Classification of NLO operators for composite-higgs models

Preprint number: CP3-Origins-2018-2 DNRF90
Authors: Tommi Alanne (MPI Heidelberg), Nicolas Bizot (Lyon Univ & CNRS/IN2p3), Giacomo Cacciapaglia (Lyon Univ & CNRS/IN2p3), and Francesco Sannino (CP3-Origins & D-IAS)
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We provide a general classification of template operators, up to NLO, that appear in chi-
ral perturbation theories based on the two flavour patterns of spontaneous symmetry breaking SU(NF)/Sp(NF) and SU(NF)/SO(NF). All possible explicit-breaking sources parametrised by spuri- ons transforming in the fundamental and in the two-index representations of the flavour symmetry are included. While our general framework can be applied to any model of strong dynamics, we specialise to composite-Higgs models, where the main explicit breaking sources are a current mass, the gauging of flavour symmetries, and the Yukawa couplings (for the top). For the top, we consider both bilinear couplings and linear ones a` la partial compositeness. Our templates provide a basis for lattice calculations in specific models. As a special example, we consider the SU(4)/Sp(4) SO(6)/SO(5) pattern which corresponds to the minimal fundamental composite- Higgs model. We further revisit issues related to the misalignment of the vacuum. In particular, we shed light on the physical properties of the singlet η, showing that it cannot develop a vacuum expectation value without explicit CP violation in the underlying theory.