Classification of NLO operators for composite Higgs models

Abstract

We provide a general classification of template operators, up to next-to-leading order, that appear in chiral perturbation theories based on the two flavour patterns of spontaneous symmetry breaking SU($N_F$)/Sp($N_F$) and SU($N_F$)/SO($N_F$). All possible explicit-breaking sources parametrised by spurions 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)$\cong$ 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 $\eta$, showing that it cannot develop a vacuum expectation value without explicit CP violation in the underlying theory.

arXiv comment38 pages plus appendices, 2 figures, 4 tables. v2 matches the published version

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Cited by in corpus (20)

• Sp(4) gauge theories on the lattice: $N_f=2$ dynamical fundamental fermions
• Baryon spectrum of SU(4) composite Higgs theory with two distinct fermion representations
• Sp(4) gauge theories on the lattice: Quenched fundamental and antisymmetric fermions
• Composite Higgs and Dark Matter Model in SU(6)/SO(6)
• Vacuum misalignment and pattern of scalar masses in the SU(5)/SO(5) composite Higgs model
• Lattice studies of the $Sp(4)$ gauge theory with two fundamental and three antisymmetric Dirac fermions
• Glueballs and Strings in $Sp(2N)$ Yang-Mills theories
• Modelling vector-like quarks in partial compositeness framework
• Loop-Generated Neutrino Masses in Composite Higgs Models
• Dark matter in (partially) composite Higgs models
• Towards top-down holographic composite Higgs: minimal coset from maximal supergravity
• Proper-time method for unequal masses
• Toward minimal composite Higgs models from regular geometries in bottom-up holography
• Gravitational waves from $\mathrm{SU}($$N$$)/Sp($$N$$)$ composite Higgs models
• Pseudoscalar pair production via off-shell Higgs in composite Higgs models
• Partial compositeness under precision scrutiny
• Electroweak precision tests of composite Higgs models
• Composite self-interacting dark matter and Higgs
• Phase transition and gravitational waves in maximally symmetric composite Higgs model
• Proper-time evaluation of the effective action: unequal masses in the loop