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

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 $\overline{\mathrm{MS}}$ scheme requires the calculation of corresponding conversion factors. The latter can only be computed in perturbation theory, by the very nature of the $\overline{\mathrm{MS}}$; 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 $\overline{\mathrm{MS}}$ scheme.

22 pages, 9 figures, 3 tables

References in corpus (11)

• The anomalous magnetic moment of the muon in the Standard Model
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass
• Five-loop renormalisation of QCD in covariant gauges
• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• Massless correlators of vector, scalar and tensor currents in position space at orders alpha_s^3 and alpha_s^4: explicit analytical results
• Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action
• Free Energy and Plaquette expectation value for gluons on the lattice, in three dimensions
• The Lattice Free Energy of QCD with Clover Fermions, up to Three-Loops
• Two-loop renormalization and mixing of gluon and quark energy-momentum tensor operators
• Non-perturbative running of renormalization constants from correlators in coordinate space using step scaling

Cited by in corpus (7)

• Gravitational form factors of the proton from lattice QCD
• Gauge Invariant Description of the $SU(2)$ Higgs model: Ward identities and Renormalization
• Gauge-invariant Renormalization of the Gluino-Glue operator
• Perturbative renormalization of the supercurrent operator in lattice $\mathcal{N}=1$ supersymmetric Yang-Mills theory
• Two-loop renormalization and mixing of gluon and quark energy-momentum tensor operators
• Nonperturbative renormalization of the supercurrent in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory
• Supercurrent Renormalization in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory