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 mπ² and mK² obtained with an accuracy of the second order in chiral symmetry breaking. The fit of the theoretical expressions for mπ² and mK² 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.