Estimating the Unquenched Strange Quark Mass from the Lattice Axial Ward Identity

TL;DR

This work determines the unquenched strange-quark mass in nf=2 QCD using the axial Ward identity with non-perturbative renormalisation on O(a) improved Wilson fermions. By computing the RI'-MOM renormalisation constants and constructing a renormalisation-group-invariant mass, then converting to the MSbar scheme at 2 GeV and performing continuum extrapolations, the authors obtain $m_s^{\overline{MS}}(2\,\mathrm{GeV})$ in the range $111$–$117$ MeV depending on the $r_0$ scale, with a ~5% NLO chiral perturbation theory correction. They also extract the light quark mass $m_{ud}^{\overline{MS}}(2\,\mathrm{GeV})$ and the chiral condensate, finding results in good agreement with phenomenology and other lattice studies, and demonstrate consistency between AWI and VWI approaches in the continuum limit. The study highlights the importance of non-perturbative renormalisation and careful scale setting (via $r_0$) for precise quark-mass determinations in dynamical fermion simulations. These findings contribute to a coherent picture of light and strange quark masses and reinforce the reliability of AWI-based determinations in lattice QCD.

Abstract

We present a determination of the strange quark mass for two flavours (nf=2) of light dynamical quarks using the axial Ward identity. The calculations are performed on the lattice using O(a) improved Wilson fermions and include a fully non-perturbative determination of the renormalisation constant. In the continuum limit we find in the MSbar scheme at 2GeV, ms = 111(6)(4)(6)MeV using the force scale r0 = 0.467fm, where the first error is statistical, the second and third are systematic due to the fit and scale uncertainties respectively. Results are also presented for the light quark mass and the chiral condensate. The corresponding results are also given for r0=0.5fm.

Figures (13)

• Figure 1: One-, two-, three- and four-loop results for $[\Delta Z_m^{\hbox{\tiny $\overline{MS}$}}(\mu)]^{-1}$ in units of $\Lambda^{\hbox{\tiny $\overline{MS}$}}$.
• Figure 2: $[\Delta Z_m^{\hbox{\tiny $R\! I^\prime\!\!-\!\! M\! O\! M$}}(\mu_p)]^{-1}$ versus $\mu_p/\Lambda^{\hbox{\tiny $\overline{MS}$}}$.
• Figure 3: $A_P$ and $B_P$ for $Z_P^{\hbox{\tiny $R\! I^\prime\!\!-\!\! M\! O\! M$}}$ for $\beta = 5.20$, and $\beta = 5.40$.
• Figure 4: $Z_{\tilde{m}}^{\hbox{\tiny $R\! G\! I$}}$ for $\beta = 5.20$ (filled circles), $\beta = 5.25$ (filled squares), $\beta = 5.29$ (filled upper triangles), $\beta = 5.40$ (filled lower triangles) together with fits as in eq. (\ref{['Zmfit']}).
• Figure 5: $Z^{\hbox{\tiny $R\! G\! I$}}_{\tilde{m}}$ versus $\beta$. The black circles are the results from Table \ref{['table_Zmrgi']}, while the open squares are the TRG-PT results from Table \ref{['table_Zmrgi_trbpt']}. Furthermore the open diamonds and triangles are the NP results from dellamorte05a, using the two different results for the axial renormalisation constant, dellamorte05c. (The empty triangle results has been slightly displaced for clarity.)