Abstract
We report on non-perturbative computations of the improvement coefficient cV and the renormalization factor ZV of the vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action. To reduce finite quark mass effects, our improvement and normalization conditions exploit massive chiral Ward identities formulated in the Schrödinger functional setup, which also allow deriving a new method to extract the ratio ZS/ZP of scalar to pseudoscalar renormalization constants. We present preliminary results of a numerical evaluation of ZV and cV along a line of constant physics with gauge couplings corresponding to lattice spacings of about 0:09 fm and below, relevant for phenomenological applications.
Highlights
A popular discretization for quark fields on the lattice are Wilson fermions
We report on non-perturbative computations of the improvement coefficient cV and the renormalization factor ZV of the vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action
To reduce finite quark mass effects, our improvement and normalization conditions exploit massive chiral Ward identities formulated in the Schrödinger functional setup, which allow deriving a new method to extract the ratio ZS/ZP of scalar to pseudoscalar renormalization constants
Summary
As a consequence of removing the unwanted doublers in the naive lattice fermion action, it exhibits leading cutoff effects of O(a) and the explicit breaking of chiral symmetry As for the former, a systematic way of resolving this is the Symanzik improvement programme, which amounts to add the so-called clover term to the action and further irrelevant operators to local composite fields, canceling their O(a) corrections, while the latter is accounted for by introducing finite renormalization constants. Potential applications of the vector current and its matrix elements include computations of semi-leptonic decay form factors and of the timelike pion form factor, as well as contributions to the anomalous magnetic moment of the muon and thermal correlators related to the di-lepton production rate in the quark-gluon plasma Another object of interest is the ratio ZS/ZP of the scalar and the pseudoscalar renormalization constants, which plays a rôle in relating renormalized PCAC and subtracted quark masses to each other. Already comply with O(a) improvement without any correction terms
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