New universality class of chiral symmetry breaking in the strongly coupled U(1) $\chi U \phi$ model

Abstract

We describe a 4D U(1) lattice gauge theory with charged scalar $\phi$ and fermion $\chi$ matter fields ($\chi U \phi$ model). At sufficiently strong gauge coupling, the chiral symmetry is broken and the mass of the unconfined composite fermion $F = \bar{\chi} \phi $ is generated dynamically by gauge interaction. The scalar supresses this symmetry breaking and induces a line of second order transitions with scaling properties similar to the Nambu--Jona-Lasinio model. However, in the vicinity of a particular, tricritical point the scaling properties are different. Here we study the effective Yukawa coupling between the massive fermion and the Goldstone boson. The perturbative triviality bound of Yukawa models is nearly saturated. The theory is similar to strongly coupled Yukawa models except the occurrence of an additional state -- a gauge ball of mass $m_S \simeq 1/2 m_F$. This, and non-classical values of tricritical exponents suggest that at the tricritical point the $\chi U \phi$ model constitutes a new universality class. Nevertheless, it might be a microscopic model for the Higgs-Yukawa mechanism of symmetry breaking.