Target mass and finite $t$ corrections to diffractive deeply inelastic scattering

TL;DR

This paper derives target mass and finite momentum transfer corrections for diffractive deep-inelastic scattering using quantum field theory, providing formulas suitable for data analysis and exploring their impact on various scattering processes.

Contribution

It introduces a detailed derivation of target mass and finite t corrections for diffractive scattering using off-cone twist-2 operators, extending previous results and enabling better data analysis.

Findings

Corrections are proportional to x|t|/Q^2, x M^2/Q^2.

Relations between kinematic amplitudes are established.

Results reduce to known limits when t, M^2 approach zero.

Abstract

The quantum field theoretic treatment of inclusive deep--inelastic diffractive scattering given in a previous paper \cite{BGR2006} is discussed in detail using an equivalent formulation with the aim to derive a representation suitable for data analysis. We consider the off-cone twist--2 light-cone operators to derive the target mass and finite $t$ corrections to diffractive deep--inelastic scattering and deep--inelastic scattering. The corrections turn out to be at most proportional to $x |t|/Q^2, x M^2/Q^2, x = x_{\rm BJ} {\rm or} x_\PP$, which suggests an expansion in these parameters. Their contribution varies in size considering diffractive scattering or meson--exchange processes. Relations between different kinematic amplitudes which are determined by one and the same diffractive GPD or its moments are derived. In the limit $t, M^2 \to 0$ one obtains the results of \cite{Blumlein:2001xf} and \cite{Blumlein:2002fw}.