Quark mass matrices in left-right symmetric gauge theories

The most general left-right symmetry for SU(2)_L×SU(2)_R×U(1) gauge theories with any number of flavours and with at most two scalar multiplets transforming as $\text{q}\text{q}$ bilinears is analyzed. In order to get additional constraints on the structure of quark mass matrices, all possible horizontal groups (continuous or discrete) are investigated. We give a complete classification of physically inequivalent quark mass matrices for four and six flavours. It is argued that our methods and results are also applicable in the case of dynamical symmetry breaking. Parity invariance and horizontal symmetry are shown to imply CP conservation on the lagrangian level. For all non-trivial three-generation models there is spontaneous CP violation, which in most cases turns out to be naturally small. Several six-flavour models predict $\text{m}{}_{\mathrm{<mtext>t</mtext>}}\text{?m}{}_{\mathrm{<mtext>b</mtext>}}\text{(}\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{m}{}_{\mathrm{<mtext>c</mtext>}}\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and are, therefore, already ruled out experimentally. In the remaining few realistic models, predictions for the weak mixing angles are made.