Abstract
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. With these inputs, we extract, in a model-independent way, the sum of the renormalization group invariant (RGI) quark masses (\hat m_u+\hat m_q):q= 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 the scale-independent mass ratios : 2m_s/(m_u+m_d) and m_s/m_d. Using the positivity of the spectral function, we also deduce new lower bounds on these running masses from the inverse Laplace transform sum rules. Our results are summarized in Table 2.