Understanding the nature of the Standard Model Higgs boson is still an open problem. An appealing possibility is that the Higgs boson be a composite particle resulting from a novel strong interaction. The lack of observation of otherwise unexplained particles interacting through this conjectured novel force and with mass comparable to that of the Higgs boson would then require a mechanism that keeps the Higgs parametrically light. Such a mechanism can be provided by the spontaneous breaking of the global flavour symmetry in the new interaction. In this framework, the Higgs boson is interpreted as a Pseudo-Nambu-Goldstone Boson (PNGB) of the novel interaction. Among candidate realisations of PNGB compositeness are Sp(2N) gauge theories. The two simplest theories in this class are Sp(2), coinciding with SU(2), and Sp(4). Given the strong nature of the novel force, first-principle calculations allow to determine quantitative predictions that are used to test the experimental viability of these theories.
In our project, we performed the first calculation of the scattering of two Goldstone bosons in the vector resonance channel for an SU(2) gauge theory with two fundamental fermions. The calculation allows to obtain the first prediction of the vector resonance effective coupling to Goldstone bosons in a phenomenologically viable model. The coupling is used by phenomenologists to constrain Composite Higgs model at the LHC and is therefore relevant to shed light on the role played by the vector resonance in a particular realisation of a Composite Higgs model.
In the Sp(4) model, we performed the first calculation of the spectrum in a phenomenologically relevant model in which the matter content is provided by two Dirac fermions in the fundamental representation and three Dirac fermions in the antisymmetric representation . In particular, we have determined the mass of the chimera baryon, a bound state whose constituents are two fermions in the fundamental representation and one in the antisymmetric representation and whose importance is related to the partial top compositeness mechanism, which has been advocated to account for the large mass of the top quark.
 V. Drach et al., Scattering of Goldstone Bosons and resonance production in a Composite Higgs model on the lattice, JHEP 04 (2021), 117 [arXiv:2012.09761]
 E. Bennett et al., Lattice studies of the Sp(4) gauge theory with two fundamental and three antisymmetric Dirac fermions, arXiv:2202.05516.