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

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 $\beta \ll 1$.

14 pages, 3 figures. Minor corrections. Accepted for publication in Phys. Rev. D

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