TMDs in Laguerre polynomial basis

TL;DR

This paper proposes a novel approach to Transverse Momentum Dependent parton distributions (TMDs) by replacing the traditional power series expansion with a Laguerre polynomial expansion, enhancing the description at small transverse distances.

Contribution

It introduces a Laguerre polynomial basis for the operator product expansion of TMDs, improving the accuracy over a wider range of transverse distances without violating TMD properties.

Findings

Laguerre polynomial expansion better describes TMDs at small $b_T$

First term of the expansion captures TMD behavior more effectively

Method compatible with existing TMD factorization frameworks

Abstract

We suggest modification of the standard approach to TMDs. The modification consists in the consideration of the small $b_T$ operator product expansion in the different operator basis. Instead of power expansion we suggest to use the Laguerre polynomial expansion. Within such a scheme the first term of OPE saturates TMDs in the wider range of $b_T$ in comparison to the power expansion that decreases the significance of non-perturbative factor at small $b_T$. The presented modification does not violate any TMD properties and can be used within any formulation of TMD factorization.