Quark masses and low energy constants in the continuum from the tadpole improved clover ensembles

TL;DR

This paper determines light-quark masses and low energy constants in continuum QCD using tadpole improved clover ensembles, providing precise values and analyzing systematic uncertainties across multiple lattice spacings and volumes.

Contribution

It presents a comprehensive calculation of quark masses and low energy constants from 2+1 flavor full-QCD ensembles with tadpole improvement, including systematic uncertainty analysis.

Findings

Quark masses: $m_u=2.45(22)(20)$ MeV, $m_d=4.74(11)(09)$ MeV, $m_s=98.8(2.9)(4.7)$ MeV.

Chiral condensate: $ eq 268.6(3.6)(0.7)$ MeV.

Pion decay constant: $F=86.6(7)(1.4)$ MeV.

Abstract

We present the light-flavor quark masses and low energy constants using the 2+1 flavor full-QCD ensembles with stout smeared clover fermion action and Symanzik gauge actions. Both the fermion and gauge actions are tadpole improved self-consistently. The simulations are performed on 11 ensembles at 3 lattice spacings $a\in[0.05,0.11]$ fm, 4 spatial sizes $L\in[2.5, 5.1]$ fm, 7 pion masses $m_{\pi}\in[135,350]$ MeV, and several values of the strange quark mass. The quark mass is defined through the partially conserved axial current (PCAC) relation and renormalized to $\overline{\mathrm{MS}}$ 2 GeV through the intermediate regularization independent momentum subtraction (RI/MOM) scheme. The systematic uncertainty of using the symmetric momentum subtraction (SMOM) scheme is also included. Eventually, we predict $m_u=2.45(22)(20)$ MeV, $m_d=4.74(11)(09)$ MeV, and $m_s=98.8(2.9)(4.7)$ MeV with the systematic uncertainties from lattice spacing determination, continuum extrapolation and renormalization constant included. We also obtain the chiral condensate $\Sigma^{1/3}=268.6(3.6)(0.7)$ MeV and the pion decay constant $F=86.6(7)(1.4) $ MeV in the $N_f=2$ chiral limit, and the next-to-leading order low energy constants $\ell_3=2.43(54)(05)$ and $\ell_4=4.322(75)(96)$.