Masses of Light Quarks

Abstract

Based on the general form of the first correction to the result of current algebra for the masses of pseudoscalar mesons, we obtain a number of sum rules relating the masses of pseudoscalars to the light quark mass ratios \({{{{m}_{u}}} \mathord{\left/ {\vphantom {{{{m}_{u}}} {{{m}_{d}}}}} \right. \kern-0em} {{{m}_{d}}}}\), \({{{{m}_{s}}} \mathord{\left/ {\vphantom {{{{m}_{s}}} {{{m}_{d}}}}} \right. \kern-0em} {{{m}_{d}}}}\). A more careful consideration involving experimental data on \(\eta \to 3\pi \) decays allows us to identify a domain in which the results of these sum rules do not contradict each other. This determines the range of acceptable values for the ratios \({{{{{{m}_{u}}} \mathord{\left/ {\vphantom {{{{m}_{u}}} {{{m}_{d}}}}} \right. \kern-0em} {{{m}_{d}}}}} \mathord{\left/ {\vphantom {{{{{{m}_{u}}} \mathord{\left/ {\vphantom {{{{m}_{u}}} {{{m}_{d}}}}} \right. \kern-0em} {{{m}_{d}}}}} {{{m}_{s}}}}} \right. \kern-0em} {{{m}_{s}}}}\). Finally, the results are compared with known phenomenological data and calculation results on a lattice.