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).
Highlights
The analysis of many high energy production processes in terms of a peripheral or single particle exchange model (PM) has proved to be very useful
ITP-160 of calculations 599 UPM which modify the PM to take into account the competing absorption processes in a manner analogous to distorted-wave Born approximation calculations of low-energy nuclear physics. These calculations, in a number of cases 9 yield good fits both to the production cross section as a function of t and the density matrix for the produced particles
We have shown that any form factor must play a small role 0 On the other hand, IJPM calculations of processes where vector particle exchanges dominate have not had the same degree of 20 success as UPM calculations where j = 0 particles are exchanged
Summary
The analysis of many high energy production processes in terms of a peripheral or single particle exchange model (PM) has proved to be very useful. ITP-160 of calculations 599 UPM (and UPMF) which modify the PM (and PMF) to take into account the competing absorption processes (for the initial and final state) in a manner analogous to distorted-wave Born approximation calculations of low-energy nuclear physics These calculations, in a number of cases 9 yield good fits both to the production cross section as a function of t and the density matrix for the produced particles. There seems to be an abundance of high spin resonances the vector at moderate energies; these might provide some structure in interaction. 21 We are presently performing a number of UPFM calculations for vector particle exchanges
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