Static Spherically Symmetric Monopole Solutions to the Yang–Mills–Higgs Model Coupled with a Dilaton

In this work, we investigate the solutions to the governing equations of the Yang–Mills–Higgs model coupled with a dilaton. These solutions describe energy-minimizing static spherically symmetric field configurations with unit topological charge. We analyze the equations for different values of the Higgs self-coupling parameter β. For any Higgs self-coupling parameter β > 0, we use a regularization method to obtain the full set of boundary conditions. In the weak coupling limit β → 0, we derive the monotonicity of the solutions. In the limit β → ∞, the governing system reduces to the equation governing a single dilaton field. We find that the Euler–Lagrange equation is equivalent to a first-order Bogomol’nyi–Prasad–Sommerfield (BPS) equation, which admits an explicit solution. Furthermore, for any β > 0, we derive the energy bounds using the monotonicity of the energy function with respect to β and calculate the magnetic charge.