Non-perturbatively renormalised light quark masses from a lattice simulation with N_f=2

TL;DR

This study determines light quark masses using lattice QCD with N_f=2 dynamical Wilson fermions and non-perturbative RI-MOM renormalisation, converting results to the MSbar scheme at 2 GeV. The authors quantify the mass renormalisation non-perturbatively and show it yields larger quark masses than one-loop perturbative estimates, with m_ud and m_s in the few MeV and ~100 MeV ranges, respectively. They find no strong evidence for dynamical-quark effects at the sea masses explored, though discretisation dominates systematic errors and finite-volume effects are controlled. The work underscores the importance of NPR for accurate quark masses and sets the stage for future studies with lighter sea quarks and a continuum extrapolation.

Abstract

We present results for the light quark masses obtained from a lattice QCD simulation with N_f=2 degenerate Wilson dynamical quark flavours. The sea quark masses of our lattice, of spacing a ~ 0.06 fm, are relatively heavy, i.e., they cover the range corresponding to 0.60 <~ M_P/M_V <~ 0.75. After implementing the non-perturbative RI-MOM method to renormalise quark masses, we obtain m_{ud}^{MS}(2 GeV)=4.3 +- 0.4^{+1.1}_{-0} MeV, and m_s^{MS}(2 GeV)=101 +- 8^{+25}_{-0} MeV, which are about 15% larger than they would be if renormalised perturbatively. In addition, we show that the above results are compatible with those obtained in a quenched simulation with a similar lattice.

Figures (5)

• Figure 1: Autocorrelations of the plaquette $C^p(t)$ (left), and of the pseudoscalar correlation function $C^{PS}(t)$ (right), as a function of the number of trajectories $t$ used to separate consecutive configurations. For $C^{PS}(t)$ the fluctuations around zero start at about $t = 30$, indicating that configurations separated by less than $30$ trajectories are correlated. The above plots refer to the run at $\beta=5.8$ ($V=24^3 \times 48$, and $\kappa_s = 0.1538$).
• Figure 2: Data-points that illustrate the functional dependencies discussed in eqs. (\ref{['eq:mvvsmp']}) and (\ref{['eq:mp2vsk']}).
• Figure 3: Renormalisation constants in the $\hbox{RI-MOM}$ scheme at the scale $a\mu_0=1$, computed according to eq. (\ref{['eq:zmu0']}), as a function of the initial renormalisation scale $(a \mu)^2$. Discretisation effects $\propto (a \mu)^2$ are eliminated by extrapolating the data from $1\leq (a\mu)^2\leq 2$, to $(a \mu)^2=0$. Illustration is provided for the data with $\kappa_s=0.1538$.
• Figure 4: Dependence of the pseudoscalar meson masses on the valence quark masses $m_v^{AWI}$ (left) and of the ratios $(M_P^2-C_0)/m_v^{AWI}$ (cf. eq. (\ref{['eq:mp2vsaro']})) on the sea quark masses $m_s^{AWI}$. The results refer to the case of the partially quenched simulations at $\beta=5.8$.
• Figure 6: Static quark potential obtained from the simulation with $N_f=2$ at $\beta=5.8$ on the lattice $24^3\times 48$.