the true events from region AB and repopulate this region with the fictitious conjugate events.One should remember when making the x 2 fits that the sample of fictitious events is highly correlated statistically to the sample of true events from which the former were constructed.The same method can be applied to study the process a provided that AB does not include the points where cosA 12 * = 0 in the A c.m.s.Finally, if one makes an analysis of what is in AB region alone and subtracts from the histograms the contributions of 0 and a, represented by the two kinds of fictitious events in the B c.m.s. andIn this paper we show that an improved (3, 3) isobar model for single pion production in pionnucleon collisions can account for the majority of the observed mass spectra and the ratio of 7T° to 77 + production in ir + -p collisions from 350 MeV to 1 BeV. This is in contrast to earlier analyses using the isobar model. i " 4 The essential new feature of the present analysis is the inclusion of the P-wave decay of the (3, 3) isobar.Although the rough features of the shape of the mass spectra predicted by the isobar model of Lindenbaum and Sternheimer 1 " 3 (called LS model hereafter) have been observed in many experiments, 5 " 8 the LS model fails to describe the IT -TT mass spectra. The main approximations of the LS model are that (a) the interference between the two isobar diagrams (see Fig. 1) can be neglected, (b) the isobar is produced in a S state and (c) the isobar decays isotropically. Bergia, Bonsignori, and Stanghellini 4 (called BBS model hereafter) in the A c.m.s., respectively, one can then study the interference (i.e., process y) by itself. One should remember, however, that in such an operation, one has subtracted the background (process 6) twice.An alternate technique to the one proposed above would be to use a rotation, in the c.m.s. of the resonance being studied, of 180° around the normal n to the plane of production (instead of the spatial parity operation used above). This is equivalent to the product of a spatial parity operation and a reflection with respect to the production plane (a good operation if over-all parity is conserved). With that alternate technique, one should remember that the conjugation inverts the components of the decay particle spins in the plane of production.Two tests to check the uniformity of the background from process 6 are (1) symmetry in eosA 2 3* for those events in band B but not in AB or A'B', (2) symmetry with respect to the quantit...

Application of Noninvariance Groups to Meson-Baryon Scattering

“…Olsson has shown that it is in excellent agreement with experiment as analyzed by Olsson and Yodh. 6 Similarly we have for the kaon-initiated re-actions T{K" +p -K° + E *°) = T(K° +p -K + + H *°) which could be expressed in terms of the isospin amplitudes A 2/ in the form A 0 = oA 2 (with the same remark about the sign convention as before). No meaningful comparison with experiment seems possible at the present time.…”

“…For example, the Olsson relation is true for the choices of 20-, 56-, or 120-dimensional representations of SU(4) or the infinite-dimensional representations of SL(4,#). The Johns on-Trie man relations and their generalizations hold with the choice of the standard 56-dimensional representation of SU (6) or the Sakita choice of 20 (or of the 70 or 700) representation; and even with baryons assigned to the representations of SL(6,#).…”

Inelastic Effects andπ−NResonances

“…The importance of A production is also seen empirically in the ^-production analysis of Olsson and Yodh. 9 It is not surprising that we get such good results. We have included the important production mechanisms while, as has been shown by Carruthers, 10 the sum of the particle-exchange Born terms that we have neglected (e.g., p and A 1 1 1 1 1 1 1 1 exchange) is quite small in this channel.…”

Pion-Nucleon Scattering in theP11State

“…Since it is known that the s-wave 7T-N forces are very weak, whereas the s-wave w-ir forces are very strong, the natural two-body configuration to consider is aN; a represents the ww 7=7=0 configuration at a mass of about 400 MeV. As a matter of fact, Brown and Singer have proposed that there is in fact a true resonance (i.e., a pole of a scattering amplitude) .^ Although much evidence has been cited in its favor, [41][42][43][44][45] the effect is noticeably absent in certain experiments such as the recent one on K e ± decays. 46 The possibility that there is an important enhancement without an actual resonance is difficult to exclude, particularly in view of the theoretical suggestion of Chew 47 that the ww phase shift may be decreasing through |TT.…”