How many parameters does a quark mass matrix model need?

Abstract

An investigation independent of matrix form is made of how many parameters, which characterize the difference between up- and down-quark mass matrices, are, at least, required from the present data on quark masses and mixings. From a general study of the model with hierarchical three-step mass generations described by the three parameters {alpha}{sub {ital q}}, {beta}{sub {ital q}}, and {gamma}{sub {ital q}} ({vert bar}{alpha}{sub {ital q}}{vert bar}{much gt}{vert bar}{beta}{sub {ital q}}{vert bar}{much gt}{vert bar}{gamma}{sub {ital q}}{vert bar}; {ital q}={ital u},{ital d}), it is pointed out that the model with {beta}{sub {ital u}}/{beta}{sub {ital d}}={gamma}{sub {ital u}}/{gamma}{sub {ital d}} (i.e., with two independent parameters {alpha}{sub {ital q}} and {beta}{sub {ital q}}) is ruled out.