The effect of dark strings on semilocal strings

TL;DR

This paper investigates how dark strings influence the stability and properties of semilocal strings within a specific Standard Model limit, revealing conditions under which semilocal strings become stable or unstable due to dark matter interactions.

Contribution

It demonstrates that dark string interactions induce stability in semilocal strings for certain mass ratios, and alters the existence of solution families compared to the non-interacting case.

Findings

Semilocal strings with non-zero condensate exist only above a critical mass ratio.

Dark string interactions lower the energy of semilocal-dark solutions, enhancing stability.

The family of solutions present without interaction disappears when dark strings are introduced.

Abstract

Dark strings have recently been suggested to exist in new models of dark matter that explain the excessive electronic production in the galaxy. We study the interaction of these dark strings with semilocal strings which are solutions of the bosonic sector of the Standard Model in the limit $\sin^2\theta_{\rm w}=1$, where $\theta_{\rm w}$ is the Weinberg angle. While embedded Abelian-Higgs strings exist for generic values of the coupling constants, we show that semilocal solutions with non-vanishing condensate inside the string core exist only above a critical value of the Higgs to gauge boson mass ratio when interacting with dark strings. Above this critical value, which is greater than unity, the energy per unit length of the semilocal-dark string solutions is always smaller than that of the embedded Abelian-Higgs-dark string solutions and we show that Abelian-Higgs-dark strings become unstable above this critical value. Different from the non-interacting case, we would thus expect semilocal strings to be stable for values of the Higgs to gauge boson mass ratio larger than unity. Moreover, the one-parameter family of solutions present in the non-interacting case ceases to exist when semilocal strings interact with dark strings.