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arXiv · 2401.01182

Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory

Gregoris Spanoudes·Martha Constantinou·Haralambos Panagopoulos
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Abstract

In this work, we study the renormalization of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line at the one-loop level in both lattice and continuum perturbation theory. These operators enter the first-principle calculation of transverse momentum-dependent parton distribution functions (TMDPDFs) in lattice QCD using the formulation of Large Momentum Effective Theory. We provide appropriate RI$'$-type conditions that address the power and logarithmic divergences, as well as the mixing among staple operators of different Dirac structures, using a number of different possible projectors. A variant of RI$'$, including calculations of rectangular Wilson loops, which cancel the pinch-pole singularities of the staple operators at infinite length and reduce residual power divergences, is also employed. We calculate at one-loop order the conversion matrix, which relates the quasi-TMDPDFs in the RI$'$-type schemes to the reference scheme $\overline{\rm MS}$ for arbitrary values of the renormalization momentum scale and of the dimensions of the staple.

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Gregoris Spanoudes, Martha Constantinou, Haralambos Panagopoulos. 2024-01-02. Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory. https://arxiv.org/abs/2401.01182

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