  We study isolated singularities of two dimensional Yang-Mills-Higgs fields
defined on a fiber bundle, where the fiber space is a compact Riemannian
manifold and the structure group is a compact connected Lie group. In general
the singularity can not be removed due to possibly non-vanishing limit holonomy
around the singular points. We establish a sharp asymptotic decay estimate of
the Yang-Mills-Higgs field near a singular point, where the decay rate is
precisely determined by the limit holonomy. Our result can be viewed as a
generalization of the classical removable singularity theorem of two
dimensional harmonic maps.
