Disentangling long and short distances in momentum-space TMDs
Markus A. Ebert, Johannes K. L. Michel, Iain W. Stewart, Z. T. Sun
Abstract
A bstract 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 Λ QCD / k T . We demonstrate that this method can be used to compute the cumulative integral of TMD PDFs over $$ {k}_T\le {k}_T^{\mathrm{cut}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>T</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:msubsup> <mml:mi>k</mml:mi> <mml:mi>T</mml:mi> <mml:mi>cut</mml:mi> </mml:msubsup> </mml:math> 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 $$ {k}_T^{\mathrm{cut}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>k</mml:mi> <mml:mi>T</mml:mi> <mml:mi>cut</mml:mi> </mml:msubsup> </mml:math> , 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 non-perturbative OPE contributions to the Collins-Soper kernel and intrinsic TMD distributions.