Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910475954946048 |
|---|---|
| author | Spanoudes, Gregoris Constantinou, Martha Panagopoulos, Haralambos |
| author_facet | Spanoudes, Gregoris Constantinou, Martha Panagopoulos, Haralambos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory Spanoudes, Gregoris Constantinou, Martha Panagopoulos, Haralambos High Energy Physics - Lattice 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. |
| title | Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2401.01182 |