Sp (4) gauge theories on the lattice: Nf = 2 dynamical fundamental fermions

Abstract

We perform lattice studies of the gauge theory with Sp(4) gauge group and two flavours of (Dirac) fundamental matter. The global SU (4) symmetry is spontaneously broken by the fermion condensate. The dynamical Wilson fermions in the lattice action introduce a mass that breaks the global symmetry also explicitly. The resulting pseudo-Nambu-Goldstone bosons describe the SU (4)/Sp(4) coset, and are relevant, in the context of physics beyond the Standard Model, for composite Higgs models. We discuss scale setting, continuum extrapolation and finite volume effects in the lattice theory. We study mesonic composite states, which span representations of the unbroken Sp(4) global symmetry, and we measure masses and decay constants of the (flavoured) spin-0 and spin-1 states accessible to the numerical treatment, as a function of the fermion mass. With help from the effective field theory treatment of such mesons, we perform a first extrapolation towards the massless limit. We assess our results by critically comparing to the literature on other models and to the quenched results, and we conclude by outlining future avenues for further exploration. The results of our spectroscopic analysis provide new input data for future phenomenological studies in the contexts of composite Higgs models, and of dark matter models with a strongly coupled dynamical origin. arXiv:1909.12662v2 [hep-lat] 22 Nov 2019 7 Comparison to other gauge theories 37 8 Continuum results: summary 42 9 Conclusions and outlook 43 A Lattice action and numerical calculations: additional details 45 A.1 Hybrid Monte Carlo 45 A.2 Of diquarks 47 A.3 Effective mass and fitting procedure 48 B Low-energy constants and global fit 50 -1 -

Sp(4) gauge theories on the lattice: Quenched fundamental and antisymmetric fermions

“…[63,64] and the more recent Refs. [65,66] and [67,68]), some of us proposed a systematic programme of exploration of the lattice dynamics of Sp(2N ) gauge theories. Our main scientific motivation is the application of the results of such studies to the CHM context.…”

“…The lattice action and its numerical treatment via Monte Carlo methods are the main topics of this section. Most of the material covered here is based upon well established processes, and we discussed its application to our programme elsewhere [62,67], hence we summarise it briefly, mostly for the purpose of defining the notation and language we adopt later in the paper.…”

“…The scale setting procedure with the GF scheme in Sp(4) theories has been first discussed in Ref. [62], both for the pure Yang-Mills and for the theory with two fundamental Dirac fermions (see also [63,67]). We follow the same procedure throughout this work: we define the flow scale w 0 by W| t=w 2 0 = W 0 [85], where W(t) is the derivative of the action density built from gauge fields at non-zero fictitious flow time t. The reference value W 0 = 0.35 has been chosen to minimise both discretisation and finite volume effects [62] (though with the caveats discussed in Refs.…”

“…Extrapolations to the continuum limit are carried out following the same procedure as in Ref. [67]. We borrow the ideas of tree-level Wilson chiral perturbation theory (WχPT), which we truncate at the next-to-leading order (NLO) in the double expansion in fermion mass and lattice spacing [96,97] (see also Ref.…”

“…4.2. Second, in order to remove potential finite-volume effects, we restrict the bare fermion mass m 0 to ensembles that satisfy the condition m PS L ≥ 7.5, in line with the results of the study with dynamical fermions [67]. Only part of the data in [62] meets this restriction, over the range of m 0 ∈ [−0.7, −0.79] at β = 7.62, measured on the lattice with extension 48 × 24 3 -corresponding to the ensemble denoted as QB1 in Table 2.…”