Exploring flavour at the energy frontier in the Little Higgs paradigm

Abstract

The Standard Model of Particle Physics is one of the most predictive and elegant theories of the History of Physics. It explains what are the fundamental constituents of matter and how they interact. This model has been tested in a wide variety of scenarios and essentially all the experimental measurements seem to agree with its predictions. However, in this framework the Higgs boson is an elementary particle. This makes the size of its mass quite unnatural. The Higgs mass, not protected by any symmetry, receives quadratically divergent contributions coming from arbitrarily large energies and thus there is no reason that justifies why the Higgs boson should be light. This is the so called hierarchy problem. One of the most elegant proposals to face this problem consists of assuming that the Higgs boson, rather than an elementary particle, is a composite state of unknown heavy fermions bounded by a new strong interacting sector. This is motivated by the treatment of mesons in Quantum Chromodynamics. As a consequence, at high energies there is no Higgs because those heavy fermions would be the fundamental constituents of a new theory that extends the Standard Model. If this idea is realized in Nature it would end, once and for all, with the hierarchy problem. The composite Higgs paradigm can be implemented in many ways, giving rise to a vast family of models. One of the frameworks that have received more attention is the Littlest Higgs model with T-parity. In this model the Higgs mass does not receive quadratically divergent contributions. Hence the Higgs is naturally light. Furthermore, the T-parity is a discrete symmetry under which the Standard Model particles are even and most of the new particles are odd. As a consequence, the contributions of these particles to precision observables are one-loop suppressed and thus under control. Within this framework we will study flavour-changing transitions. In particular, we are interested in the contributions of a heavy fermion singlet that can be either T-even or T-odd under the discrete symmetry. We will show that the contributions of the T-odd singlet to lepton flavour-changing Higgs decays and to neutrino masses do not decouple in the limit of a heavy singlet mass. These issues are not present in the T-even singlet case. Motivated by the anomalous behaviour of the singlet, we will prove that the Littlest Higgs model with T-parity is not invariant under its gauge group. As a consequence, we will develop a new Littlest Higgs model with T-parity compatible with gauge invariance. For that purpose, the global symmetry group will be minimally enlarged with respect to the original model and new fermion and scalar degrees of freedom will be introduced. To show explicitly the viability of the model we will impose current constraints on exotic quarks; we will consider that the usual dark photon, the lightest T-odd particle, accounts for all the dark matter relic density of the Universe; and we will demand that the masses of the new scalar fields do not exceed the TeV. This fixes the value of certain parameters while others get correlated, so the particle spectrum gets bounded from below and above, keeping the model viable. Finally, we will study the main decay channels of the new scalar fields to show that their decay rate is comparable to that of the Higgs. In terms of production rates, they are relatively heavy and generated by an electroweak interaction so they are not significantly produced at the LHC.