We perform lattice studies of meson mass spectra and decay constants of the Sp(4) gauge theory in the quenched approximation. We consider two species of (Dirac) fermions as matter field content, transforming in the 2-index antisymmetric and the fundamental representation of the gauge group, respectively. All matter fields are formulated as Wilson fermions. We extrapolate to the continuum and massless limits, and compare to each other the results obtained for the two species of mesons. In the case of two fundamental and three antisymmetric fermions, the long-distance dynamics is relevant for composite Higgs models. This is the first lattice study of this class of theories. The global SU (4) × SU (6) symmetry is broken to the Sp(4) × SO(6) subgroup, and the condensates align with the explicit mass terms present in the lattice formulation of the theory.The main results of our quenched calculations are that, with fermions in the 2-index antisymmetric representation of the group, the masses squared and decay constant squared of all the mesons we considered are larger than the corresponding quantities for the fundamental representation, by factors that vary between ∼ 1.2 and ∼ 2.7. We also present technical results that will be useful for future lattice investigations of dynamical simulations, of composite chimera baryons, and of the approach to large-N in the Sp(2N ) theories considered. We briefly discuss their high-temperature behaviour, where symmetry restoration and enhancement are expected. We acknowledge useful discussions withWe summarise in this Appendix our conventions in the treatment of spinors, which are useful, for example, in switching between the 2-component and the 4-component notation (see also Ref. [50]). The former is best suited to highlight the symmetries of the system, while the latter is the formalism adopted as a starting point for the lattice numerical

Abstract. We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2 + 1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents Nτ = 4, 6 and 8 and aspect ratios of Ns/Nτ ≥ 4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3Tc (Tc being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2πT from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2πT . The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4Tc. Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3Tc, indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.