Testing a non-perturbative mechanism for elementary fermion mass generation: lattice setup

¹ Johann Wolfgang Goethe-Universität Frankfurt am Main, Institut für Theoretische Physik, Max-von-Laue-Straße 1, D-60438 Frankfurt am Main, Germany
² Dipartimento di Fisica, Università di Roma “Tor Vergata” and INFN, Sezione di Roma 2, Via della Ricerca Scientifica - 00133 Rome, Italy
³ Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Compendio del Viminale, Piazza del Viminiale 1, I-00184, Rome, Italy
⁴ Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, Scotland, UK
⁵ Helmholtz Institut für Strahlen-und Kernphysik (Theorie), Nussallee 14-16 Bethe Center for Theoretical Physics, Nussallee 12 Universität Bonn, D-53115 Bonn, Germany

^* Speaker, e-mail: s1459858@sms.ed.ac.uk

Published online: 26 March 2018

Abstract

In this contribution we lay down a lattice setup that allows for the nonperturbative study of a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an “irrelevant” Wilson-like term. Using naive fermions in quenched approximation and based on the renormalizedWard identities induced by purely fermionic chiral transformations, lattice observables are discussed that enable: a) in theWigner phase, the determinations of the critical Yukawa coupling value where the purely fermionic chiral transformation become a symmetry up to lattice artifacts; b) in the Nambu-Goldstone phase of the resulting critical theory, a stringent test of the actual generation of a fermion mass term of non-perturbative origin. A soft twisted fermion mass term is introduced to circumvent the problem of exceptional configurations, and observables are then calculated in the limit of vanishing twisted mass.