Eur. Phys. J. C (2010) 65: 523-536
https://doi.org/10.1140/epjc/s10052-009-1211-z

Regular Article - Theoretical Physics

Standard Model without elementary scalars and high energy Lorentz violation

¹ Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Largo Pontecorvo 3, 56127, Pisa, Italy
² Sezione di Pisa, INFN, Pisa, Italy

^* e-mail: damiano.anselmi@df.unipi.it

Received: 6 August 2009
Published online: 25 November 2009

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.