Understanding the nature of the Standard Model Higgs boson is still an open problem. Extensions of the Standard Model in which its fields have a composite origin provide a compelling first-principle explanation of the existence of the Higgs boson and explain its mass in terms of spontaneous breaking of enlarged global symmetries of a novel strong interaction. Among candidate realisations of Higgs 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 scalar resonance channel for an SU(2) gauge theory with two fundamental fermions. The inevitable presence of a resonance in the scalar channel can affect the predictions for the LHC. Our work contributes to the understanding of the role of resonances in the phenomenology of the class of composite models characterised by the strong sector we are considering, irrespectively of its embedding. Using the Lüscher quantization condition, we have been able to put non-perturbative constraints on the singlet scattering amplitude reported in Fig. 1 (left). This work represents the first study of the singlet channel in four-dimensional gauge theories beyond QCD.
Among the possible realisations of this idea, another particularly attractive is the one based on an Sp(4) gauge theory with two Dirac fermions in the fundamental representation and three in the antisymmetric representation because in addition, it admits bound states of mixed representation fermions—chimera baryons—that can be coupled to the QCD top quark, providing an explanation for its comparatively large mass. This mechanism is known as partial top compositeness. Our project has provided the first simulation of the Sp(4) model underlying partial top compositeness, simultaneously measuring both masses of mesons involving quarks in the same representation and of the chimera baryons. A first example of the resulting spectrum is reported in Fig. 1 (right).