Non-perturbative determination of improvement $b$-coefficients in $N_f=3$

TL;DR

This paper reports preliminary non-perturbative calculations of improvement coefficients and renormalization ratios in lattice QCD with three dynamical flavors, using finite-volume Schrödinger functional methods.

Contribution

It extends previous methods to determine improvement coefficients and renormalization ratios non-perturbatively for $N_f=3$ lattice QCD.

Findings

Determined $b_A - b_P$, $b_m$, and $Z_P Z_m / Z_A$ ratios.

Used Schrödinger functional boundary conditions with improved Wilson fermions.

Results relevant for lattice spacings around 0.09 fm and below.

Abstract

We present our preliminary results of the non-perturbative determination of the valence mass dependent coefficients $b_\mathrm{A}-b_\mathrm{P}$ and $b_\mathrm{m}$ as well as the ratio $Z_\mathrm{P} Z_\mathrm{m}/ Z_\mathrm{A}$ entering the flavour non-singlet PCAC relation in lattice QCD with $N_f=3$ dynamical flavours. We apply the method proposed in the past for quenched approximation and $N_f=2$ cases, employing a set of finite-volume ALPHA configurations with Schr\"odinger functional boundary conditions, generated with $O(a)$ improved Wilson fermions and the tree-level Symanzik-improved gauge action for a range of couplings relevant for simulations at lattice spacings of about $0.09 \,$fm and below.