Perturbatively improving regularization-invariant momentum scheme renormalization constants

Constantinou, Martha; Costa, Marios; Göckeler, M.; Horsley, R.; Panagopoulos, H.; Perlt, H.; Rakow, P. E. L.; Schierholz, G.; Schiller, A.

doi:10.1103/physrevd.87.096019

Cited by 28 publications

(24 citation statements)

References 17 publications

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“…[54,55]. This has been successfully applied for local and one-derivative fermion operators eliminating lattice artifacts from non-perturbative estimates [56,57].…”

Section: Summary -Future Workmentioning

confidence: 99%

Perturbative renormalization of quasi-parton distribution functions

2017

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In this paper we present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one-loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions.The extended nature of such 'long-link' operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors.On the lattice there is also mixing among certain subsets of these nonlocal operators; we calculate the corresponding finite mixing coefficients, which are necessary in order to disentangle individual matrix elements for each operator from lattice simulation data. Finally, extending our perturbative setup, we present non-perturbative prescriptions to extract the linearly divergent contributions.

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“…[54,55]. This has been successfully applied for local and one-derivative fermion operators eliminating lattice artifacts from non-perturbative estimates [56,57].…”

Section: Summary -Future Workmentioning

confidence: 99%

Perturbative renormalization of quasi-parton distribution functions

2017

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“…So we proceed in a similar way: As fermionic n-point functions depend on the gauge, we first fix both the NSPT and the nonperturbative (quenched lattice QCD) configurations to Landau gauge and measure the two-and threepoint functions. The only difference is in the use of the algebraic operations for NSPT and how the chiral limit is achieved: The nonperturbative Z-factors are obtained on a 32 4 lattice from a linear extrapolation to zero quark mass of data for three values of the hopping parameter κ = 0.1489, 0.1507 and 0.1520 [7]. For NSPT we can measure directly in the chiral limit, as we only need the tree-level Feynman propagator for the inversion of the Dirac operator (cf.…”

Section: Ri -Mom Factors From Numerical Stochastic Perturbation Theorymentioning

confidence: 99%

“…In our setup, we solve the Langevin equation using the simplest Euler integration scheme for three different step sizes ε = 0.01, 0.02, 0.03 and extrapolate our results afterwards linearly to ε = 0. We simulate lattices of sizes N 4 = 16 4 , 24 4 and 32 4 to resolve finite size effects. Renormalization factors in the RI -MOM scheme are defined in the chiral limit, for example,…”

Section: Ri -Mom Factors From Numerical Stochastic Perturbation Theorymentioning

confidence: 99%

“…For determinations of renormalization factors in the context of RI-MOM schemes [1] the finite lattice spacing causes for instance so called hypercubic lattice artifacts in the data for the renormalization factors. Their origin lies in the breaking of the Euclidean continuum symmetry O(4) to the hypercubic subgroup of reflections and permutations, H (4). This has the consequence that lattice results for the renormalization factors in momentum space depend on the direction of momentum, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…In practice, such a subtraction has been used in [2] using diagrammatic LPT calculations at 1-loop order in g 2 0 and also in [3,4] to order a 2 . However, a 1-loop subtraction often appears to be insufficient.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Using NSPT for the Removal of Hypercubic Lattice Artifacts

Simeth¹,

Göckeler²,

Sternbeck³

et al. 2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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The treatment of hypercubic lattice artifacts is essential for the calculation of non-perturbative renormalization constants of RI-MOM schemes. It has been shown that for the RI'-MOM scheme a large part of these artifacts can be calculated and subtracted with the help of diagrammatic Lattice Perturbation Theory (LPT). Such calculations are typically restricted to 1-loop order, but one may overcome this limitation and calculate hypercubic corrections for any operator and action beyond the 1-loop order using Numerical Stochastic Perturbation Theory (NSPT). In this study, we explore the practicability of such an approach and consider, as a first test, the case of Wilson fermion bilinear operators in a quenched theory. Our results allow us to compare boosted and unboosted perturbative corrections up to the 3-loop order.

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Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

Mondal

Gupta

Park

et al. 2021

J. High Energ. Phys.

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A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, 〈x〉u − d, helicity moment, 〈x〉Δu − Δd, and the transversity moment, 〈x〉δu − δd, of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass Mπ. The final results are obtained using a simultaneous fit in the lattice spacing a, pion mass Mπ and the finite volume parameter MπL keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme at 2 GeV, are 〈x〉u − d = 0.155(17)(20), 〈x〉Δu − Δd = 0.183(14)(20) and 〈x〉δu − δd = 0.220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.

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Perturbatively improving regularization-invariant momentum scheme renormalization constants

Cited by 28 publications

References 17 publications

Perturbative renormalization of quasi-parton distribution functions

Perturbative renormalization of quasi-parton distribution functions

Using NSPT for the Removal of Hypercubic Lattice Artifacts

Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

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