Renormalization group improved determination of light quark masses from Borel-Laplace sum rules

Abstract

We determine masses of light quarks ($m_u$,$m_d$,$m_s$) using Borel-Laplace sum rules and renormalization group summed perturbation theory (RGSPT) from the divergence of the axial vector current. The RGSPT significantly reduces the scale dependence of the finite order perturbative series for the renormalization group (RG) invariant quantities such as spectral function, the second derivative of the polarization function of the pseudoscalar current correlator, and its Borel transformation. In addition, the convergence of the spectral function is significantly improved by summing all running logarithms and kinematical $\pi^2$-terms. Using RGSPT, we find $m_s(2 GeV)=104.34_{-4.21}^{+4.23}\hs\MeV$, and $m_d(2 GeV)=4.21_{-0.45}^{+0.48}\hs\MeV$ leading to $m_u(2 GeV)=2.00_{-0.40}^{+0.33}\hs\MeV$.