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

## TL;DR

This paper compares the dispersion method and dimensional regularization in calculating the $H o Z \gamma$ decay amplitude, demonstrating their agreement and highlighting the dispersion method's advantage of avoiding regularization.

## Contribution

It shows that the dispersion method, respecting the Goldstone boson equivalence theorem, yields results consistent with dimensional regularization in the $H o Z \gamma$ decay calculation.

## Key findings

- Dispersion method results coincide with DimReg when GBET boundary conditions are used.
- Dispersion method works with finite quantities, eliminating the need for regularization.
- Both methods produce identical decay amplitudes under the specified conditions.

## 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.