Kinematics, Gauge Invariance, Helicity Conservation forπV→πVand Related Reactions

Abstract

A detailed discussion of the kinematics and Reggeization of pion and vector-meson scattering and crossed reactions is presented in terms of helicity amplitudes and invariant amplitudes. It is shown that the gauge-invariance condition allows a smooth limit to the case of massless vector mesons, i.e., photons. Particular attention is paid to the importance of kinematic constraints. It is shown how they are necessary in obtaining the pion pole in Compton scattering. The total photoabsorption cross section is considered, and it is seen that in order to obtain a finite, nonzero asymptotic value of the cross section, the introduction of a singularity in the appropriate residue is unavoidable, but compatible with kinematic and gauge-invariance constraints. Finally, the conservation of helicity is investigated. It is found that the factorization of the pion residue functions is a necessary condition for conservation of helicity in the $\mathrm{VV}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ channel. In Compton scattering, we find that the kinematic constraints imply the conservation of helicity, provided the total photoabsorption cross section approaches a finite and nonzero limit.