Standard Model Without Elementary Scalars And High Energy Lorentz Violation

TL;DR

This paper proposes a Lorentz-violating extension of the Standard Model that, through dynamical symmetry breaking, reproduces low-energy physics with composite Higgs bosons, avoiding non-renormalizable ambiguities.

Contribution

It introduces a scalar-suppressed, Lorentz-violating Standard Model variant that achieves dynamical symmetry breaking and generates Standard Model particles as composites.

Findings

Lorentz violation does not affect low-energy physics

Fermion and gauge boson masses are generated dynamically

Predicts relations among Standard Model parameters

Abstract

If Lorentz symmetry is violated at high energies, interactions that are usually non-renormalizable can become renormalizable by weighted power counting. Recently, a CPT invariant, Lorentz violating extension of the Standard Model containing two scalar-two fermion interactions (which can explain neutrino masses) and four fermion interactions (which can explain proton decay) was proposed. In this paper we consider a variant of this model, obtained suppressing the elementary scalar fields, and argue that it can reproduce the known low energy physics. In the Nambu--Jona-Lasinio spirit, we show, using a large N_c expansion, that a dynamical symmetry breaking takes place. The effective potential has a Lorentz invariant minimum and the Lorentz violation does not reverberate down to low energies. The mechanism generates fermion masses, gauge-boson masses and scalar bound states, to be identified with composite Higgs bosons. Our approach is not plagued by the ambiguities of approaches based on non-renormalizable vertices. The low-energy effective action is uniquely determined and predicts relations among parameters of the Standard Model.