Improved light quark masses from pseudoscalar sum rules

Understand

Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point \mu in addition to the ones of the usual tau spectral sum rule variable and continuum threshold t_c, we extract the \pi(1300) and K(1460) decay constants to order \alpha_s^4 of perturbative QCD by including power corrections up to dimension-six condensates, tachyonic gluon mass, instanton and finite width corrections.

• Using these inputs with enlarged generous errors, we extract, in a model-independent and conservative ways, the sum of the scale-independent renormalization group invariant (RGI) quark masses (m_u+ m_q):q\equiv d,s and the corresponding running masses (m_u+m_q) evaluated at 2 GeV.
• By giving the value of the ratio m_u/m_d, we deduce the running quark masses m_{u,d,s} and condensate <\bar uu> and the scale-independent mass ratios : 2m_s/(m_u+m_d) and m_s/m_d.
• Using the positivity of the QCD continuum contribution to the spectral function, we also deduce, from the inverse Laplace transform sum rules, for the first time to order \alpha_s^4, new lower bounds on the RGI masses which are translated into the running masses at 2 GeV and into upper bounds on the running quark condensate <\bar uu>.