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arXiv · 2005.01352

Ward identity determination of $Z_\mathrm{S}/Z_\mathrm{P}$ for $N_\mathrm{f}=3$ lattice QCD in a Schr\"odinger functional setup

Jochen Heitger·Fabian Joswig·Anastassios Vladikas
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Abstract

We derive chiral Ward identities for lattice QCD with Wilson quarks and $N_\mathrm{f} \geq 3$ flavours, on small lattices with Schr\"odinger functional boundary conditions and vanishingly small quark masses. These identities relate the axial variation of the non-singlet pseudoscalar density to the scalar one, thus enabling the non-perturbative determination of the scale-independent ratio $Z_\mathrm{S}/Z_\mathrm{P}$ of the renormalisation parameters of these operators. We obtain results for $N_\mathrm{f}=3$ QCD with tree-level Symanzik-improved gluons and Wilson-Clover quarks, for bare gauge couplings which cover the typical range of large-volume $N_\mathrm{f} = 2+1$ simulations with Wilson fermions at lattice spacings below $0.1\,$fm. The precision of our results varies from 0.3\% to 1\%, except for the coarsest lattice, where it is 2\%. We discuss how the $Z_\mathrm{S}/Z_\mathrm{P}$ ratio can be used in the non-perturbative calculations of $\mathrm{O}(a)$ improved renormalised quark masses.

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Jochen Heitger, Fabian Joswig, Anastassios Vladikas. 2020-05-04. Ward identity determination of $Z_\mathrm{S}/Z_\mathrm{P}$ for $N_\mathrm{f}=3$ lattice QCD in a Schr\"odinger functional setup. https://arxiv.org/abs/2005.01352

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