Disentangling long and short distances in momentum-space TMDs
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13130_2022_Article_18778.pdf
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Author(s)
Ebert, Markus A.
Michel, Johannes K. L.
Stewart, Iain W.
Sun, Zhiquan
Date Issued
July 20, 2022
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2022 Jul 20;2022(7):129
Version
Final published version
Abstract
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 ΛQCD/kT. We demonstrate that this method can be used to compute the cumulative integral of TMD PDFs over
k
T
≤
k
T
cut
$$ {k}_T\le {k}_T^{\mathrm{cut}} $$
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
cut
$$ {k}_T^{\mathrm{cut}} $$
, 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 non-perturbative OPE contributions to the Collins-Soper kernel and intrinsic TMD distributions.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP07(2022)129
