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

Abstract

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.

Holographic models of composite Higgs in the Veneziano limit. Part I. Bosonic sector

“…Given that in these papers the gauge [12] and flavour [12,13] groups are different from the ones considered here, and that moreover both simulations may not be close to near-conformal dynamics, 6 a quantitative comparison with our results is not pertinent. We can nevertheless examine if some qualitative features reasonably match, by considering our Model II, with sizeable values of ∆ φ and φ c , controlling the explicit breaking of conformal symmetry, x F ∼ 1, and fermionic anomalous dimension presumably not too far from its canonical value, ∆ R 9/2.…”

“…where we also quote the mass of the lightest vector meson for comparison. Quite recently, results for fermionic bound states were also obtained for an Sp(4) gauge symmetry [13], with two dynamical, Dirac fermions in the fundamental and three in the antisymmetric representations. From Figure 4 of [13], one extracts…”

“…However, so far little is known about the spectrum of such fermionic states. On the lattice, the fermionic spectra of SU (4) and Sp(4) gauge theories have been studied in [12] and [13], respectively, while consequences for partial compositeness have been further explored in [14].…”

Lattice studies of the $Sp(4)$ gauge theory with two fundamental and three antisymmetric Dirac fermions

“…The combination of all of the above demonstrates that our lattice programme is now ready to start an intensive process of numerical studies focused on the spectra of mesons and chimera baryons in this theory, making contact with the model-building literature. While for the purposes of this publication we used point-like and stochastic Z 2 wall sources for the measurements of the 2-point correlation functions, to improve the signal to noise ratio in the numerical studies we will use smearing techniques, both for the sources and for the dynamical configurations, and both of which have been tested successfully on this model [117,118]. By further combining these techniques with the implementation of an appropriate basis for the variational problem, and of a scale-setting process based on the Wilson flow, such studies will provide access also to some of the excited states in the theory, and we will be able, by varying the lattice parameters, to extrapolate our spectroscopy results towards the continuum limit, in the large region of parameter space with intermediate fermion masses that is of direct interest for models of composite Higgs and partial top compositeness.…”

“…We will deliver further publications on the topology of Sp(2N ) gauge theories, and their quenched meson spectra, as well as on the (partially quenched) dynamical theory with n f = 3 dynamical antisymmetric fermions-preliminary results have been presented in Ref. [117,118].…”