  The Sp(4) gauge theory with two Dirac fundamental flavours provides a
candidate for the microscopic origin of composite-Higgs models based on the
SU(4)/Sp(4) coset. We employ a combination of two different, complementary
strategies for the numerical lattice calculations, based on the Hybrid Monte
Carlo and on the Heat Bath algorithms. We perform pure Yang-Mills, quenched
computations and exploratory studies with dynamical Wilson fermions. We present
the first results in the literature for the spectrum of glueballs of the pure
Sp(4) Yang-Mills theory, an EFT framework for the interpretation of the masses
and decay constants of the lightest pion, vector and axial-vector mesons, and a
preliminary calculation of the latter in the quenched approximation. We show
the first numerical evidence of a bulk phase transition in the lattice theory
with dynamical Wilson fermions, and perform the technical steps necessary to
set up future investigations of the mesonic spectrum of the full theory.
