One-loop renormalization of staple-shaped operators in continuum and lattice regularizations

Constantinou, Martha; Panagopoulos, H.; Spanoudes, Gregoris

doi:10.1103/physrevd.99.074508

Cited by 50 publications

(67 citation statements)

References 72 publications

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“…This was pointed out by one of us in Ref. [70] and later confirmed at one-loop order in lattice perturbation theory [71]. The latter calculation also found that more generally, the pattern of mixing depends only on the direction with which the Wilson lines hit the quark fields, which is consistent with the prediction of the auxiliary field approach.…”

Section: A Piecewise Straight Pathssupporting

confidence: 77%

Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach

2020

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Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD. The nonlocality makes it difficult to understand the renormalization and improvement of these operators using standard methods. In previous work, we showed that by introducing an auxiliary field on the lattice, one can understand an on-axis Wilson-line operator as the product of two local operators in an extended theory. In this paper, we provide details about the calculation in perturbation theory of the factor for conversion from our lattice-suitable renormalization scheme to the MS scheme. Extending our work, we study Symanzik improvement of the extended theory to understand the pattern of discretization effects linear in the lattice spacing, a, which are present even if the lattice fermion action exactly preserves chiral symmetry. This provides a prospect for an eventual O(a) improvement of lattice calculations of PDFs. We also generalize our approach to apply to Wilson lines along lattice diagonals and to piecewise-straight link paths. * jeremy.green@cern.ch 1 A similar analysis for gluonic Wilson-line operators in the continuum was done in Refs.

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Section: A Piecewise Straight Pathssupporting

confidence: 77%

Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach

2020

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“…Note that for b z = 0, the corresponding MS conversion kernel for the quasi beam functionB q has been calculated in Ref. [121], which is sufficient for the lattice studies of the x-moments of TMDPDFs carried out in Refs. [34][35][36][37][38], but does not suffice for the determination of the Collins-Soper kernel which requires the calculation for nonvanishing b z .…”

Section: Ri /Mom Renormalization and Matchingmentioning

confidence: 99%

“…For the staple-shaped operators discussed here, the multiplicative renormalization has also been used in Ref. [121], which carried out the RI /MOM renormalization for the special case b z = 0, i.e. vanishing longitudinal separation of the staple.…”

Section: Ri /Mom Renormalization and Matchingmentioning

confidence: 99%

“…Such a calculation has also been carried out in Ref. [121] for staple-shaped Wilson line operators at vanishing longitudinal separation, which is connected to the calculations needed for determining TMDPDFs. In particular it corresponds to a special case of the quasi-TMDPDF operators studied here, which will involve stapleshaped Wilson lines but with an additional separation along the longitudinal direction.…”

Section: Introductionmentioning

confidence: 99%

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Renormalization and matching for the Collins-Soper kernel from lattice QCD

Ebert

Stewart

Zhao

2020

J. High Energ. Phys.

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The Collins-Soper kernel, which governs the energy evolution of transversemomentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularizationindependent momentum subtraction (RI /MOM) scheme, as well as the conversion factor from the RI /MOM-renormalized quasi-TMDPDF to the MS scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.

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“…Other approaches for computing the x-dependence of PDFs and related quantities have also been suggested [8][9][10][11][12][13][14][15][16][17][18][19]. Some of them are closely related to the concept of quasi-PDFs.By now there has been important progress in understanding the renormalization of quasi-PDFs [20][21][22][23][24][25][26][27][28][29][30][31][32]. A variety of other aspects of quasi-PDFs and, generally, Euclidean correlators have also been extensively studied .…”

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confidence: 99%

Studying twist-2 GPDs through quasi-distributions in a scalar diquark model

Bhattacharya¹,

Cocuzza²,

Metz³

2019

Proceedings of XXVII International Workshop on Deep-Inelastic Scattering and Related Subjects — PoS(DIS2019)

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Quasi parton distributions (quasi-PDFs) are currently under intense investigation. Quasi-PDFs are defined through spatial correlation functions and are thus accessible in lattice QCD. They gradually approach their corresponding standard (light-cone) PDFs as the hadron momentum increases. Recently, we investigated the concept of quasi-distributions in the case of generalized parton distributions (GPDs) by calculating the twist-2 vector GPDs in the scalar diquark spectator model. In the present work, we extend this study to the remaining six leading-twist GPDs. For large hadron momenta, all quasi-GPDs analytically reduce to the corresponding standard GPDs. We also study the numerical mismatch between quasi-GPDs and standard GPDs for finite hadron momenta. Furthermore, we present results for quasi-PDFs, and explore higher-twist effects associated with the parton momentum and the longitudinal momentum transfer to the target. We study the dependence of our results on the model parameters as well. Finally, we discuss the lowest moments of quasi distributions, and elaborate on the relation between quasi-GPDs and the total angular momentum of quarks. The moment analysis suggests a preferred definition of several quasi-distributions. I. INTRODUCTIONParton distribution functions (PDFs) are important objects encoding information about the quark and gluon structure of hadrons [1]. They can be extracted from data for a large class of hard scattering processes, where the key underlying tool is factorization theorems in quantum chromodynamics (QCD) that separate the perturbatively calculable short distance part of a cross section from the long-distance part described by PDFs and other potential non-perturbative quantities [2]. On the other hand, first-principles calculations of PDFs using lattice QCD have remained challenging due to their explicit time-dependence. As a result, in the past almost all related studies in lattice QCD focused on moments of PDFs which are defined through time-independent local operators, while the full dependence of PDFs on the parton momentum fraction x remained elusive.The recently proposed quasi parton distributions (quasi-PDFs) offer a way to directly access the x-dependence of the PDFs in lattice QCD [3,4]. Quasi-PDFs are defined through spatial equal-time operators that can be computed on four-dimensional Euclidean lattices. They reduce to their corresponding standard (light-cone) PDFs if the hadron momentum P 3 = | P | → ∞, prior to renormalization. However, for lattice calculations one first renormalizes, and P 3 is finite. This leads to two sources of discrepancies between quasi-PDFs and standard PDFs: higher-twist corrections that are suppressed by powers of 1 P 3 , and a different ultraviolet (UV) behavior for these two types of PDFs. The UV disparities can be cured order by order in perturbative QCD through a so-called matching procedure -see for instance . Other approaches for computing the x-dependence of PDFs and related quantities have also been suggested [8][9][10][11][12][13][14][15...

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One-loop renormalization of staple-shaped operators in continuum and lattice regularizations

Cited by 50 publications

References 72 publications

Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach

Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach

Renormalization and matching for the Collins-Soper kernel from lattice QCD

Studying twist-2 GPDs through quasi-distributions in a scalar diquark model

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