The dispersion method and dimensional regularization applied to the decay $H \to Z \gamma$

Abstract

We have calculated the $W$-loop contribution to the amplitude of the decay $H \to Z \gamma$ in the unitary gauge through the dispersion method and in the $R_\xi$ gauge using dimensional regularization (DimReg). We show that the results of the calculations with DimReg and the dispersion method, adopting the boundary condition at the limit $M_W \to 0$ defined by the Goldstone boson equivalence theorem (GBET), completely coincide. This implies that the dispersion method obeying the GBET is compatible with DimReg. The advantage of the applied dispersion method is that we work with finite quantities and no regularization is required.