Renormalising vector currents in lattice QCD using momentum-subtraction schemes

Abstract

We examine the renormalisation of flavour-diagonal vector currents in lattice QCD with the aim of understanding and quantifying the systematic errors from nonperturbative artefacts associated with the use of intermediate momentum-subtraction schemes. Our study uses the Highly Improved Staggered Quark (HISQ) action on gluon field configurations that include $n_f=2+1+1$ flavours of sea quarks, but our results have applicability to other quark actions. Renormalisation schemes that make use of the exact lattice vector Ward-Takahashi identity for the conserved current also have renormalisation factors, $Z_V$, for nonconserved vector currents that are free of contamination by nonperturbative condensates. We show this by explicit comparison of two such schemes: that of the vector form factor at zero momentum transfer and the RI-SMOM momentum-subtraction scheme. The two determinations of $Z_V$ differ only by discretisation effects (for any value of momentum-transfer in the RI-SMOM case). The RI${}^{\prime }$-MOM scheme, although widely used, does not share this property. We show that $Z_V$ determined in the standard way in this scheme has $\mathcal{O}(1\%)$ nonperturbative contamination that limits its accuracy. Instead we define an RI${}^{\prime }$-MOM $Z_V$ from a ratio of local to conserved vector current vertex functions and show that this $Z_V$ is a safe one to use in lattice QCD calculations. We also perform a first study of vector current renormalisation with the inclusion of quenched QED effects on the lattice using the RI-SMOM scheme.

arXiv commentMinor changes to the text and references added. Version accepted by Phys. Rev. D

References in corpus (38)

• On the Viability of Lattice Perturbation Theory
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• High-precision scale setting in lattice QCD
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• High Precision determination of the pi, K, D and D_s decay constants from lattice QCD
• Constrained Curve Fitting
• Renormalization and Running of Quark Mass and Field in the Regularization Invariant and MS-bar Schemes at Three and Four Loops
• Scaling studies of QCD with the dynamical HISQ action
• Renormalization of quark bilinear operators in a momentum-subtraction scheme with a nonexceptional subtraction point
• Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks
• Electromagnetic Splittings and Light Quark Masses in Lattice QCD
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• Nonperturbative Renormalisation of Composite Operators in Lattice QCD
• QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons
• Precision tests of the J/ψ from full lattice QCD: mass, leptonic width and radiative decay rate to η_c
• Electromagnetic and strong isospin-breaking corrections to the muon $g-2$ from Lattice QCD+QED
• Hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment from four-flavor lattice QCD
• Non-perturbative renormalization of quark bilinear operators with Nf=2 (tmQCD) Wilson fermions and the tree-level improved gauge action
• Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
• High-precision determination of the light-quark masses from realistic lattice QCD
• Strange and charm quark contributions to the anomalous magnetic moment of the muon
• Lattice study of semileptonic form factors with twisted boundary conditions
• Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
• Step Scaling with off-shell renormalisation
• Prediction of the $D_s^{\ast }$ width from a calculation of its radiative decay in full lattice QCD
• Perturbative Corrections for Staggered Four-Fermion Operators
• Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study
• V_cs from D_s to ϕlν semileptonic decay and full lattice QCD
• Determination of quark masses from ${\mathbf{n}}_{\mathbf{f}}=4$ lattice QCD and the RI-SMOM intermediate scheme
• Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions
• Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action
• Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three
• Nonperturbative comparison of clover and HISQ quarks in lattice QCD and the properties of the phi meson
• One loop calculation of the renormalised anisotropy for improved anisotropic gluon actions on a lattice
• Non-perturbative Renormalization for Improved Staggered Bilinears
• Perturbation theory vs. simulation for tadpole improvement factors in pure gauge theories
• Renormalization factors of quark bilinears using the DCI operator with dynamical quarks

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