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

(2) INFN; Anastassios Vladikas (2) ((1) Muenster U.; Fabian Joswig (1); Jochen Heitger (1); Rome2 & Rome U.; Tor Vergata)

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

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arxiv 2005.01352 v2 pith:OE6IJ6OU submitted 2020-05-04 hep-lat

Jochen Heitger (1) , Fabian Joswig (1) , Anastassios Vladikas (2) ((1) Muenster U. , (2) INFN , Rome2 & Rome U. , Tor Vergata) This is my paper · ORCID

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keywords mathrmlatticedeterminationfunctionalidentitiesmassesnon-perturbativeodinger

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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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$\mathrm{O}(a)$ improvement of the flavour singlet scalar density in a setup with Wilson fermions
hep-lat 2025-02 conditional novelty 7.0 of 10

A Ward identity analysis provides the first non-perturbative estimates of the O(a) improvement coefficient g_S for the flavour singlet scalar density in three-flavour QCD.

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