Transverse Momentum Dependent PDFs in Chiral Effective Theory

TL;DR

This paper introduces a framework connecting transverse momentum dependent PDFs with chiral effective theory, enabling calculations of TMD PDFs through convolution with hadronic distributions and operator product expansion.

Contribution

It develops a novel theoretical approach to match TMD PDFs onto chiral effective theory operators, including explicit calculations for the proton's isovector TMD distributions.

Findings

Derived convolution formulas for TMD PDFs in chiral theory

Applied operator product expansion to high-energy TMD matching coefficients

Calculated proton's isovector TMD distributions at leading order

Abstract

We develop a theoretical framework to match transverse momentum dependent parton distribution functions (TMD PDFs) onto chiral effective theory operators. In this framework the TMD PDF is expressed as a convolution of TMD hadronic distribution functions, which describe fluctuations of initial states into intermediate hadrons in chiral perturbation theory, and short distance matching coefficients, which are the TMD PDFs of intermediate hadrons in the chiral limit. The various limits of the matching condition are explored and an operator product expansion is applied to the high energy TMD matching coefficients, allowing them to be written in terms of the collinear valence PDFs of intermediate hadrons. As an example, we calculate the isovector TMD hadronic distribution functions for the proton at leading order in the chiral expansion.