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

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 ${\ell }_4=4.322(75)(96)$.

Comments: Version accepted by PRD. 7 pages, 4 figures, with more details in the appendix