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 ($\sim2\%$) for the ratio $m_u/m_d = 0.455(8)$. The absolute values of the quark masses have been then obtained.