S-wave π-π scattering phase shifts

Using an absorptive one-pion exchange mechanism for the reaction x p x m n, a fit is made to experimental data at 4 GeV/c in order to extract the x-n scattering phase shifts. The analysis was carried out up to D waves in the x-x amplitude. The best results indicate a very broad I = 0 S-wave resonance with Mz —— 820 MeV and 1" = 600 MeV.

S-Wave n-ir Scattering Phase Shifts* H. Kim  Using an absorptive one-pion exchange mechanism for the reaction x p x m n, a fit is made to experimental data at 4 GeV/c in order to extract the x-n scattering phase shifts. The analysis was carried out up to D waves in the x-x amplitude. The best results indicate a very broad I = 0 S-wave resonance with Mz --820 MeV and 1"= 600 MeV.
The determination of low-energy w-w scattering phase shifts has been pursued over the last several years. -Two recent works in this direction are corrections to determine the m-m scattering parameters. These data have been previously analyzed'4 and the improvement in the present analyses consists in the inclusion of an I= 0 D-wave amplitude in m-m scattering. Though our analysis has been restricted to m &900 MeV, the tail of the f' resonance is seen to be important:.
The process under study is the reaction m p v+p n at 4 GeV/c incident momentum. The production mechanism was assumed to be due to a onepion exchange modified by initialand final-state absorption. The details of this calculation are presented in a subsequent paper. ' A cut in t, the momentum transfer between the proton and final neutron, was made and events with~t~&3m, ' were considered. It is hoped that with this assumption the peripheral hypothesis will be valid. Likewise, we feel that 4 GeV/c is a more desirable incident momentum for this kind of analysis than is 7 GeV/c, which was used in the analysis of Ref. l. trajectories may have to be taken into account.
The w-m scattering amplitude was parametrized in an energy-dependent way. The P and D waves were taken to be resonance-dominated by the p and f' mesons, respectively. The positions and widths were not varied but were set at the accepted values. ' In the case of the P wave, a radius of inter-action was included and varied in the fit. For the D wave no such radius was included as we were always on the low side of the resonance. The S wave was parametrized by an effective-range expression, with q and s the relative momentum and effective mass squared of the final 11-11 system. Though all the distributions were fitted, the one most useful in determining the phase shifts was the cos0 distribution, where 0 is the scattering angle in the 11-11 center-of-mass system. At each 11-11 effective mass, the distribution was expanded in a power series in cos 0, d dN9 = t C n cos n 0.

COS n=o
(2) In Fig. 1 we show the experimental values of the expansion coefficients as well as the best fits with and without a D-wave contribution, Whereas the previous analysis of these data 3 • 4 had difficulty in obtaining a good fit to the magnitude of the forward backward asymmetry, the inclusion of the D wave reduces the discrepancy. We likewise present, in at 820 MeV with a width r = 600 MeV. This is consistent with the findings of other groups. 6 To recapitulate, the results we obtain for the  amplitudes are (the quantities in square brackets were not varied) q . A graphical presentation of these results is given in Fig. 3