Sum Rules for Total Cross-Sections of Hadron Photo-Production on Pseudoscalar Mesons and Octet Baryons

TL;DR

This paper derives universal sum rules connecting hadron static parameters with integrals over differences in total photo-production cross-sections, using high-energy scattering and analytic properties of Compton amplitudes.

Contribution

It introduces new sum rules linking hadron electromagnetic form factors and static parameters to photo-production cross-section differences, expanding theoretical understanding.

Findings

Derived sum rules relating form factors to cross-section integrals

Established universal relations for hadron static parameters

Connected high-energy scattering data with static hadron properties

Abstract

Considering very high energy peripheral electron-hadron scattering with a production of hadronic state X moving closely to the direction of initial hadron the Weizs\"acker-Williams like expression, relating the difference of q^2-dependent differential cross-sections of DIS processes to the convergent integral over the difference of the total hadron photo-production cross-sections on hadros, is derived. Then, exploiting analytic properties of the forward retarded Compton scattering amplitude on the same hadrons, first, the sum rules are derived bringing into relation hadron electromagnetic form factors with the difference of the q^2-dependent differential cross-sections of DIS, then using Weizs\"acker-Williams like expression and taking the derivative of both sides according to ${\bf q^2}$ for ${\bf q^2} \to 0$ one comes to new universal hadron sum rules relating hadron static parameters to the convergent integral over the difference of the total hadron photo-production cross-sections on hadrons.