Light Quark Masses in the Theory with the Dynamical Breaking of Chiral Symmetry

Abstract

Mass formulas and decay constants of pseudoscalar π and K mesons have been obtained in the theory with four-quark interactions. To calculate the quark determinant, a Volterra series, which makes it possible to take into account the inequality of the constituent quark masses {{M}_{u}} ne {{M}_{d}} ne {{M}_{s}} in the expansion of the effective action in the powers of 1/M2, has been used for the first time. It is additionally assumed that the masses of light quarks are {{m}_{i}} sim mathcal{O}(1{text{/}}{{N}_{{text{c}}}}). It has been shown that the theory not only reproduces known inequalities for ratios of the masses of light quarks but also allows one to calculate some parameters characterizing the degree of breaking of chiral symmetry.