Sp(4) gauge theories and beyond the standard model physics

<jats:p>We review numerical results for models with gauge group <jats:italic>Sp</jats:italic>(2N), discussing the glueball spectrum in the large-<jats:italic>N</jats:italic> limit, the quenched meson spectrum of <jats:italic>Sp</jats:italic>(4) with Dirac fermions in the fundamental and in the antisymmetric representation and the <jats:italic>Sp</jats:italic>(4) gauge model with two dynamical Dirac flavours. We also present preliminary results for the meson spectrum in the <jats:italic>Sp</jats:italic>(4) gauge theory with two fundamental and three antisymmetric Dirac flavours. The main motivation of our programme is to test whether this latter model is viable as a realisation of Higgs compositeness via the pseudo Nambu Goldstone mechanism and at the same time can provide partial top compositeness. In this respect, we report and briefly discuss preliminary results for the mass of the composite baryon made with two fundamental and one antisymmetric fermion (chimera baryon), whose physical properties are highly constrained if partial top compositeness is at work. Our investigation shows that a fully non-perturbative study of Higgs compositeness and partial top compositeness in <jats:italic>Sp</jats:italic>(4) is within reach with our current lattice methodology.</jats:p>