Understanding which novel interactions can give rise to the emergence of the Standard Model at a low energy scale of about 1 TeV without conflicting with the high precision tests of the latter theory is one of the biggest challenges of current Particle Physics. This problem requires robust input from Quantum Field Theory and phenomenology that can guide current and future experimental searches. Composite Higgs models are based on a new fundamental interaction which features an emergent Higgs boson which properties are similar to the Standard Model Higgs boson, a key requirement motivated by the current experimental results provided by the LHC experiments. Among the restricted class of gauge theories that feature all the key requirements, particularly relevant are those based on the symplectic group Sp(2N).
Our project has provided insights in the dynamics of Sp(2N) gauge theories relevant for experimental searches of composite dynamics. We finalised the first calculation of the low energy parameter of the Goldstone Boson in Sp(2)=SU(2) gauge theory that controls the production of new vector resonances and which is constrained by vector boson scattering processes at the LHC . Our predictions is currently being used to constrain further the model and to study the constraints provided by future colliders. In addition, our project has performed a benchmark calculation of the scattering properties of the Goldstone boson in the singlet channel. Ultimately, such a quantity will allow to constrain from first principle the Higgs properties in a Composite Higgs scenario. Furthermore a detailed study of the spectrum of Sp(2N) purely gluonic bound states in the absence of matter was performed[3,4].
The study shed light on the dependence of the spectrum on the underlying gauge symmetry, addressing a fundamental question to inform model building. A smooth variation of the spectrum with the number of colours N has been found, showing that the effect of the finite value of N can be seen as a correction to well-defined infinite-N masses of the various states.
 V. Drach et al., Scattering of Goldstone Bosons and resonance production in a Composite Higgs model on the lattice, accepted for publication in JHEP [arxiv:2012.09761]
 V. Drach et al., Scattering of Goldstone Bosons in SU(2) model with Nf=2 fundamental fermions, Asia Pacific Symposium for Lattice Field Theory, August 2020 (paper in preparation).
 E. Bennett et al., Color dependence of tensor and scalar glueball masses in Yang-Mills theories, Phys Rev D.102.011501 [arXiv:2004.11063]
 E. Bennett et al., Glueballs and Strings in Sp(2N) Yang-Mills theories, accepted for publication in Phys. Rev. D [arxiv:2010.15781]