Real and complex fundamental partial compositeness

Abstract

We complete the analysis of the effective field theory at the electroweak scale for minimal models of fundamental partial compositeness. Specifically, we consider fermions in the complex and real representation of the gauge group underlying the composite Higgs dynamics, since the pseudo real representation was investigated earlier. The minimal models feature the cosets SU(4)×SU(4)/SU(4) D and SU(5)/SO(5) respectively for the complex and real representations. We determine the vacuum alignment, the electroweak precision constraints as well as additional collider constraints. We finally discuss the main differences among the different models of minimal partial compositeness.

Fundamental Composite Dynamics: A Review

“…The class of models that we shall consider here [115,254,260,261] implement the partial compositeness framework at a microscopic level. This new paradigm was termed Fundamental Partial Compositeness (FPC).…”

“…For complex FPC-color representation the maximum scalar symmetry is U(N S ). Below we will summarize the minimal FPC investigated in [254,260], which corresponds to the template model of Chapter 2, while the generalization to real and complex representations can be found in [261].…”

Flavour observables and composite dynamics: leptons

“…PC for leptons has been considered in , mostly from a low-energy point of view and via holographic methods. More recently, UV complete realizations of partially composite leptons have been envisaged, considering the fundamental degrees of freedom and the dynamics that leads to the bound states that mix linearly with the elementary fermions, which adds structure and potentially correlations to the setups [34][35][36][37][38][39][40]. Some promising scenarios, which are dubbed "fundamental partial compositeness" (FPC) [38][39][40] and will be very briefly reviewed below, assume the fermionic bound states to be composed of an elementary fermion F and a scalar S, each.…”

“…More recently, UV complete realizations of partially composite leptons have been envisaged, considering the fundamental degrees of freedom and the dynamics that leads to the bound states that mix linearly with the elementary fermions, which adds structure and potentially correlations to the setups [34][35][36][37][38][39][40]. Some promising scenarios, which are dubbed "fundamental partial compositeness" (FPC) [38][39][40] and will be very briefly reviewed below, assume the fermionic bound states to be composed of an elementary fermion F and a scalar S, each. The inclusion of scalars has the advantage that the scaling dimension of the corresponding composite operator O F is expected to vary moderately around the canonical value of [O F ] 0 = [F] + [S] = 5/2, which would allow to reproduce a viable spectrum of fermion masses via modest anomalous dimensions.…”

Lepton Flavor in Composite Higgs Models

“…PC for leptons has been considered in , mostly from a low-energy perspective and via holographic methods. UV completions have been envisaged, too, considering the fundamental constituents and the dynamics forming the bound states that mix with the elementary SM-like fermions [37][38][39][40][41][42][43] (see also [44,45]). A subclass, dubbed "fundamental partial compositeness" (FPC) [41][42][43], assumes the composite fermions to consist of an elementary fermion F and a scalar S. In contrast to 3-fermion states, the scaling dimension of the composite operator O 𝐹 is then expected close to the canonical…”