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.
Highlights
We examine the renormalization of flavor-diagonal vector currents in lattice QCD with the aim of understanding and quantifying the systematic errors from nonperturbative artifacts associated with the use of intermediate momentum-subtraction schemes
Lattice QCD is the method of choice for the accurate calculation of hadronic matrix elements needed for a huge range of precision particle physics phenomenology aimed at uncovering new physics
We show explicitly that this is true for the highly improved staggered quark (HISQ) action
Summary
Lattice QCD is the method of choice for the accurate calculation of hadronic matrix elements needed for a huge range of precision particle physics phenomenology aimed at uncovering new physics. Renormalization schemes for nonconserved currents that make use (not necessarily explicitly) of ratios of matrix elements for conserved and nonconserved vector currents have a special status because nonperturbative contributions from higher-dimension operators are suppressed by powers of a2 They give renormalization constants, ZV, for nonconserved lattice vector currents that are exact in the a → 0 limit. One standard exact method for renormalizing nonconserved vector currents in lattice QCD is to require (electric) charge conservation i.e., that the vector form factor between identical hadrons at zero momentum transfer should have value 1. Since this result would be obtained for the conserved current, ZV is implicitly a ratio of nonconserved to conserved current matrix elements between the two hadrons. ZxVðAÞ renormalizes the lattice vector current x (cons, loc, 1link) to match the continuum current (in e.g., MS) and has been calculated in the scheme A (F(0), SMOM, MOM)
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