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Mixed Electroweak-QCD Corrections to $H\to γγ$

Wen-Long Sang, Feng Feng, Yu Jia

TL;DR

This paper computes the complete three-loop mixed electroweak–QCD correction ${\cal O}(\alpha\alpha_s)$ to $H\to\gamma\gamma$, using three on-shell $\alpha$ schemes and a full on-shell renormalization framework. The authors decompose the amplitude into a single form factor $T_4$, extract it with covariant projectors, and evaluate all three-loop diagrams with state-of-the-art algebraic and numerical tools, verifying Ward identities. They find the mixed correction can reach ${\sim}0.5$–$0.6\%$ of the LO width (larger than the pure ${\cal O}(\alpha_s^2)$ term) and that including it substantially reduces scheme dependence, yielding state-of-the-art SM predictions: $\Gamma(H\to\gamma\gamma)=9.389\div 9.420$ keV and ${\cal B}(H\to\gamma\gamma)=(2.31\pm 0.09)\times 10^{-3}$. These results provide essential theoretical benchmarks for precision Higgs physics at current and future colliders.

Abstract

We present for the first time the complete three-loop mixed electroweak-QCD ($\mathcal{O}(αα_s)$) corrections for the decay channel $H \to γγ$, by implementing three different on-shell $α$ schemes in computing the electroweak correction. Our studies indicate that the $\mathcal{O}(α_s)$ correction amounts to approximately $1.7\%$ of the leading-order prediction for the diphoton width, while the $\mathcal{O}(α)$ correction varies from $-4.8\%$ to $1.4\%$ depending on the specific $α$ scheme. The three-loop mixed electroweak-QCD correction may reach $0.6\%$, $0.5\%$, and $0.2\%$ of the LO diphoton width in $α(0)$, $α(M_Z)$, and $G_μ$ schemes, respectively, which is much more significant than the less-than-$0.1\%$ contribution from the three-loop QCD correction. It is also worth noting that the inclusion of the ${\cal O}(αα_s)$ correction significantly reduces the scheme dependence of the partial width from $0.6$ keV at leading order down to $0.03$ keV. The state-of-the-art Standard Model predictions are $Γ[H \to γγ] = 9.389÷9.420$ keV, providing a valuable theoretical benchmark for future Higgs factory collider program.

Mixed Electroweak-QCD Corrections to $H\to γγ$

TL;DR

This paper computes the complete three-loop mixed electroweak–QCD correction to , using three on-shell schemes and a full on-shell renormalization framework. The authors decompose the amplitude into a single form factor , extract it with covariant projectors, and evaluate all three-loop diagrams with state-of-the-art algebraic and numerical tools, verifying Ward identities. They find the mixed correction can reach – of the LO width (larger than the pure term) and that including it substantially reduces scheme dependence, yielding state-of-the-art SM predictions: keV and . These results provide essential theoretical benchmarks for precision Higgs physics at current and future colliders.

Abstract

We present for the first time the complete three-loop mixed electroweak-QCD () corrections for the decay channel , by implementing three different on-shell schemes in computing the electroweak correction. Our studies indicate that the correction amounts to approximately of the leading-order prediction for the diphoton width, while the correction varies from to depending on the specific scheme. The three-loop mixed electroweak-QCD correction may reach , , and of the LO diphoton width in , , and schemes, respectively, which is much more significant than the less-than- contribution from the three-loop QCD correction. It is also worth noting that the inclusion of the correction significantly reduces the scheme dependence of the partial width from keV at leading order down to keV. The state-of-the-art Standard Model predictions are keV, providing a valuable theoretical benchmark for future Higgs factory collider program.

Paper Structure

This paper contains 10 sections, 15 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Building diphoton width out of form factors
  3. LO result for $H\to\gamma\gamma$
  4. On-shell renormalization scheme
  5. Outline of Calculation
  6. Phenomenology
  7. Input parameters
  8. Numerical predictions for $T_4$
  9. Numerical predictions for diphoton width and branching fraction
  10. summary

Figures (3)

  • Figure 1: Some representative LO diagrams for $H\to \gamma\gamma$.
  • Figure 2: Some representative two-loop diagrams for $H\to \gamma\gamma$. $(a)$ represents a sample diagram for the NLO QCD correction, while $(b)$-$(f)$ represent sample diagrams for NLO electroweak correction.
  • Figure 3: Some representative three-loop diagrams for $H\to \gamma\gamma$. $(a)$ represents a sample diagram for the NNLO QCD correction, while $(b)$-$(f)$ represent sample diagrams for the NNLO ${\cal O}(\alpha \alpha)_s$ correction.