Abstract
We show that the potential of Nambu-Goldstone bosons can have two or more local minima e.g. at antipodal positions in the vacuum manifold. This happens in many models of composite Higgs and of composite Dark Matter. Trigonometric potentials lead to unusual features, such as symmetry non-restoration at high temperature. In some models, such as the minimal SO(5)/SO(4) composite Higgs with fermions in the fundamental representation, the two minima are degenerate giving cosmological domain-wall problems. Otherwise, an unusual cosmology arises, that can lead to supermassive primordial black holes; to vacuum or thermal decays; to a high-temperature phase of broken SU(2)L, possibly interesting for baryogenesis.
Highlights
Gauge and Yukawa interactions present in the Standard Model (SM) are corrected by trigonometric functions; the potential, restricted for simplicity along the physical Higgs direction h = (2H†H)1/2 with period 2πf can be written as a Fourier series in h2
Our work differs from these references as we do not modify the electroweak phase transition around the tuned vacuum and we study the implications of minima existing at temperatures below the confinement phase transitions that gives rise to the Goldstone bosons
Pseudo-Goldstone bosons, such as the composite scalars arising from new strong dynamics, can be described by low-energy effective theories where the scalar fields form a coset with non-trivial topology
Summary
Composite Higgs models are often studied from a low-energy effective theory perspective, as present experiments only offer bounds from this limited point of view. A possible UV realisation of composite Higgs models has been proposed in [8] This construction employs a new gauge interaction GDC to generate the spontaneous breaking of global symmetries, and elementary scalars to obtain the needed flavour structure through partially composite fermions.. For symmetric cosets the Nambu-Goldstone bosons (that include the Higgs doublet H) can be parametrised with the unitary matrix U = exp (2iΠ/f ) where Π = T aπaare the broken generators Different periodicities might be possible in fundamental composite Higgs theories, depending on the confining gauge group [8].
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