Abstract
Perturbative expansions for short-distance quantities in QCD are factorially divergent and this deficiency can be turned into a useful tool to investigate nonperturbative corrections. In this work, we use this approach to study the structure of power corrections to parton quasi-distributions and pseudo-distributions which appear in lattice calculations of parton distribution functions. As the main result, we predict the functional dependence of the leading power corrections to quasi(pseudo)-distributions on the Bjorken $x$ variable. We also show that these corrections can be strongly affected by the normalization procedure.
Highlights
Lattice calculations in QCD have demonstrated the ability to complement, and in certain cases with the exceeding precision, significant amount of experimental measurements
The existing actual proposals [1,2,3,4,5,6] differ in details but have a common general scheme: parton distribution functions (PDFs) are extracted from the lattice calculations of suitable Euclidean correlation functions using QCD collinear factorization in the continuum theory
A popular suggestion [5] that has triggered a lot of recent activity [7,8,9,10,11,12,13,14,15,16,17,18,19,20], introduces a concept of a parton quasidistribution defined as a Fourier transform of the nonlocal quark-antiquark operator connected by the Wilson line
Summary
Lattice calculations in QCD have demonstrated the ability to complement, and in certain cases with the exceeding precision, significant amount of experimental measurements. The idea of the renormalon model of the power corrections [30,31,32,33,34,35] is that, with a replacement of μF by a suitable nonperturbative scale, this contribution reflects the order and the functional form of actual power-suppressed contribution Assuming this “ultraviolet dominance” [28,29,40] one obtains the following model: Q4ðx; p; μFÞ 1⁄4 κΛ2QCD x y qðy; μFÞ; ð4Þ with the dimensionless coefficient κ 1⁄4 Oð1Þ which cannot be fixed within theory and remains a free parameter. The difference between these two options in the present context is that the normalization to the vacuum correlator does not affect the leading Oðv2z2Þ power corrections that are subject of this work (since there is no gauge-invariant operator), whereas the normalization to the value at zero momentum, as we will see, has a substantial effect
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