Drell-Yan hadron tensor: contour gauge and gluon propagator

TL;DR

This paper investigates the gauge invariant Drell-Yan hadron tensor, emphasizing the role of non-standard diagrams and contour gauge in fixing gluon propagator ambiguities, with implications for understanding twist-three functions.

Contribution

It introduces a contour gauge approach to clarify the gluon propagator structure in the Drell-Yan process, highlighting the importance of non-standard diagrams for gauge invariance.

Findings

Contour gauge simplifies gluon propagator analysis.

Non-standard diagrams are crucial for gauge invariance.

Gluon pole contributions are clarified using Wilson lines.

Abstract

We consider the gauge invariant Drell-Yan hadron tensor which includes the standard and non-standard diagram contributions. The non-standard diagram contribution is appeared owing to the complexity of the twist three $B^V(x_1,x_2)$-function where the gluon pole manifests. We use the contour gauge conception which allows us to fix easily the spurious uncertainties in the gluon propagator. The contour gauge condition is generated by the corresponding Wilson lines in both the standard and non-standard diagrams. We demonstrate the substantial role of the non-standard diagram for forming of the relevant contour in the Wilson path-ordered exponential that leads to the spurious singularity fixing.