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arXiv · 2010.09539

The renormalised $\mathrm{O}(a)$ improved vector current in three-flavour lattice QCD with Wilson quarks

Jochen Heitger·Fabian Joswig
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Abstract

We present the results of a non-perturbative determination of the improvement coefficient $c_\mathrm{V}$ and the renormalisation factor $Z_\mathrm{V}$, which define the renormalised vector current in three-flavour $\mathrm{O}(a)$ improved lattice QCD with Wilson quarks and tree-level Symanzik-improved gauge action. In case of the improvement coefficient, we consider both lattice descriptions of the vector current, the local as well as the conserved (i.e., point-split) one. Our improvement and normalisation conditions are based on massive chiral Ward identities and numerically evaluated in the Schrödinger functional setup, which allows to eliminate finite quark mass effects in a controlled way. In order to ensure a smooth dependence of the renormalisation constant and improvement coefficients on the bare gauge coupling, our computation proceeds along a line of constant physics, covering the typical range of lattice spacings $0.04\,\mathrm{fm}\lesssim a\lesssim 0.1\,\mathrm{fm}$ that is useful for phenomenological applications. Especially for the improvement coefficient of the local vector current, we report significant differences between the one-loop perturbative estimates and our non-perturbative results.

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Jochen Heitger, Fabian Joswig. 2020-10-19. The renormalised $\mathrm{O}(a)$ improved vector current in three-flavour lattice QCD with Wilson quarks. https://doi.org/10.1140/epjc%2Fs10052-021-09037-4

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