A UV complete compositeness scenario: LHC constraints meet the lattice

Abstract

We investigate a recently proposed UV-complete composite Higgs scenario in the light of the first LHC runs. The model is based on a SU(4) gauge group with global flavour symmetry breaking SU(5) → SO(5), giving rise to pseudo Nambu-Goldstone bosons in addition to the Higgs doublet. This includes a real and a complex electroweak triplet with exotic electric charges. Including these, as well as constraints on other exotic states, we show that LHC measurements are not yet sensitive enough to significantly constrain the model's low energy constants. The Higgs potential is described by two parameters which are on the one hand constrained by the LHC measurement of the Higgs mass and Higgs decay channels and on the other hand can be computed from correlation functions in the UV-complete theory. Hence to exclude the model at least one constant needs to be determined and to validate the Higgs potential both constants need to be reproduced by the UV-theory. Due to its UV-formulation, a certain number of low energy constants can be computed from first principle numerical simulations of the theory formulated on a lattice, which can help in establishing the validity of this model. We assess the potential impact of lattice calculations for phenomenological studies, as a preliminary step towards Monte Carlo simulations.

Radiative contribution to the composite-Higgs potential in a two-representation lattice model

“…In the notation of [17], this result translates toĉ LR = 1 2 (3g 2 + g 2 )(C LR /f 4 P 6 ) = 19(5)(3). Certain combinations ofĉ LR with other low-energy constants in the theory must be of order 10 −2 to reproduce the observed properties of the Higgs boson, so this result implies some amount of fine-tuning in the theory.…”

Effective potential in ultraviolet completions for composite Higgs models

“…The form of the resulting effective potential is very restricted. It depends on just two trigonometric functions of α, and we may take it to be [6,23,32] V eff = const. − A cos(α) + B cos 2 (α) .…”

“…By contrast, the EHC four-fermion interaction ψΨΨΨ allows for a linear coupling of a Standard Model fermion to a hyperbaryon, thereby giving rise to a partially composite state. 32 The basic problem is that the same ETC or EHC dynamics that gives rise to the desired four-fermion interactions can, generically, also give rise to four-fermion interactions ∼ ψψψψ, namely interactions that involve four Standard Model fermions. These interactions will trigger flavor-changing processes that, if too strong, will be in conflict with experiment.…”

“…Of course, one has to take into account quantum effects. If again the theory is nearly conformal, the induced top mass is of order Λ HC z 4−2γ ′ HC , where γ ′ is the (again, approximately constant) anomalous dimension of the 32 In principle, a given EHC theory may induce both ψψΨΨ and ψΨΨΨ type four-fermion interactions, in which case both mechanisms for fermion mass generation will be operative (see, e.g., Ref. [13]).…”

BSM physics and the lattice

“…They are obtained from field correlators in the strongly-interacting sector, as discussed in Refs. [36,35,37]. Even though these computations are very demanding from the numerical point of view, they would yield first principle results that would quantify the viability of this model.…”