Two-loop electroweak corrections to the Higgs-boson decay H -> gamma gamma

TL;DR

The paper delivers a full two-loop electroweak calculation for the Higgs decay to two photons, focusing on heavy-boson and top-quark contributions and integrating them with previously known light-fermion EW and QCD corrections. By employing the Background Field Method, renormalization in the on-shell scheme, and a Taylor expansion in $q_{4w}$ with Tarasov reduction, the authors obtain finite, gauge-invariant results for the 1PI heavy-sector corrections. Numerically, the heavy-sector corrections are moderate and negative in the Higgs mass range $100$–$150$ GeV, and the total EW+QCD correction remains under $1.5\%$, indicating a highly stable perturbative prediction for $\Gamma(H\to\gamma\gamma)$. The results enhance the precision of SM predictions and provide a stringent testable target for future high-precision measurements.

Abstract

The complete set of two-loop electroweak corrections to the decay width of the Higgs boson into two photons is presented. Two-loop contributions involving weak bosons and the top quark are computed in terms of an expansion in the Higgs external momentum. Adding these results to the previously known light fermion contributions, we find that the total electroweak corrections for a Higgs boson with 100 GeV <m_H < 150 GeV are moderate and negative, between -4% < delta_EW < 0%. Combination with the QCD corrections, which are small and positive, gives a total correction to the one-loop results of | delta_{EW+QCD}|< 1.5 %.

Figures (6)

• Figure 1: Representative diagrams of the one-loop contributions to $H\to \gamma \gamma$. Diagram (a) represents the bosonic contributions where the photons couple to charged bosons, unphysical scalars and ghosts. In diagram (b) the Higgs couples to the fermion line so that only heavy quarks give a non-negligible contribution.
• Figure 2: The three classes of two-loop diagrams contributing to $H\to \gamma \gamma$. Diagram (a) represents purerely bosonic contributions, which are the corrections to the corresponding diagram (a) of Fig. \ref{['fig:one-loop']}. Diagrams (b) and (c) are both corrections to the diagram (b) of Fig. \ref{['fig:one-loop']}. Leptons and light quarks start contributing at two loops through diagrams of type (c).
• Figure 3: Diagram for studying the cut structure of the amplitude.
• Figure 4: A two-loop diagram containing a quadratically divergent subdiagram (self-energy) associated to the unphysical scalars $\phi$.
• Figure 5: Various contributions to $\delta_{EW}$ as a function of the Higgs mass. Lepton (summed over three families) and light quark contributions ($u,d,c,s$) are the two central curves. Purely bosonic (YM) and third generation quarks are the top and the bottom curves respectively. The large top-mass approximation ($m_t^2$), which is a subset of the third generation contribution, is also shown (dotted line).