Disentangling Long and Short Distances in Momentum-Space TMDs

TL;DR

This paper introduces a model-independent method to isolate perturbative contributions in momentum-space TMDs, enabling more accurate extraction of nonperturbative physics and reducing ambiguities caused by different prescriptions.

Contribution

It proposes a set of integral functionals that restrict TMD observables to the perturbative domain, systematically reducing artifacts from truncation and improving the extraction of nonperturbative effects.

Findings

Method computes cumulative TMD PDFs from collinear PDFs with radiative corrections.

When scales are near $k_T^{ m cut}$, corrections are at percent level.

Enables model-independent limits on nonperturbative contributions with experimental data.

Abstract

The extraction of nonperturbative TMD physics is made challenging by prescriptions that shield the Landau pole, which entangle long- and short-distance contributions in momentum space. The use of different prescriptions then makes the comparison of fit results for underlying nonperturbative contributions not meaningful on their own. We propose a model-independent method to restrict momentum-space observables to the perturbative domain. This method is based on a set of integral functionals that act linearly on terms in the conventional position-space operator product expansion (OPE). Artifacts from the truncation of the integral can be systematically pushed to higher powers in $\Lambda_{\rm QCD}/k_T$. We demonstrate that this method can be used to compute the cumulative integral of TMD PDFs over $k_T \le k_T^\mathrm{cut}$ in terms of collinear PDFs, accounting for both radiative corrections and evolution effects. This yields a systematic way of correcting the naive picture where the TMD PDF integrates to a collinear PDF, and for unpolarized quark distributions we find that when renormalization scales are chosen near $k_T^\mathrm{cut}$, such corrections are a percent-level effect. We also show that, when supplemented with experimental data and improved perturbative inputs, our integral functionals will enable model-independent limits to be put on the nonperturbative OPE contributions to the Collins-Soper kernel and intrinsic TMD distributions.