Dynamical Fermion Masses Under the Influence of Kaluza-Klein Fermions and a Bulk Abelian Gauge Field

TL;DR

This paper investigates how a bulk abelian gauge field influences dynamical fermion mass generation on a 3-brane within a 5D space-time, analyzing phase transitions and the effects of extra-dimensional parameters.

Contribution

It introduces a detailed analysis of fermion mass spectrum and symmetry breaking in a 5D brane-world model with a bulk gauge field and Kaluza-Klein fermions, including the effects of the $A_5$ component.

Findings

Finite and vanishing fermion mass phases identified.

Critical values for $A_5$, coupling, and radius determined.

Dependence of fermion masses on extra-dimensional parameters analyzed.

Abstract

The dynamical fermion mass generation on a 3-brane in the 5D space-time is discussed in a model with bulk fermions in interaction with fermions on the brane assuming the presence of a constant abelian gauge field component $A_5$ in the bulk. We calculate the effective potential as a function of the fermion masses and the gauge field component $A_5$. The masses can be found from the stationarity condition for the effective potential (the gap equation). We formulate the equation for the mass spectrum of the 4D--fermions. The phases with finite and vanishing fermion masses are studied and the dependence of the masses on the radius of the 5th dimension is analyzed. The influence of the $A_5$-component of the gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable. The critical values of the $A_5$ field, the coupling constant and the radius are examined.