Abstract
We consider the direct photon production in two hadron collision with one of the hadrons being transversely polarized. By using the contour gauge for gluon fields, we find that there are new twist-$3$ terms present in the hadron tensor of the considering process in addition to the standard twist-$3$ terms. In this work, we demonstrate that the significance of these new terms are two-fold: first, they are crucial to both the QED and QCD gauge invariance and, second, their contributions to the hadron tensor are at least the same as those from the standard ones. We also study the resuting effects which are responsible for the universality breaking of the corresponding twist-$3$ parton distributions.
Highlights
The problem of the electromagnetic (QED) gauge invariance in the deeply virtual Compton scattering and similar exclusive processes has intensively been discussed during the last few years
We explore both the QED and the QCD gauge invariance of the hadron tensor for the direct photon production in two hadron collision where one of the hadrons is transversely polarized
We present the important details related to the use of the contour gauge for the Drell–Yan process with essential transverse polarizations
Summary
The problem of the electromagnetic (QED) gauge invariance in the deeply virtual Compton scattering and similar exclusive processes has intensively been discussed during the last few years (for example, see [1,2,3,4,5,6]). After combining with the twoparticle correlator contributions, one gets the gauge-invariant expressions for the physical amplitudes or, in the case of lepton–hadron processes, for the corresponding hadron tensors [7] This scheme was originally developed in the case of the particular inclusive processes with transverse polarized hadrons, like structure function g2 in DIS [7] and single spin asymmetry (SSA) [8] due to the soft quark (fermionic poles [9]). We show that the new (“non-standard”) terms do contribute to the hadron tensor exactly as the “standard” terms known previously This is exactly similar to the case of the Drell–Yan process studied in [16,17]
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