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

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.

9 pages, LaTeX2e, no figures

References in corpus (1)

• Confining strings and RG flow in the (2+1)-dimensional Georgi-Glashow model and its SU(3)-generalization

Cited by in corpus (4)

• String representation of the SU(N)-inspired dual Abelian-Higgs-type theory with the $\Theta$-term
• k-string tensions in the 3-d SU(N) Georgi-Glashow model
• SU(N) fundamental and adjoint confining strings
• Higgs-inspired corrections to the RG flow in the finite-temperature 3D Georgi-Glashow model and its SU(N)-generalization