SU(2) gauge theory with two fundamental flavors: A minimal template for model building

Abstract

We investigate the continuum spectrum of the SU (2) gauge theory with N f = 2 flavours of fermions in the fundamental representation. This model provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics that range from composite (Goldstone) Higgs theories to several intriguing types of dark matter candidates, such as the SIMPs. We improve our previous lattice analysis [1] by adding more data at light quark masses, at two additional lattice spacings, by determining the lattice cutoff via a Wilson flow measure of the w 0 parameter, and by measuring the relevant renormalisation constants non-perturbatively in the RI'-MOM scheme. Our results for the lightest isovector states in the vector and axial channels, in units of the pseudoscalar decay constant, are m V /F PS ∼ 13.1(2.2) and m A /F PS ∼ 14.5(3.6) (combining statistical and systematic errors).In the context of the composite (Goldstone) Higgs models, our result for the spin-one resonances are m V > 3.2(5) TeV and m A > 3.6(9) TeV, which are above the current LHC constraints. In the context of dark matter models, for the SIMP case our results indicate the occurrence of a compressed spectrum at the required large dark pion mass, which implies the need to include the effects of spin-one resonances in phenomenological estimates.

Fundamental partial compositeness

“…In general, whenever there is one Higgs doublet, the custodial symmetry is ensured when the unbroken global symmetry group contains a subgroup SO(4) ⊃ SU(2) L ⊗ SU(2) R . Lattice simulations [43][44][45] find that the pattern of chiral symmetry breaking envisioned above is indeed achieved for the minimal SU(2) ∼ Sp(2) case. …”

“…Compositeness allows for the introduction of new TC-scalars and its non-perturbative dynamics can be further investigated via first principle lattice simulations. In this respect, we foresee some immediate advantages of 'scalarphilic' fundamental theories because of the following concrete reasons: a) Adding TC-scalars on the lattice is less computationally demanding than adding TCfermions; b) We do not rely on nearly-conformal dynamics, hence lattice computations do not need the usual extremely large volumes; c) The state-of-the-art simulations of SU (2) gauge theories [43][44][45] can be readily extended with the TC-scalars needed in the model of section 3.3. This will jump-start the investigation of realistic composite theories from ab-initio computations.…”

“…We consider models where the Higgs doublet is a TCπ made of two TC-fermions, FF c if G TC = SU(N ) TC and FF otherwise. 18 We then 16 State-of-the-art lattice simulations [43][44][45] are providing vital informations on the pattern of chiral symmetry breaking, spin-one spectrum, decay constants, TC-fermion mass dependence, and scattering lengths for the minimal fundamental composite Higgs scenario [51] discussed in subsection 3.3, but without TC-scalars. It would be interesting to investigate the dynamics of this theory including TC-scalars, in particular to estimate the spectrum of composite baryons constituted by a TC-fermion and a TC-scalar.…”

Nonperturbative analysis of the spectrum of meson resonances in an ultraviolet-complete composite-Higgs model

“…The resonance masses in units of f ≡ √ 2F G may be compared with recent lattice studies of the same model [73,74], which provide scalar and vector masses in the same units. 10 Actually, the lattice simulations performed to date for this model are available only for an underlying SU (2) gauge theory, thus equivalent to the special case Sp(2) of our more general Sp(2N ) study.…”

Flavour anomalies after the R K ∗ measurement

“…In view of the resulting breaking of the TC-chiral symmetry, the Higgs doublet H (identified with pseudo Goldstone bosons of the theory) and other composite scalars remain lighter. Lattice simulations [89][90][91] of the most minimal fundamental composite theories [92][93][94], without techni-scalars, have demonstrated the actual occurrence of chiral symmetry breaking with the relevant breaking pattern, and furthermore provided the spectrum of the spin one vector and axial techni-resonances with masses m V = 3.2(5) TeV/ sin θ and m A = 3.6(9) TeV/ sin θ where θ is the electroweak embedding angle to be determined by the dynamics, that must be smaller than about 0.2.…”