Light quark masses and pseudoscalar decay constants from Nf=2 Lattice QCD with twisted mass fermions

TL;DR

This study determines light and strange quark masses and kaon decay constants from N_f=2 lattice QCD using twisted mass fermions at maximal twist. It analyzes the quark-mass dependence of pseudoscalar observables with PQChPT (including NNLO local terms) and polynomial fits, incorporating finite-volume corrections, and renormalizes masses non-perturbatively via RI-MOM. By matching lattice results to experimental ratios and fixing the scale with f_pi, it delivers precise values for m_ud, m_s, f_K, and f_K/f_pi, and extracts |V_us| in agreement with CKM unitarity constraints. The work underscores the impact of non-perturbative renormalization and sets the stage for continuum extrapolation through multiple lattice spacings. Overall, it provides a robust lattice determination of light-quark parameters and CKM-related quantities within an N_f=2 framework and discusses systematic uncertainties from chiral extrapolations and discretization effects.

Abstract

We present the results of a lattice QCD calculation of the average up-down and strange quark masses and of the light meson pseudoscalar decay constants with Nf=2 dynamical fermions. The simulation is carried out at a single value of the lattice spacing with the twisted mass fermionic action at maximal twist, which guarantees automatic O(a)-improvement of the physical quantities. Quark masses are renormalized by implementing the non-perturbative RI-MOM renormalization procedure. Our results for the light quark masses are m_ud^{msbar}(2 GeV)= 3.85 +- 0.12 +- 0.40 MeV, m_s^{msbar}(2 GeV) = 105 +- 3 +- 9 MeV and m_s/m_ud = 27.3 +- 0.3 +- 1.2. We also obtain fK = 161.7 +- 1.2 +- 3.1 MeV and the ratio fK/fpi=1.227 +- 0.009 +- 0.024. From this ratio, by using the experimental determination of Gamma(K-> mu nu (gamma))/Gamma(pi -> mu nu (gamma)) and the average value of |Vud| from nuclear beta decays, we obtain |Vus|=0.2192(5)(45), in agreement with the determination from Kl3 decays and the unitarity constraint.

Figures (6)

• Figure 1: Effective masses of pseudoscalar mesons, as a function of the time, in the degenerate cases $\mu_S=\mu_1=\mu_2$. Error bars are smaller than the symbol sizes.
• Figure 2: Lattice results for $a^2 M_{PS}^{\,2}$ (top), $a^2 M_{PS}^{\,2}/ \frac{1}{2}(a\mu_1+a\mu_2)$ (center) and $a f_{PS}$ (bottom) as a function of the valence quark mass $a\mu_2$, with $a\mu_1=a\mu_S$. The solid, dashed and dotted curves represent the results of the polynomial, PQChPT and C-PQChPT fits respectively. For better clarity, results at only two values of the see quark mass have been shown in the center plot.
• Figure 3: PQChPT fits of the pseudoscalar meson masses and decay constants performed with (solid lines) and without (dashed lines) including the finite volume corrections of eq. (\ref{['eq:mf12fse']}). The results are shown as a function of the valence quark mass $a\mu_2$, with $a\mu_1 = a\mu_S$.
• Figure 4: Lattice QCD determinations of the strange quark mass obtained from simulations with $N_f=2$AliKhan:2001tx-Blum:2007cy and $N_f=2+1$Aubin:2004ckMason:2005bjBernard:2006wxIshikawa:2007nn dynamical fermions. The PDG average (from lattice only) pdg is also shown for comparison.
• Figure 5: Lattice QCD determinations of the ratio $f_K/f_\pi$ obtained from simulations with $N_f=2$AliKhan:2001txAoki:2002ucAoki:2004ht and $N_f=2+1$Bernard:2006wx, Aubin:2004fs-Follana:2007uv dynamical fermions. The results are also compared with the PDG 2006 average pdg and with the average based on the updated determination of $V_{us}$ from $K_{\ell 3}$ decays isidori.