Masses of the u, d, and s Quarks

Ratios m_s/m_d and m_u/m_d 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 m_s/m_d and m_u/m_d, which is described by a third-order curve. The application of the lattice calculation result m_s/m_ud = 27.23(10), where m_ud = (m_u + m_d)/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 m_u/m_d = 0.455(8). The absolute values of the quark masses have been then obtained.