Dispersion theoretic calculation of the $H\rightarrow Z+\gamma$ amplitude

TL;DR

This paper compares two methods for calculating the W-loop contribution to the Higgs decay into Z and gamma, demonstrating their consistency and the compatibility of dimensional regularization with the dispersion approach using the Goldstone boson equivalence theorem.

Contribution

It introduces a dispersion method calculation of the $H ightarrow Z+\gamma$ amplitude and shows its agreement with traditional dimensional regularization results.

Findings

Dispersion and DimReg methods yield identical results.

The dispersion method with GBET is consistent with DimReg.

Validation of the dispersion approach for Higgs decay amplitude.

Abstract

We have calculated the $W$-loop contribution to the amplitude of the decay $H\rightarrow Z+\gamma$ in two different methods: 1) in the $R_\xi$-gauge using dimensional regularization (DimReg), and 2) in the unitary gauge through the dispersion method. Using the dispersion method we have followed two approaches: i) without subtraction and ii) with subtraction, the subtraction constant being determined adopting the Goldstone boson equivalence theorem (GBET) at the limit $M_W\to 0$. The results of the calculations in $R_\xi$-gauge with DimReg and the dispersion method with the GBET completely coincide, which shows that DimReg is compatible with the dispersion method obeying the GBET.