The structure of cosmic strings of a $U(1)$ gauge field for the conservation of $B-L$

TL;DR

This paper extends the Standard Model by gauging the B-L symmetry with an Abelian gauge field, introduces a non-standard Higgs field to give mass to right-handed neutrinos, and analyzes the formation of cosmic strings through numerical solutions of the coupled field equations.

Contribution

It proposes a consistent B-L extension with a non-standard Higgs field and studies cosmic string formation via numerical solutions of the coupled fields.

Findings

Cosmic string profiles depend on Higgs winding numbers.

Boundary conditions are satisfied in the numerical solutions.

The model naturally conserves B-L with minimal additional fields.

Abstract

We consider an extension of the Standard Model, where the difference between the baryon number $B$ and the lepton number $L$ is gauged with an Abelian gauge field, in order to explain the exact conservation of $B-L$. To avoid a gauge anomaly, we add a right-handed neutrino $\nu_{\rm R}$ to each fermion generation. Here it is not sterile, so the usual Majorana term is excluded by gauge invariance. We provide a mass term for $\nu_{\rm R}$ by adding a non-standard 1-component Higgs field, thus arriving at a consistent extension of the Standard Model, where the conservation of $B-L$ is natural, with a modest number of additional fields. We study the possible formation of cosmic strings by solving the coupled field equations of the two Higgs fields and the non-standard U(1) gauge field. Numerical methods provide the corresponding string profiles, depending on the Higgs winding numbers, such that the appropriate boundary conditions in the string center and far from it are fulfilled.