Asymptotic analysis of the monopole structure

We analyze the behavior of the magnetic-monopole equations as a function of the ratio of Higgs-scalar-to-vector-meson mass $\frac{M_H}{M_W}$. For very small $\frac{M_H}{M_W}$, we find that the mass of the monopole deviates from the Prasad-Sommerfield limit $\frac{M_W}{\alpha }$ by $\frac{M_H}{2\alpha }$, independently of the particular details of the symmetry-breaking potential. In the opposite limit $\frac{M_H}{M_W}\to \infty$, the scalar field contributes negligibly to the mass, which is found to be $\left(\frac{M_W}{\alpha }\right)(1.787-2.228\mathrm{}\frac{M_W}{M_H}+\cdots )$.