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 q2-independent term in T , ( v , q 2 ) (a "Kronecker delta" 6,, term) and a J = 0 fixed pole in T, (v, q2). 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 a is thus justified.

Compton scattering from nuclei and photo-absorption sum rules

“…Thus at asymptotically high energies point-like interactions involving photons can contribute an energyindependent constant to the amplitude, which corresponds to a Regge pole at α = 0 [2][3][4][5][6][7][8][9][10], as is shown schematically in Fig. 1.…”

Towards a fitting procedure for deeply virtual Compton scattering at next-to-leading order and beyond

“…On the theoretical side studies in the partonic [127,128] or light-cone [129,130] approach lead to a real term in the transversal part of the (forward) Compton amplitude that in the language of Reggeization was interpreted as a J = 0 fixed pole. Nevertheless, via a subtracted sum rule [131,132,127,128] it is related to the imaginary part of the Compton amplitude. This would imply that there is no separate D-term contribution in the central GPD region.…”

Light-cone representation of the spin and orbital angular momentum of relativistic composite systems

“…[25,26]. The light-cone framework of the model resembles that of the covariant parton model of Landshoff, Polkinghorne and Short [27,28], in which the power behavior of the spectral integral at high masses corresponds to the Regge behavior of the deep inelastic structure functions. Although the model is based on just two Fock constituents, it is relativistic and satisfies self-consistency conditions such as in the point-like limit where R 2 M 2 → 0, the anomalous moment vanishes.…”