Higgs compositeness in Sp(2N) gauge theories – Determining the low-energy constants with lattice calculations

Abstract

As a first step towards a quantitative understanding of the SU(4)/Sp(4) composite Higgs model through lattice calculations, we discuss the low energy effective field theory resulting from the SU(4) → Sp(4) global symmetry breaking pattern. We then consider an Sp(4) gauge theory with two Dirac fermion flavours in the fundamental representation on a lattice, which provides a concrete example of the microscopic realisation of the SU(4)/Sp(4) composite Higgs model. For this system, we outline a programme of numerical simulations aiming at the determination of the low-energy constants of the effective field theory and we test the method on the quenched theory. We also report early results from dynamical simulations, focussing on the phase structure of the lattice theory and a calculation of the lowest-lying meson spectrum at coarse lattice spacing.Combined contributions of B. Lucini

Vacuum misalignment and pattern of scalar masses in the SU(5)/SO(5) composite Higgs model

“…The strict requirement that the underlying theory at low energies (i.e., around the condensation scale) is not conformal leaves only 7 models with the SU(5)/ SO(5) symmetry breaking pattern [22]. It is remarkable that some of these models are being studied on the lattice for HC groups Sp(4) [23,24] and SU(4) [25,26]. Throughout this paper we will only consider chimera baryons of the form ψχψ, leading to composite fermionic partners transforming in two-index irreducible representations of SU (5).…”

Composite Higgs and Dark Matter model in SU(6)/SO(6)

“…As a final comment, we would like to recall that such underlying theory can be studied on the lattice, thus allowing to calculate the properties of the low energy states, including masses and couplings of the resonances. Studies of theories with two species of fermions are already available in the literature, but only based on Sp(4) [56][57][58] and SU (4) [59][60][61][62] gauge groups, while no result is available for the HC groups leading to our model.…”

Light Scalars in Composite Higgs Models

“…This includes lowenergy constants, which are crucial for the generation of the Higgs misalignment potential and the Higgs boson mass [40]. So far, theories based on confining SU(4) [25,41] and Sp(4) [42][43][44][45] are being studied. For SU(4), preliminary results on the spectra [25] show that the chimera baryons tend to be heavy and beyond the reach of the LHC, while first calculations of the relevant form factors [46] show a suppressed mixing to the top.…”