Bounds on the Light Quark Masses: the scalar channel revisited

Abstract

We evaluate lower bounds on the sum of the up and down quark masses. The bounds follow from the constraints provided by the dispersion relation obeyed by the two--point function of the scalar current density when combined with properties of the scalar spectral function at long--distances and perturbative QCD at short--distances. Our results point to values of $m_u+m_d$ somewhat higher than those reported recently in the literature using lattice QCD simulations.

Comments: 7 pages, 3figures. A few sentences have been added to improve clarity. One reference added. To be published in PLB