Simulation of Sp(2N) gauge theories for Composite Higgs models

Simulation of Sp(2N) gauge theories for Composite Higgs models

Figure 1: The figure (from [1]) shows the mass squared of the lowest-lying vector particle versus the mass squared of the pseudoscalar particle in the continuum for Sp(4) gauge theory with static (blue) and dynamical (red) fermions. The bands represent the error of the corresponding best fit to the data. The effect of unquenching the fermions are clearly visible in the figure.

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, in order for the former to be validated experimentally as viable theories, first-principle calculations would need to be performed that allows us to determine quantitative predictions from these models. These calculations can be executed numerically formulating the models on a spacetime lattice.

Figure 2: The figure shows the phase shift as a function the centre of mass energy of the scattering process of two Goldstone bosons in the SU(2) gauge theory. The slope of a linear fit allows to constrain the coupling of the PNGBs to the vector resonance in the composite Higgs framework.

Our project has provided the first numerical calculation in the Sp(4) gauge model with two fundamental flavours and the first determination of its lowest-lying meson spectrum and of the corresponding decay constants in the continuum limit. This has enabled us to determine the coefficients of an effective field theory that can be used to compare the predictions of the model with experimental results [1]. Our study of the Sp(2N) Yang-Mills model combined with results in the literature for SU(N) and SO(N) gauge theories has unravelled that in both three and four spacetime dimensions the ratio of the mass of the tensor glueball over the mass of the scalar glueball is independent of the gauge group [2]. This result provides further insights on the phenomenon of confinement, which characterises non-Abelian gauge models and provides striking experimental signatures such as jets in high-energy experiments involving the standard model strong force.

Our project also provided the first calculation in a composite Higgs scenario of the scattering amplitude of two PNGBs in the SU(2) model. The amplitude controls the production cross section of a new resonance expected to be produced at the LHC in a Composite Higgs scenario. The results therefore constrain the viability of the model and shed light on a key observable to test composite Higgs models using lattice simulations.


  • [1] E. Bennett et al., Sp(4) gauge theories on the lattice: Nf=2 dynamical fundamental fermions, JHEP 12 (2019) 053 [arXiv:1909.12662]
  • [2] E. Bennett et al., On the colour dependence of tensor and scalar glueball masses in Yang-Mills theories, Phys. Rev. D Rapid Communications to appear [arXiv:2004.11064]
  • [3] V. Drach et al., Resonance study of SU(2) model with 2 fundamental flavours of fermions, Proceedings of Science [arxiv:1910.13847] – paper in preparation.