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

We review numerical results for models with gauge group Sp(2N), discussing the glueball spectrum in the large-N limit, the quenched meson spectrum of Sp(4) with Dirac fermions in the fundamental and in the antisymmetric representation and the Sp(4) gauge model with two dynamical Dirac flavours. We also present preliminary results for the meson spectrum in the Sp(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 Sp(4) is within reach with our current lattice methodology.

Regge theory in a holographic dual of QCD in the Veneziano limit

We initiate the study of Regge theory in a bottom-up holographic model for QCD in the Veneziano limit, where the backreaction of the quarks to the gluon dynamics is included. We determine the parameters of the model by carrying out a precise fit to the meson spectrum in QCD. The spectrum for spin-one and pseudoscalar mesons is well reproduced. We then generalise the model to incluce higher spin fields in the bulk trajectories dual to the Pomeron and meson Regge trajectories at the boundary. With this setting, we fit the masses of the mesons with spins J = 2, 3, and 4, as well as the experimental data of the total cross-sections σ(γγ → X), σ(γp → X) and σ(pp → X). For the cross sections we obtain a $$ {\chi}_{\mathrm{d}.\mathrm{o}.\mathrm{f}}^2 $$ χ d . o . f 2 of 0.74 for a total of 199 experimental points.

Meson spectrum in the large N limit

We present the result of our computation of the lowest lying meson masses for SU(N) gauge theory in the large N limit (with Nf /N → 0). The final values are given in units of the square root of the string tension, and with errors which account for both statistical and systematic errors. By using 4 different values of the lattice spacing we have seen that our results scale properly. We have studied various values of N (169, 289 and 361) to monitor the N-dependence of the most sensitive quantities. Our methodology is based upon a first principles approach (lattice gauge theory) combined with large N volume independence. We employed both Wilson fermions and twisted mass fermions with maximal twist. In addition to masses in the pseudoscalar, vector, scalar and axial vector channels, we also give results on the pseudoscalar decay constant and various remormalization factors.