Fermion masses and mixing angles: A test for string vacua

Abstract

The way in which the observed structure of fermion masses and quark mixing angles imposes restrictions on string vacua is examined. Special attention is paid to the Z 3 orbifold with background fields, but scenarios for other Z n and Z n ×Z m orbifolds are also addressed. Many vacuum configurations can be excluded on these grounds. An additional stage of gauge symmetry breaking after compactification is also found to be absolutely essential for quark mixing. For the surviving configurations the prospects are very encouraging. The observed fermion mass hierarchy can be obtained in connection with the deformations of the compactified space (moduli). Furthermore a generic ansatz for the quark mass matrices emerges naturally in orbifold compactifications and yields sensible results (and even predictions) for the relevant physical quantities (the three mixing angles and the weak CP violation angle).