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.
Highlights
This situation prompted theorists to focus on effective field theories that supposedly capture the low energy manifestation of some unknown underlying strongly-coupled dynamics, especially in the flavor sector
If the same phenomenology can be obtained from models without our elementary scalars, they would reappear as composite states
A detailed dynamical study goes beyond the scope of this work, where we just describe the possible patterns of chiral symmetry breaking in the scalar sector stemming from scalar bilinears
Summary
We consider a theory with gauge group GTC ⊗ GSM and vectorial TC-fermions and TCscalars in the fundamental of GTC with UV Lagrangian. We use a compact notation for the particle spectrum quantum numbers under the SM gauge group GSM = SU(3)c ⊗ SU(2)L ⊗ U(1)Y that we exemplify via the SM fermion fields:. We indicate Weyl TC-fermions by F and generically complex TC-scalars by S. In the following we will consider for GTC either SU(N ), SO(N ) or Sp(N ) gauge groups and we will assume TC-fermions and TC-scalars to live in the fundamental of these groups, which minimize the contributions to gauge β functions, as needed for successful models. We will consider TC-fermions vector-like with respect to GTC (in the SU(N )TC case for each TC-fermion F in the fundamental there will be F c in the anti-fundamental) and to GSM
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