Accounting for the finiteness of the Higgs-boson mass in the 3D Georgi-Glashow model

TL;DR

This paper investigates the (2+1)-dimensional Georgi-Glashow model with a finite Higgs boson mass, deriving key physical quantities and establishing bounds on the number of colors for the model's validity.

Contribution

It provides new analytical results for the Higgs mass effects in the Georgi-Glashow model and extends the analysis to SU(N), including bounds on the number of colors.

Findings

Derived the Debye mass of the dual photon.

Established an upper bound on the number of colors.

Calculated string tension and rigidity coupling for arbitrary colors.

Abstract

(2+1)-dimensional Georgi-Glashow model is explored in the regime when the Higgs boson is not infinitely heavy, but its mass is rather of the same order of magnitude as the mass of the W boson. In the weak-coupling limit, the Debye mass of the dual photon and the expression for the monopole potential are found. The cumulant expansion applied to the average over the Higgs field is checked to be convergent for the known data on the monopole fugacity. These results are further generalized to the SU(N)-case. In particular, it is found that the requirement of convergence of the cumulant expansion establishes a certain upper bound on the number of colours. This bound, expressed in terms of the parameter of the weak-coupling approximation, allows the number of colours to be large enough. Finally, the string tension and the coupling constant of the so-called rigidity term of the confining string are found at arbitrary number of colours.