Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in $N_{\mathrm{f}}=3$ QCD with Wilson quarks

Abstract

We determine non-perturbatively the normalisation factor $r_{\mathrm{m}}\equiv Z_{\mathrm{S}}/Z_{\mathrm{S}}^0$, where $Z_{\mathrm{S}}$ and $Z_{\mathrm{S}}^0$ are the renormalisation parameters of the flavour non-singlet and singlet scalar densities, respectively. This quantity is required in the computation of quark masses with Wilson fermions and for instance the renormalisation of nucleon matrix elements of scalar densities. Our calculation involves simulations of finite-volume lattice QCD with the tree-level Symanzik-improved gauge action, $N_{\mathrm{f}}=3$ mass-degenerate $\mathrm{O}(a)$ improved Wilson fermions and Schrödinger functional boundary conditions. The slope of the current quark mass, as a function of the subtracted Wilson quark mass is extracted both in a unitary setup (where nearly chiral valence and sea quark masses are degenerate) and in a non-unitary setup (where all valence flavours are chiral and the sea quark masses are small). These slopes are then combined with $Z\equiv Z_{\mathrm{P}}/(Z_{\mathrm{S}}{Z}_{\mathrm{A}})$ in order to obtain $r_{\mathrm{m}}$. A novel chiral Ward identity is employed for the calculation of the normalisation factor $Z$. Our results cover the range of gauge couplings corresponding to lattice spacings below $0.1$fm, for which $N_{\mathrm{f}}=2+1$ QCD simulations in large volumes with the same lattice action are typically performed.

28 pages, 9 figures

References in corpus (10)

• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Critical slowing down and error analysis in lattice QCD simulations
• Accelerating Dynamical Fermion Computations using the Rational Hybrid Monte Carlo (RHMC) Algorithm with Multiple Pseudofermion Fields
• Non-perturbative improvement of quark mass renormalization in two-flavour lattice QCD
• Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
• Nonperturbative Renormalization in Lattice QCD with three Flavors of Clover Fermions: Using Periodic and Open Boundary Conditions
• Light quark masses in N_f = 2+1 lattice QCD with Wilson fermions
• Excited states in nucleon structure calculations
• Determination of the charm quark mass in lattice QCD with $2+1$ flavours on fine lattices
• The renormalised $\mathrm{O}(a)$ improved vector current in three-flavour lattice QCD with Wilson quarks

Cited by in corpus (3)

• Window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD
• pyerrors: a python framework for error analysis of Monte Carlo data
• Scale setting and the light baryon spectrum in $N_f=2+1$ QCD with Wilson fermions