Renormalization and Factorization Scale-Invariant Predictions for the Higgs Rare Decay $H\to J/ψ+γ$ via the Principle of Maximum Conformality

Qi-Sha Ran; Xing-Gang Wu; Jiang Yan; Xu-Chang Zheng; Chang-Xin Liu

Renormalization and Factorization Scale-Invariant Predictions for the Higgs Rare Decay $H\to J/ψ+γ$ via the Principle of Maximum Conformality

Qi-Sha Ran, Xing-Gang Wu, Jiang Yan, Xu-Chang Zheng, Chang-Xin Liu

Abstract

We investigate the $J/ψ$ direct production mechanism in the rare exclusive Higgs decay $H\to J/ψ+γ$ within nonrelativistic QCD (NRQCD), which provides a clean probe for extracting the charm-quark Yukawa coupling to the Higgs boson. The Principle of Maximum Conformality (PMC) is used to remove conventional renormalization-scheme and scale ambiguities in the next-to-next-to-leading-order (N$^2$LO) perturbative QCD series. Large logarithmic contributions arising from Yukawa coupling renormalization are resummed, providing a reliable foundation for subsequent analyses. Using the experimentally measured leptonic decay width of $J/ψ$ and the N$^2$LO perturbative result, we extract the factorization-scale-dependent long-distance matrix element $\langle J/ψ({\bm ε})|ψ^{\dagger}{\bm σ}\cdot{\bm ε}χ(μ_Λ) |0\rangle$. Combining this with the factorization-scale-dependent short-distance coefficient, we obtain a factorization-scale-invariant decay width for the channel. Compared with earlier predictions in the literature, our fixed-order result for $Γ(H\to J/ψ+γ)$ is more robust and precise, with good convergence and no renormalization- or factorization-scale dependence. We find $Γ(H\to J/ψ+γ) = (6.4574^{+0.3995}_{-0.3995}) \times 10^{-11}$ GeV, where the uncertainty is the quadratic sum of contributions from $Δα_s(m_Z) = \pm 0.0009$, $ΔΓ_{J/ψ\to e^+e^-} = \pm 0.10\ \text{GeV}$, $Δ\overline{m}_c(\overline{m}_c) = \pm 0.0046\ \text{GeV}$, and the estimated magnitude of N$^3$LO contributions from Bayesian analysis. This work demonstrates for the first time how the PMC can be applied to obtain fixed-order perturbative predictions that are invariant under both renormalization and factorization scale variations.

Renormalization and Factorization Scale-Invariant Predictions for the Higgs Rare Decay $H\to J/ψ+γ$ via the Principle of Maximum Conformality

Abstract

We investigate the

direct production mechanism in the rare exclusive Higgs decay

within nonrelativistic QCD (NRQCD), which provides a clean probe for extracting the charm-quark Yukawa coupling to the Higgs boson. The Principle of Maximum Conformality (PMC) is used to remove conventional renormalization-scheme and scale ambiguities in the next-to-next-to-leading-order (N

LO) perturbative QCD series. Large logarithmic contributions arising from Yukawa coupling renormalization are resummed, providing a reliable foundation for subsequent analyses. Using the experimentally measured leptonic decay width of

and the N

LO perturbative result, we extract the factorization-scale-dependent long-distance matrix element $\langle J/ψ({\bm ε})|ψ^{\dagger}{\bm σ}\cdot{\bm ε}χ(μ_Λ) |0\rangle$. Combining this with the factorization-scale-dependent short-distance coefficient, we obtain a factorization-scale-invariant decay width for the channel. Compared with earlier predictions in the literature, our fixed-order result for $Γ(H\to J/ψ+γ)$ is more robust and precise, with good convergence and no renormalization- or factorization-scale dependence. We find $Γ(H\to J/ψ+γ) = (6.4574^{+0.3995}_{-0.3995}) \times 10^{-11}$ GeV, where the uncertainty is the quadratic sum of contributions from $Δα_s(m_Z) = \pm 0.0009$,

, $Δ\overline{m}_c(\overline{m}_c) = \pm 0.0046\ \text{GeV}$, and the estimated magnitude of N

LO contributions from Bayesian analysis. This work demonstrates for the first time how the PMC can be applied to obtain fixed-order perturbative predictions that are invariant under both renormalization and factorization scale variations.

Paper Structure (21 equations, 2 figures)

This paper contains 21 equations, 2 figures.

Figures (2)

Figure 1: The $\mu_{\Lambda}$-independent total decay width $\Gamma_{\rm dir}(H\to J/\psi+\gamma)$ up to N$^2$LO QCD corrections versus the renormalization scale $\mu_r$ under the conventional and PMC scale-setting methods, respectively. The LO results are the same. The PMC fixed-order predictions are scale-invariant.
Figure 2: Comparison of the calculated central values (CV) of the total decay width $\Gamma_{\rm dir}(H\to J/\psi+\gamma)$ with the predicted credible intervals of the corresponding pQCD approximants (with DoB = $95.5\%$) up to N$^3$LO. The green hollow diamonds and red hollow squares represent the central values of the known fixed-order pQCD predictions obtained using the conventional (Conv.) and PMC scale-setting methods, respectively. The green solid diamonds and red solid squares with error bars represent the predicted credible intervals obtained using the BA method.