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arXiv · 2102.00858

Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor

M. Costa·I. Karpasitis·G. Panagopoulos·H. Panagopoulos·T. Pafitis·A. Skouroupathis·G. Spanoudes
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Abstract

We consider a gauge-invariant, mass-independent prescription for renormalizing composite operators, regularized on the lattice, in the spirit of the coordinate space (X-space) renormalization scheme. The prescription involves only Green's functions of products of gauge-invariant operators, situated at distinct space-time points, in a way as to avoid potential contact singularities. Such Green's functions can be computed nonperturbatively in numerical simulations, with no need to fix a gauge: thus, renormalization to this "intermediate" scheme can be carried out in a completely nonperturbative manner. Expressing renormalized operators in the $\overline{\rm MS}$ scheme requires the calculation of corresponding conversion factors. The latter can only be computed in perturbation theory, by the very nature of the $\overline{\rm MS}$; however, the computations are greatly simplified by virtue of the following attributes: i) In the absense of operator mixing, they involve only massless, two-point functions; such quantities are calculable to very high perturbative order. ii) They are gauge invariant; thus, they may be computed in a convenient gauge. iii) Where operator mixing may occur, only gauge-invariant operators will appear in the mixing pattern: Unlike other schemes, involving mixing with gauge-variant operators (which may contain ghost fields), the mixing matrices in the present scheme are greatly reduced. Still, computation of some three-point functions may not be altogether avoidable. We exemplify the procedure by computing, to lowest order, the conversion factors for fermion bilinear operators of the form $\bar\psi\Gamma\psi$ in QCD. We also employ the gauge-invariant scheme in the study of mixing between gluon and quark energy-momentum tensor operators: We compute to one loop the conversion factors relating the nonperturbative mixing matrix to the $\overline{\rm MS}$ scheme.

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M. Costa, I. Karpasitis, G. Panagopoulos, H. Panagopoulos, T. Pafitis, A. Skouroupathis, G. Spanoudes. 2021-02-01. Gauge-invariant Renormalization Scheme in QCD: Application to fermion bilinears and the energy-momentum tensor. https://doi.org/10.1103/physrevd.103.094509

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