In the minimal composite Higgs model (MCHM), the size of the Higgs mass and vacuum expectation value is determined, via the Higgs potential, by the size of operators that violate the global SO(5) symmetry. In 5D holographic realisations of this model, this translates into the inclusion of brane localised operators. However, the inclusion of all such operators results in a large and under-constrained parameter space. In this talk I will discuss the level of fine-tuning involved in such a parameter space, focusing on the MCHM${}_5$. It is demonstrated that the gauge contribution to the Higgs potential can be suppressed by brane localised kinetic terms, but this is correlated with an enhancement to the S parameter. While the fermion contribution can be enhanced or suppressed. However this does not significantly improve the level of fine tunings, since the Higgs squared term, in the potential, requires a cancellation between the fermion and gauge contributions.
Summary
I will give a brief talk on some work which is finished and the paper should appear on the arxiv in the next couple of weeks. I will start by introducing the minimal composite Higgs model, explaining that the relative lightness of the Higgs could be explained if it is a pseudo-Nambu-Goldstone boson analogous to the pion in chiral symmetry breaking. I will then examine the Higgs potential, computed in the 5D holographic description, including all IR localised SO(4) invariant operators up to mass dimension 4. I will focus on how much fine tuning is required in order to realise electroweak symmetry breaking with the correct Higgs mass, given the constraints from electroweak precision tests and the failure to observe a new fermion resonance at the LHC.