Quark-Lepton Complementarity in Unified Theories

As pointed out by many authors, recent observations are consistent with an intriguing relation between the Cabibbo angle ${\theta }_C$ and the solar neutrino mixing angle ${\theta }_{12}$, namely ${\theta }_{12}\simeq \pi \mathrm{/}4-{\theta }_C$. Such quark-lepton complementarity (QLC) may be a signal of an underlying quark-lepton unification at short distances. We discuss possible ways to realize this relation in realistic quark-lepton unification theories by identifying a minimal set of operators that lead to QLC while remaining consistent with other known data. The purpose of this paper is to present the first elements of a unified model at the GUT scale capable of predicting the QLC relation. A generic prediction of our proposed class of models is the new relation for the lepton mixing angle ${\theta }_{13}\simeq {\theta }_C$, which allows these models to be confirmed or excluded by the current generation of neutrino oscillation experiments.