Non-perturbative determination of improvement coefficients $$b_\mathrm{m}$$ and $$b_\mathrm{A}-b_\mathrm{P}$$ and normalisation factor $$Z_\mathrm{m}Z_\mathrm{P}/Z_\mathrm{A}$$ with $$N_\mathrm{f}= 3$$ Wilson fermions

Abstract

We determine non-perturbatively the normalisation parameter Z m Z P /Z A as well as the Symanzik coefficients b m and b A − b P , required in O(a) improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in N f = 3 QCD with O(a) improved massless sea and non-degenerate valence quarks in the finite-volume Schrödinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume N f = 2+1 QCD simulations with Wilson fermions at lattice spacings below 0.1 fm, are of particular use for the non-perturbative calculation of O(a) improved renormalised quark masses.

Light quark masses in $${N_\mathrm{f}=2+1}$$ lattice QCD with Wilson fermions

“…In ref. [22], results are quoted for two values of constant Physics, dubbed LCP-0 and LPC-1. In LCP-0, R AP and R Z are obtained with all masses in the chiral limit.…”

“…The covariance matrices of the fit parameters of R AP as well as those of R Z are provided in ref. [22]. We assume that the covariance matrix between fit parameters of R AP and R Z is nil.…”

$Z_\mathrm{S}/Z_\mathrm{P}$ from three-flavour lattice QCD

“…We are currently examining its effects along the lines described above. As a final crosscheck we will be able to compare our results with the ongoing determination of Z = Z P /(Z S Z A ), reported in [21,22], combining it with the axial vector renormalization constant.…”

Light and strange quark masses for $N_f = 2 + 1$ simulations with Wilson fermions

“…The coefficient (b A −b P ) is known in 1-loop perturbation theory and has the value (b A −b P ) = −0.0012g 2 0 . However, we use a preliminary value from a non-perturbative determination from the ALPHA Collaboration [14]:…”