Classical sum rules and spin correlations in photoabsorption and photoproduction processes

Abstract

In this paper we study the possibility of generalizing the classical photoabsorption ($γa \to b c$) sum rules, to processes $b c \to γa$ and crossed helicity amplitudes. In the first case, using detailed balance, the sum rule is written as $\int_{ν_{th}}^\infty {\frac{dν}ν} KΔσ_{Born} (ν)=0$ where $K$ is a kinematical constant which depends only on the mass of the particles and the center of mass energy. For other crossed helicity amplitudes, we show that there is a range of values of $s$ and $t$ for which the differential cross section for the process $γb \to a c$ or $a c \to γb$ in which the helicities of the photon and particle $a$ have specific values, is equal to the differential cross section for the process in which one of these two helicities is reversed (parallel-antiparallel spin correlation).