Transverse momentum distributions at large-$x$

TL;DR

This paper develops a method to resum large-$x$ asymptotics in transverse momentum dependent distributions, improving theoretical predictions and constraining nonperturbative models in high-energy physics.

Contribution

It introduces a process-independent resummation technique for TMD distributions at large-$x$, valid for all but the pretzelosity, enhancing perturbative accuracy.

Findings

Resummation formulas valid for all TMDs except pretzelosity.

Improved perturbative convergence and estimation of higher-order effects.

Resummation can reach N$^3$LL accuracy, surpassing known coefficient functions.

Abstract

We investigate the collinear matching of transverse momentum dependent (TMD) distributions at large values of $x$, computing and resumming the leading large-$x$ asymptotics for matching coefficients. The large-$x$ resummation is done directly within TMD distributions, ensuring the process-independence of the result. The derived resummation formulas are valid for all TMD distributions (except the pretzelosity). Their application improves perturbative convergence, provides practical estimation for unknown higher-order contributions, and sets restrictions for the nonperturbative part of models. Using the known anomalous dimensions, resummation can reach N$^3$LL, often exceeding the accuracy of known coefficient functions.