O(a^2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons

Abstract

We calculate corrections to the fermion propagator and to the Green's functions of all fermion bilinear operators of the form $\bar{\Psi }\Gamma \Psi$, to one-loop in perturbation theory. We employ the Wilson/clover action for fermions and a family of Symanzik improved actions for gluons. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, $O(a^2)$. Consequently, they have addressed a number of new issues, most notably the appearance of loop integrands with strong IR divergences (convergent only beyond 6 dimensions). Such integrands are not present in $O(a^1)$ improvement calculations; there, IR divergent terms are seen to have the same structure as in the $O(a^0)$ case, by virtue of parity under integration, and they can thus be handled by well-known techniques. We explain how to correctly extract the full $O(a^2)$ dependence; in fact, our method is generalizable to any order in $a$. The $O(a^2)$ corrections to the quark propagator and Green's functions computed in this paper are useful to improve the nonperturbative RI-MOM determination of renormalization constants for quark bilinear operators. Our results depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible to the reader, we have included them in the distribution package of this paper, as an ASCII file named: Oa2results.m ; the file is best perused as Mathematica input.

37 pages, 3 figures, 27 tables. Results are also presented online, in a Mathematica input file. Version 2 (to appear in JHEP): Added a comment regarding Fig.3, corrected typo on Eq.A3

References in corpus (4)

• Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice
• High-loop perturbative renormalization constants for Lattice QCD (I): finite constants for Wilson quark currents
• Perturbative renormalization in parton distribution functions using Overlap fermions and Symanzik improved gluons
• Renormalization constants for Lattice QCD: new results from Numerical Stochastic Perturbation Theory

Cited by in corpus (48)

• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD
• Perturbative Renormalization of quasi-PDFs
• Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass
• QED Corrections to Hadronic Processes in Lattice QCD
• Nucleon form factors and moments of generalized parton distributions using $N_f=2+1+1$ twisted mass fermions
• Non-perturbative renormalization of quark bilinear operators with Nf=2 (tmQCD) Wilson fermions and the tree-level improved gauge action
• Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass
• Nucleon axial, tensor and scalar charges and $\sigma$-terms in lattice QCD
• Nucleon axial form factors using lattice QCD simulations with a physical value of the pion mass
• Valence parton distribution of pion from lattice QCD: Approaching continuum
• Nucleon isovector structure functions in (2+1)-flavor QCD with domain wall fermions
• ΔS=2 and ΔC=2 bag parameters in the SM and beyond from Nf=2+1+1 twisted-mass LQCD
• Magnetic susceptibility of QCD at zero and at finite temperature from the lattice
• First Physics Results at the Physical Pion Mass from $N_f=2$ Wilson Twisted Mass Fermions at Maximal Twist
• Perturbative and Nonperturbative Renormalization in Lattice QCD
• Moments of nucleon generalized parton distributions from lattice QCD
• Renormalization functions for Nf=2 and Nf=4 Twisted Mass fermions
• Matrix elements of the electromagnetic operator between kaon and pion states
• Quark propagator with two flavors of O(a)-improved Wilson fermions
• Renormalization constants of local operators for Wilson type improved fermions
• Renormalization constants for 2-twist operators in twisted mass QCD
• BK-parameter from Nf = 2 twisted mass lattice QCD
• Renormalization of local quark-bilinear operators for Nf=3 flavors of SLiNC fermions
• Neutron electric dipole moment using $N_f=2+1+1$ twisted mass fermions
• Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action
• Renormalisation of quark propagators from twisted-mass lattice QCD at $N_f$=2
• Quark mass and chiral condensate from the Wilson twisted mass lattice quark propagator
• The scalar, vector and tensor form factors for the pion and kaon from lattice QCD
• Kaon Mixing Beyond the SM from Nf=2 tmQCD and model independent constraints from the UTA
• Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions
• Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD
• The chromomagnetic operator on the lattice
• K -> pi matrix elements of the chromagnetic operator on the lattice
• Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory. (II) The gluon propagator in Landau gauge
• Nonperturbative renormalization of asymmetric staple-shaped operators in twisted mass lattice QCD
• Perturbative renormalization factors and O(a^2) corrections for lattice 4-fermion operators with improved fermion/gluon actions
• Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory. (I) The ghost propagator in Landau gauge
• Perturbative renormalization functions of local operators for staggered fermions with stout improvement
• Improved renormalization scheme for nonlocal operators
• Perturbative renormalization of the supercurrent operator in lattice $\mathcal{N}=1$ supersymmetric Yang-Mills theory
• High-loop perturbative renormalization constants for Lattice QCD (III): three-loop quark currents for Iwasaki gauge action and n_f=4 Wilson fermions
• Restoring rotational invariance for lattice QCD propagators
• Perturbatively improving RI-MOM renormalization constants
• Non-perturbative renormalization in lattice QCD
• Nonperturbative renormalization of the supercurrent in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory
• Perturbative renormalization of GPDs to O(a^2), for various fermion/gluon actions
• The Beauty of Lattice Perturbation Theory: The Role of Lattice Perturbation Theory in B Physics