Complete Two-Loop Corrections to H -> gamma gamma

TL;DR

The paper delivers a complete numerical computation of the full two-loop QCD and electroweak corrections to the Higgs boson decay H→γγ, without relying on mass or kinematic expansions. It employs a gauge-invariant complex-mass scheme to tame threshold singularities such as the WW threshold and to maintain Ward identities. The main findings show near threshold the corrections are small due to cancellations below threshold, while above threshold the QCD and electroweak corrections are positive, giving up to ~4% enhancement of the decay width. The approach and techniques are general for 1→2 processes at two loops and provide a framework for precision Higgs phenomenology.

Abstract

In this paper the complete two-loop corrections to the Higgs-boson decay, H -> gamma gamma, are presented. The evaluations of both QCD and electroweak corrections are based on a numerical approach. The results cover all kinematical regions, including the WW normal-threshold, by introducing complex masses in the relevant (gauge-invariant) parts of the LO and NLO amplitudes.

Figures (8)

• Figure 1: Symmetries of the $V^{{{E}}}$-family: The first diagram represents the $V^{{{E}}}$-family (a). Its integral remains unchanged by exchanging $m_1\leftrightarrow m_2$ (b) as well as if one interchanges $m_3 \leftrightarrow m_4$ and $p_2 \leftrightarrow -P$ simultaneously (c). The last diagram (d) is a combination of the first (b) and the second (c) symmetry. One can also perform a total reflection of all external momenta, which is not shown in the figure and leaves the integral also unchanged.
• Figure 2: Example of a collinear-divergent two-loop vertex diagram. Dashed lines represent particles with a small mass $m$ and the wavy (external) line is massless. We introduced $L_m = \ln(m^2/|P^2|)$.
• Figure 3: Contraction of a $V^{{{M}}}$ configuration leading to a $\beta^{-1}$-behavior at the normal $m$-threshold.
• Figure 4: The irreducible, scalar, two-loop vertex diagram $V^{{{K}}}$ with logarithmic divergency. Solid lines represent a massive particle with mass $m$, whereas wavy lines correspond to massless particles.
• Figure 5: Real and imaginary part of the one-loop $H \to \gamma \gamma$ amplitude with real and complex $W\,$-boson mass.