Average up/down, strange and charm quark masses with Nf=2 twisted mass lattice QCD

TL;DR

The paper tackles precise determination of the light, strange, and charm quark masses using $N_f=2$ twisted mass lattice QCD with four lattice spacings and pion masses down to $M_\ {pi}\approx 270$ MeV. It employs non-perturbative RI-MOM renormalization and multiple meson inputs ($K$, $\eta_s$, $D$, $D_s$, $\eta_c$) to extract $\overline{m}_{ud}$, $\overline{m}_s$, and $\overline{m}_c$ in the $\overline{\rm{MS}}$ scheme, performing controlled chiral and continuum extrapolations and accounting for finite-size effects. The main results are $\overline{m}_{ud}(2{\rm GeV}) = 3.6(2)$ MeV, $\overline{m}_s(2{\rm GeV}) = 95(6)$ MeV, and $\overline{m}_c(\overline{m}_c) = 1.28(4)$ GeV, with ratio tests $m_s/m_{ud} = 27.3(9)$ and $m_c/m_s = 12.0(3)$. The work demonstrates robust lattice control over discretization and chiral uncertainties, while noting the absence of strange and charm sea-quark vacuum polarization effects as a systematic limitation and pointing to future $N_f=2+1+1$ simulations for comprehensive coverage.

Abstract

We present a high precision lattice calculation of the average up/down, strange and charm quark masses performed with Nf=2 twisted mass Wilson fermions. The analysis includes data at four values of the lattice spacing and pion masses as low as ~270 MeV, allowing for accurate continuum limit and chiral extrapolation. The strange and charm masses are extracted by using several methods, based on different observables: the kaon and the eta_s meson for the strange quark and the D, D_s and eta_c mesons for the charm. The quark mass renormalization is carried out non-perturbatively using the RI-MOM method. The results for the quark masses in the MSbar scheme read: m_ud(2 GeV)= 3.6(2) MeV, m_s(2 GeV)=95(6) MeV and m_c(m_c)=1.28(4) GeV. We also obtain the ratios m_s/m_ud=27.3(9) and m_c/m_s=12.0(3).

Figures (6)

• Figure 1: Left: Dependence of $r_0\,m_\pi^2/{\bar{m}}_l$ on the renormalized light quark mass at the four lattice spacings. Right: Dependence of $(r_0\,m_\pi)^2$ on the squared lattice spacing, for a fixed reference light quark mass ($\overline{m}_{ud}^{ref}=50\,{\rm~MeV}$). Empty diamonds represent continuum limit results.
• Figure 2: Left: Dependence of $m_K^2$ and $m_{\eta_s}^2$ on the renormalized light quark mass, for a fixed reference strange quark mass ($\overline{m}_s^{ref}=95\,{\rm~MeV}$) and at the four lattice spacings. The orange vertical line corresponds to the physical up/down mass. Right: Dependence of $m_K^2$ and $m_{\eta_s}^2$ on the squared lattice spacing, for a fixed reference strange quark mass ($\overline{m}_s^{ref}=95\,{\rm~MeV}$) and at the physical up/down mass. Empty diamonds represent continuum limit results.
• Figure 3: Dependence of $m_K^2$ and $m_{\eta_s}^2$, in the continuum limit and at the physical up/down mass, on the strange quark mass. The strange mass results obtained from the SU(2)-ChPT analyses of kaon and $\eta_s$ mesons are also shown, with empty diamonds.
• Figure 4: Left: Dependence of $m_D$ (left) and $m_{D_s}$ and $m_{\eta_c}$ (right) on the light quark mass, at fixed reference charm quark mass ($\overline{m}_c^{ref}=1.16\,{\rm~GeV}$) and for the four simulated lattice spacings. For the $D_s$ meson the strange quark mass is fixed to the reference value $\overline{m}_s^{ref}=95 \,{\rm~MeV}$.
• Figure 5: Left: Dependence of $m_D$, $m_{D_s}$ and $m_{\eta_c}$, at fixed reference charm quark mass ($\overline{m}_c^{ref}=1.16\,{\rm~GeV}$) and at physical up/down and strange quark mass, on the squared lattice spacing. Empty diamonds represent continuum limit results. Right: Dependence of $m_D$, $m_{D_s}$ and $m_{\eta_c}$, in the continuum limit and at physical up/down and strange quarks, on the charm quark mass. The charm mass results from the three determinations are also shown, with empty diamonds.