Gauge-invariant renormalization scheme in QCD: Application to fermion bilinears and the energy-momentum tensor

Costa, Marios; Karpasitis, I.; Pafitis, T.; Panagopoulos, George; Panagopoulos, H.; Skouroupathis, A.; Spanoudes, Gregoris

doi:10.1103/physrevd.103.094509

Cited by 16 publications

(15 citation statements)

References 52 publications

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“…In order to extract non-perturbative physical results from numerical simulations on the lattice, we employ a non-perturbative gauge-invariant renormalization scheme (GIRS) [5], which is applicable in both continuum and lattice regularizations so as to make contact with the continuum schemes. In particular, we consider Green's functions which involve products of two gauge-invariant operators, O 1 , O 2 , at distinct spacetime points, in such a way as to avoid potential contact terms:…”

Section: Girs Schemementioning

confidence: 99%

“…Finally, we address the mixing which occurs among the operators and the supercurrent beyond tree level. In the same context, a gauge invariant renormalization scheme (GIRS) [5] is used to extract the renormalization of 𝑆 𝜇 ; the renormalization factors and the mixing coefficients in GIRS scheme can be obtained also in a fully non-perturbative manner and the GIRS non-perturbative results can be connected with MS via conversion factors.…”

Section: Introductionmentioning

confidence: 99%

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Supercurrent Renormalization in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory

Bergner¹,

Costa²,

Panagopoulos³

et al. 2021

Preprint

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In this work we study the renormalization of the SUSY Noether current in Supersymmetric N = 1 Yang-Mills (SYM) theory on the lattice. In particular, we study the mixing of the current with all other compatible operators of dimension 7/2 and 5/2, leading from the lattice-regularized to the MS-renormalized operator basis. We perform our task in two ways: (a) We compute, in dimensional regularization, the conversion factors relating the MS scheme to an intermediate gauge-invariant coordinate-space scheme. In this second scheme, renormalization can be performed via lattice simulations. This could help to investigate the breaking of SUSY on the lattice and strategies towards simulations of supersymmetric QCD. Here we present some preliminary numerical results. (b) We use lattice perturbation theory and compute, to one loop, various two-and three-point functions. We consider mixing with all relevant gauge-noninvariant operators, which contain also ghost fields.

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Section: Girs Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Supercurrent Renormalization in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory

Bergner¹,

Costa²,

Panagopoulos³

et al. 2021

Preprint

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“…The presence of symmetries, which are preserved by the SYM action, both in the continuum and on the lattice, forbids other operators from mixing with the Gluino-Glue operator. There are no gauge-invariant operators which mix with O Gg ; thus, by applying Gauge Invariant Renormalization Scheme (GIRS) [4] we only need to calculate one Green's function (Eq. (3.1)) to extract the multiplicative renormalization factor of O Gg , which contributes in physical matrix elements.…”

Section: Gluino-glue Operatormentioning

confidence: 99%

Perturbative study of the Gluino-Glue operator in SYM

Costa¹,

Panagopoulos²,

Panagopoulos³

et al. 2021

Preprint

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We investigate the renormalization of the Gluino-Glue operator, using both Lattice Perturbation Theory (LPT) and a Gauge Invariant Renormalization Scheme (GIRS). The latter scheme involves gauge-invariant Green's functions of two operators at different space-time points, which can be also computed via numerical simulations. There is no need to fix a gauge and the mixing with gauge noninvariant operators is inconsequential. We calculate perturbatively the conversion factor relating GIRS with the Modified Minimal Subtraction scheme. On the other hand, the Gluino-Glue operator being mixes with several gauge noninvariant operators which have the same quantum numbers. The determination of the mixing matrix on the lattice demands the calculation of 2-pt and 3-pt Green's functions with external gluon, gluino and ghost fields using LPT. We compute at one-loop order the renormalization of the Gluino-Glue operator and all operator mixing coefficients.

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“…Three conditions can be obtained by considering two-point functions between the two EMT operators: For the explicit definitions, see Ref. [6]. A fourth condition can be obtained by considering three-point functions among an EMT operator and two lower dimensional operators, e.g., two fermion bilinears :…”

Section: Application Of Girs To the Qcd Traceless Energy-momentum Tensormentioning

confidence: 99%

“…A long write-up of our work, together with an extended list of references, can be found in Ref. [6].…”

Section: Introductionmentioning

confidence: 99%

Gauge-invariant renormalization of fermion bilinears and energy-momentum tensor on the lattice

Spanoudes¹,

Costa²,

Karpasitis³

et al. 2021

Preprint

Self Cite

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We study a gauge-invariant renormalization scheme (GIRS) for composite operators, regularized on the lattice, by extending the coordinate space (X-space) scheme proposed some years ago. In this scheme, Green's functions of products of gauge-invariant operators located at different spacetime points are considered. Due to the gauge-invariant nature of GIRS, gauge fixing is not needed in the lattice simulations. Also, when operator mixing occurs, the gauge-variant operators (BRST variations and operators which vanish by the equations of motion) can be safely excluded from the renormalization process. We propose a number of variants of GIRS, including integration over time slices of the operator insertion point in a Green's function, which may lead to reduced statistical noise in lattice simulations. We employ these variants in the renormalization of fermion bilinear operators and the study of mixing between the gluon and quark energy-momentum tensor operators. We extract the one-loop conversion factors relating the nonperturbative renormalization factors in different versions of GIRS to the reference scheme of MS.

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Gauge-invariant renormalization scheme in QCD: Application to fermion bilinears and the energy-momentum tensor

Cited by 16 publications

References 52 publications

Supercurrent Renormalization in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory

Supercurrent Renormalization in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory

Perturbative study of the Gluino-Glue operator in SYM

Gauge-invariant renormalization of fermion bilinears and energy-momentum tensor on the lattice

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