Absorptive Corrections and Form Factors in the Peripheral Model

Abstract

Absorptive corrections applied to the peripheral model have provided a relatively successful interpretation of a variety of high-energy production processes. There exist, however, a number of difficulties associated with these calculations. We consider the reaction $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\rho}N$, which is dominated by $\ensuremath{\pi}$ exchange, in order to study the following three ambiguities: (i) the actual dependence of the absorptive corrections on the initial- and final-state elastic-scattering phase shifts, (ii) the role of a form factor, and (iii) the numerical values of the final-state elastic-scattering phase shifts. The comparison of our calculation with the experimental data, in particular the density matrix of the $\ensuremath{\rho}$, leads to the following results. The $j=\frac{1}{2}$ partial waves must be totally suppressed by the absorptive corrections and the form factor must play a very minor role in order to fit the observed deviation of the $\ensuremath{\rho}'\mathrm{s}$ density matrix from that predicted by the exchange of a $\ensuremath{\pi}$ in the peripheral model. (A form factor cuts down the low partial waves in a manner which leaves the density matrix unmodified from the simple peripheral model and thus reduces the effect of absorption corrections on the density matrix.) We expect any form factor associated with $\ensuremath{\pi}$ exchange to have a weak $t$ dependence, since there exists no resonance with the appropriate quantum numbers (to couple to the $\ensuremath{\pi}$) with energy \ensuremath{\lesssim}1.3 BeV. It is plausible that form factors (in addition to the absorptive corrections), while unimportant for $\ensuremath{\pi}$ exchange, may play a significant role in vector exchange (since there seems to be an abundance of high-spin resonances).