Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice

Abstract

We compute the two-loop renormalization functions, in the RI ${}^{\prime }$ scheme, of local bilinear quark operators $\bar{\psi }\Gamma \psi$, where $\Gamma$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, $Z_m$. As a prerequisite for the above, we also compute the quark field renormalization, $Z_{\psi }$, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge. Finally, we present our results in the $\overline{MS}$ scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, are included in an Appendix.

30 pages, 15 figures. Correction of a minor mistake in the 2-loop result for $Z_S$ and $Z_P$. The mistake affects (very slightly) Eqs.(51-54); the change in numerical values is too small to alter the ensuing plots. All conclusions remain unchanged

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• Volume independence in large Nc QCD-like gauge theories
• Non-perturbative quark mass renormalization in two-flavor QCD
• Three loop anomalous dimension of non-singlet quark currents in the RI' scheme
• High-precision determination of the light-quark masses from realistic lattice QCD
• Proton decay matrix elements with domain-wall fermions
• Scaling and Goldstone effects in a QCD with two flavours of adjoint quarks
• Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action
• Non-perturbative renormalization of the static axial current in two-flavour QCD
• Exploring twisted mass Lattice QCD with the Clover term
• Free Energy and Plaquette expectation value for gluons on the lattice, in three dimensions
• Hadron spectrum, quark masses and decay constants from light overlap fermions on large lattices
• Nonperturbative renormalization of composite operators with overlap fermions
• Adjoint modes as probes of gauge field structure
• Non-perturbative QCD: renormalization, O(a)-improvement and matching to Heavy Quark Effective Theory
• Gluino zero-modes for non-trivial holonomy calorons

Cited by in corpus (22)

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• Perturbative and Nonperturbative Renormalization in Lattice QCD
• Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice
• O(a^2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons
• Renormalization constants of local operators for Wilson type improved fermions
• Thermal quarkonium physics in the pseudoscalar channel
• One-loop renormalization of staple-shaped operators in continuum and lattice regularizations
• η and η' mesons from Nf=2+1+1 twisted mass lattice QCD
• Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action
• Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
• Supersymmetric QCD on the Lattice: An Exploratory Study
• Supersymmetric QCD: Renormalization and Mixing of Composite Operators
• Perturbative renormalization functions of local operators for staggered fermions with stout improvement
• Two-loop additive mass renormalization with clover fermions and Symanzik improved gluons
• High-loop perturbative renormalization constants for Lattice QCD (II): three-loop quark currents for tree-level Symanzik improved gauge action and n_f=2 Wilson fermions
• Higher loop renormalization of fermion bilinear operators
• Renormalization of Flavor Singlet and Nonsinglet Fermion Bilinear Operators
• Two-loop renormalization of fermion bilinear operators on the lattice
• Three-loop QCD Mass Relation between the $\overline{\mathrm{MS}}$ and Symmetric-momentum Subtraction Scheme Away from the Chiral Limit
• Meson masses and decay constants at large $N$
• O(a^2) corrections to the propagator and bilinears of Wilson / clover fermions