Gauge-Invariant Scaling Model of Current Interactions with Regge Behavior and Finite Fixed-Pole Sum Rules

Abstract

A general nonperturbative model for the entire Compton amplitude which incorporates Bjorken scaling, gauge invariance, and Regge behavior is presented. We show that a covariantly regularized model based on the infinite-momentum-frame techniques of Drell, Levy, and Yan is equivalent to the manifestly covariant nonperturbative parton model of Landshoff, Polkinghorne, and Short. We also demonstrate that a general consequence of composite theories of hadrons with field-theoretic constituents which incorporates the above properties is the existence of a constant energy-independent and ${q}^{2}$-independent term in ${T}_{1}(\ensuremath{\nu}, {q}^{2})$ (a "Kronecker delta" ${\ensuremath{\delta}}_{J0}$ term) and a $J=0$ fixed pole in ${T}_{2}(\ensuremath{\nu}, {q}^{2})$. Sum rules for general Compton amplitudes are derived and a discussion of mass renormalization for electromagnetic self-energy corrections of hadrons is presented. We demonstrate that such sum rules are always finite, even in the presence of Regge behavior, when subtraction terms in the underlying parton-proton $u$-channel dispersion relation are taken into account. Analytic continuation in $\ensuremath{\alpha}$ is thus justified.