Time-reversal invariance-like relations for spin-effects in elastic and inelastic reactions; vector-meson photoproduction versus compton scattering from nucleons

Abstract

For elastic scattering, relations between spin-effects (for example, the well-known asymmetry-polarization equality) follow from time-reversal invariance. We show that if certain amplitude combinations vanish, there are strikingly similar relations between spin-effects for elastic and also inelastic reactions. This vanishing of amplitude combinations (denoted M-purity) corresponds asymptotically to purely natural or purely unnatural parity in the crossed channel. The M-purity relations hold for spin-configurations much more general than do the corresponding time-reversal invariance relations. The experimental evidence for purely natural parity exchanges in high energy vector meson photoproduction from nucleons is shown to be good for all amplitudes involving nonzero meson helicity, but less conclusive for the zero helicity ones. Using time-reversal invariance and a vector meson-dominance argument, this implies no unnatural parity contributions in high energy Compton scattering from nucleons. Because of this empirical evidence for M-purity in these two processes, a detailed application to spin-effects in Compton scattering and in vector meson photoproduction is made. Some time-reversal invariance relations in Compton scattering resemble the corresponding M-purity relations though the applicability of the two is different, and there are examples where only one of the two exists. Out of our illustrations, the only M-purity relations which change in form due to the extra amplitudes present in the inelastic reaction are the M-purity analogue and extensions of the asymmetry-polarization equality (of Compton scattering) referring to the photon; the change is the appearance of the elements ϱ 00 of the vector meson density-matrix ϱ. Our other examples of M-purity relations do not change in form in going over from the elastic reaction (Compton scattering) to the inelastic reaction (vector meson photoproduction).