6533b7d0fe1ef96bd125a160

RESEARCH PRODUCT

Nonperturbative renormalization and O(a) -improvement of the nonsinglet vector current with Nf=2+1 Wilson fermions and tree-level Symanzik improved gauge action

Harvey B. MeyerTim HarrisAntoine Gérardin

subject

QuarkPhysicsQuantum chromodynamics010308 nuclear & particles physicsHigh Energy Physics::LatticeHigh Energy Physics::PhenomenologyLattice field theoryLattice QCDFermionMass matrix01 natural sciencesRenormalizationLattice (order)0103 physical sciences010306 general physicsMathematical physics

description

In calculating hadronic contributions to precision observables for tests of the Standard Model in lattice QCD, the electromagnetic current plays a central role. Using a Wilson action with $\mathrm{O}(a)$ improvement in QCD with ${N}_{\mathrm{f}}$ flavors, a counterterm must be added to the vector current in order for its on-shell matrix elements to be $\mathrm{O}(a)$ improved. In addition, the local vector current, which has support on one lattice site, must be renormalized. At $\mathrm{O}(a)$, the breaking of the $\mathrm{SU}({N}_{\mathrm{f}})$ symmetry by the quark mass matrix leads to a mixing between the local currents of different quark flavors. We present a nonperturbative calculation of all the required improvement and renormalization constants needed for the local and the conserved electromagnetic current in QCD with ${N}_{\mathrm{f}}=2+1$ $\mathrm{O}(a)$-improved Wilson fermions and tree-level Symanzik improved gauge action, with the exception of one coefficient, which we show to be order ${g}_{0}^{6}$ in lattice perturbation theory. The method is based on the vector and axial Ward identities imposed at finite lattice spacing and in the chiral limit. We make use of lattice ensembles generated as part of the coordinated lattice simulations initiative.

https://doi.org/10.1103/physrevd.99.014519