Abstract
The transverse component of the axial-vector correlation function of quark fields is a natural starting object for lattice calculations of twist-3 nucleon parton distribution functions. In this work we derive the corresponding factorization expression in terms of twist-2 and twist-3 collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for the axial-vector quasi- and pseudodistributions.
Highlights
Background field techniqueThe separation of coefficient functions and operator matrix elements in a certain amplitude can be understood in the spirit of Wilson’s approach to the renormalization group as integrating out the high-momentum degrees of freedom
In this expression q and A can be considered as given fields which satisfy classical QCD equations of motion (EOM)
This is achieved by starting with a suitable γ5 definition in d = 4 − 2 dimensions [85,86,87] aided by a finite renormalization that effectively restores the anticommutation property {γμ, γ5} = 0
Summary
In the present work we study the twist expansion of a product of quark and antiquark fields. In renormalization schemes with an explicit regularization scale, the Wilson line in eq (2.1) suffers from an additional linear ultraviolet divergence [57] which has to be removed This can be done by the renormalization of a residual mass term, to the heavy quark effective theory, or, alternatively, by forming a suitable ratio of matrix elements involving the same operator [58, 59]. This issue is well known and does not require an extra elaboration. In this paper we derive the leading-power factorization theorem for the qITD GT distribution to NLO (one-loop) accuracy It incorporates twist-2 and twist-3 collinear distributions.
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