Masses of the u, d, and s Quarks

Abstract

Ratios ms/md and mu/md of the light quark masses have been determined from expressions for squared masses of pseudoscalar mesons $$m_{\pi }^{2}$$ and $$m_{K}^{2}$$ obtained with an accuracy of the second order in chiral symmetry breaking. The fit of the theoretical expressions for $$m_{\pi }^{2}$$ and $$m_{K}^{2}$$ to their phenomenological values leads to a functional relation between the ratios ms/md and mu/md, which is described by a third-order curve. The application of the lattice calculation result ms/mud = 27.23(10), where mud = (mu + md)/2, reported by the flavor lattice averaging group (FLAG) for the case of four quark flavors provides an additional constraint, which significantly reduces the error (~2%) for the ratio mu/md = 0.455(8). The absolute values of the quark masses have been then obtained.