Numerical and asymptotic analysis of the 't Hooft-Polyakov magnetic monopole

TL;DR

This paper presents a high-precision numerical study of the 't Hooft-Polyakov magnetic monopole equations, refining previous asymptotic analyses and providing detailed monopole mass dependence on the Higgs to gauge boson mass ratio.

Contribution

It introduces advanced numerical methods to accurately compute monopole mass across a wide parameter range and corrects earlier asymptotic results for small beta values.

Findings

Precise monopole mass as a function of beta.

Correction of previous asymptotic analysis for small beta.

Enhanced numerical techniques for monopole solutions.

Abstract

A high precision numerical analysis of the static, spherically symmetric SU(2) magnetic monopole equations is carried out. Using multi-shooting and multi-domain spectral methods, the mass of the monopole is obtained rather precisely as a function of $\beta=M_H/M_W$ for a large $\beta$-interval ($M_H$ and $M_W$ denote the mass of the Higgs and gauge field respectively). The numerical results necessitated the reexamination and subsequent correction of a previous asymptotic analysis of the monopole mass in the literature for $\beta\ll1$.