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The bounds on the light quark masses are obtained by fitting the squares of pseudoscalar meson masses m_² and mK² to second order in 1/Nc expansion. The result is an algebraic cubic curve whose coefficients are the known Weinberg values for the quark mass ratios mᵤ/md and mₛ/md. Additional restrictions arise when using the ratio mₛ/mₔ₃=27. 23 (10) quoted by FLAG for lattice simulations with four quark flavors. This provides a tight constraint on the ratio mᵤ/md = 0. 455 (8).
A. A. Osipov (Sun,) studied this question.