Magnetic monopoles in pure SU (2) Yang-Mills theory with a gauge-invariant mass

In this paper, we show the existence of magnetic monopoles in the pure SU(2) Yang-Mills theory when a gauge-invariant mass term is introduced. This result follows from the recent proposal for obtaining gauge field configurations in the Yang-Mills theory from the solutions of the field equations in the "complementary" gauge-scalar model. The gauge-invariant mass term is obtained through a change of variables and a gauge-independent description of the Brout-Englert-Higgs mechanism, which relies neither on the spontaneous breaking of gauge symmetry nor on the assumptions of the nonvanishing vacuum expectation value of the scalar field. We solve under the static and spherically symmetric ansatz the field equations of the SU(2) Yang-Mills theory coupled to a single adjoint scalar field whose radial degree of freedom is eliminated. We show that the solution can be identified with the gauge field configuration of a magnetic monopole with a minimum magnetic charge in the massive Yang-Mills theory. Moreover, we compare the magnetic monopole of the massive Yang-Mills theory obtained in this way with the Wu-Yang magnetic monopole in the pure Yang-Mills theory and the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow gauge-scalar model.