Topological terms in Composite Higgs models

Abstract

We apply a recent classification of topological action terms to Composite Higgs models based on a variety of coset spaces G/H and discuss their phenomenology. The topological terms, which can all be obtained by integrating (possibly only locally-defined) differential forms, come in one of two types, with substantially differing consequences for phenomenology. The first type of term (which appears in the minimal model based on SO(5)/SO(4)) is a field theory generalization of the Aharonov-Bohm phase in quantum mechanics. The phenomenological effects of such a term arise only at the non-perturbative level, and lead to P and CP violation in the Higgs sector. The second type of term (which appears in the model based on SO(6)/SO(5)) is a field theory generalization of the Dirac monopole in quantum mechanics and has physical effects even at the classical level. Perhaps most importantly, measuring the coefficient of such a term can allow one to probe the structure of the underlying microscopic theory. A particularly rich topological structure, with 6 distinct terms, is uncovered for the model based on SO(6)/SO(4), containing 2 Higgs doublets and a singlet. Of the corresponding couplings, one is an integer and one is a phase.