Wilson lines in transverse-momentum dependent parton distribution functions with spin degrees of freedom

TL;DR

This paper introduces a new framework for transverse-momentum dependent parton distribution functions incorporating a generalized gauge invariance with the Pauli term, affecting their renormalization and evolution, especially for spinning particles.

Contribution

It proposes a novel approach including the Pauli term in Wilson lines, analyzing its effects on distribution functions' properties and evolution, with new Feynman rules and phenomenological insights.

Findings

Pauli term preserves twist-two distributions' probabilistic interpretation

Introduces additional pole contributions to twist-three distributions

Induces a process-dependent phase affecting distribution functions

Abstract

We propose a new framework for transverse-momentum dependent parton distribution functions, based on a generalized conception of gauge invariance which includes into the Wilson lines the Pauli term $\sim F^{\mu\nu}[\gamma_\mu, \gamma_\nu]$. We discuss the relevance of this nonminimal term for unintegrated parton distribution functions, pertaining to spinning particles, and analyze its influence on their renormalization-group properties. It is shown that while the Pauli term preserves the probabilistic interpretation of twist-two distributions---unpolarized and polarized---it gives rise to additional pole contributions to those of twist-three. The anomalous dimension induced this way is a matrix, calling for a careful analysis of evolution effects. Moreover, it turns out that the crosstalk between the Pauli term and the longitudinal and the transverse parts of the gauge fields, accompanying the fermions, induces a constant, but process-dependent, phase which is the same for leading and subleading distribution functions. We include Feynman rules for the calculation with gauge links containing the Pauli term and comment on the phenomenological implications of our approach.