Calculability inSU(2)L⊗SU(2)R⊗U(1): The Mass Matrix andCP-Invariance Violation

Abstract

It is shown that calculability of the mixing angles in a class of $n$-generation, leftright-symmetric $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\otimes \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\otimes \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ models restricts the fermion mass matrix to be of the form ${{\Sigma }_{m=0\mathrm{}}}^n\oplus I_m{A}_m$ with the constraint ${{\Sigma }_{m=0\mathrm{}}}^{n}m{I}_m=n$, where $A_m$ is a nonsingular $m\times m$ Hermitian or complex symmetric block containing $2m-1$ elements and $I_m$ is the number of such blocks. Such a mass matrix cannot supply $\mathrm{CP}$-invariance-violating phases.