Fundamental partial compositeness

Abstract

We construct renormalizable Standard Model extensions, valid up to the Planck scale, that give a composite Higgs from a new fundamental strong force acting on fermions and scalars. Yukawa interactions of these particles with Standard Model fermions realize the partial compositeness scenario. Under certain assumptions on the dynamics of the scalars, successful models exist because gauge quantum numbers of Standard Model fermions admit a minimal enough 'square root'. Furthermore, right-handed SM fermions have an SU(2) R -like structure, yielding a custodially-protected composite Higgs. Baryon and lepton numbers arise accidentally. Standard Model fermions acquire mass at tree level, while the Higgs potential and flavor violations are generated by quantum corrections. We further discuss accidental symmetries and other dynamical features stemming from the new strongly interacting scalars. If the same phenomenology can be obtained from models without our elementary scalars, they would reappear as composite states.

Flavour anomalies after the R K ∗ measurement

“…Fundamental theories with a Higgs as a composite state that are also able to generate SM fermion masses appeared in ref. [82]. These theories feature both techni-scalars S and techni-fermions F .…”

“…The composite theory does not address the SM naturalness issue and it is fundamental in the sense that it can be extrapolated till the Planck scale [82]. Having a fundamental theory of composite Higgs, we use it to investigate the flavour anomalies.…”

“…In general, there can be a flavour-violating mixing matrix in the lepton sector. In particular, the mixing angle θ eµ generates µ → eγ, but only when effects at higher order in the Yukawa couplings are included [82]. Focusing on effects enhanced by the large coupling y Lµ one has…”

SU(2) with fundamental fermions and scalars

“…In order to overcome these difficulties, a model of "fundamental" partial compositeness has recently been proposed [15]. This is a composite Goldstone Higgs model in which the new strongly interacting sector contains as matter fields not only fermions (F ), but also strongly interacting scalars (S).…”

“…The baryonic operator F S has an engineering dimension of 5/2, therefore requiring no large anomalous dimensions. It can also be argued that since any purely fermionic model of partial compositeness must involve baryons with scaling dimensions close to 5/2, these baryons would effectively behave as if they were made by a fermion and a composite scalar similar to the fundamental scalar appearing in this model [15]. An interesting feature of this new kind of composite Higgs model is that it can be used to simultaneously explain the R K , R K * and g − 2 anomalies provided the Yukawa coupling to the muon is large (∼ 1.5) [16].…”