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.
Highlights
The calculation of the Higgs decay rate into two photons through the W-loop has become the subject of a controversy
We have calculated the W-loop contribution to the amplitude of the decay H → Z þ γ in two different methods: (1) in the Rξ-gauge using dimensional regularization (DimReg), and (2) in the unitary gauge through the dispersion method
The problem with the dispersion method is that it determines the amplitude merely up to an additive subtraction constant
Summary
The calculation of the Higgs decay rate into two photons through the W-loop has become the subject of a controversy. Responding to a criticism, [7], which points out that the delicate cancellation of divergences is ambiguous and one needs a regularization, the result of [5] was confirmed in [8] by applying unsubtracted dispersion relations in a calculation that deals only with absolutely convergent integrals. Before we go into the details it shall be mentioned that in this study we have used a couple of helpful Mathematica packages, [18,19,20,21,22,23]
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