Non-perturbative O(a)-improvement of Wilson quark action in three-flavor QCD with plaquette gauge action

TL;DR

This paper non-perturbatively determines the O(a)-improvement coefficient c_SW for Wilson quarks in three-flavor QCD, providing formulas to improve lattice QCD simulations across a range of couplings.

Contribution

It presents the first non-perturbative determination of c_SW and K_c in three-flavor QCD with the plaquette gauge action, including an interpolation formula for practical use.

Findings

Derived an interpolation formula for c_SW and K_c as functions of the bare coupling.

Found finite volume effects on c_SW are not significant on the studied lattice.

Explored N_f dependence of c_SW through additional simulations for different flavors.

Abstract

We perform a non-perturbative determination of the O(a)-improvement coefficient c_SW for the Wilson quark action in three-flavor QCD with the plaquette gauge action. Numerical simulations are carried out in a range of \beta=12.0-5.2 on a single lattice size of 8^3x16 employing the Schr\"odinger functional setup of lattice QCD. As our main result, we obtain an interpolation formula for c_SW and the critical hopping parameter K_c as a function of the bare coupling. This enables us to remove O(a) scaling violation from physical observables in future numerical simulation in the wide range of \beta. Our analysis with a perturbatively modified improvement condition for c_SW suggests that finite volume effects in c_SW are not large on the 8^3x16 lattice. We investigate N_f dependence of c_SW by additional simulations for N_f=4, 2 and 0 at \beta=9.6. As a preparatory step for this study, we also determine c_SW in two-flavor QCD at \beta=5.2. At this \beta, several groups carried out large-scale calculations of the hadron spectrum, while no systematic determination of c_SW has been performed.