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

Abstract

We investigate the \(J/\psi\) direct production mechanism in the rare exclusive Higgs decay \(H\to J/\psi+\gamma\) 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 \(J/\psi\) and the N\(^2\)LO perturbative result, we extract the factorization-scale-dependent long-distance matrix element \(\langle J/\psi({\bm \epsilon})|\psi^{\dagger}{\bm \sigma}\cdot{\bm \epsilon}\chi(\mu_\Lambda) |0\rangle\). 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 \(\Gamma(H\to J/\psi+\gamma)\) is more robust and precise, with good convergence and no renormalization- or factorization-scale dependence. We find \(\Gamma(H\to J/\psi+\gamma) = (6.4574^{+0.3995}_{-0.3995}) \times 10^{-11}\) GeV, where the uncertainty is the quadratic sum of contributions from \(\Delta\alpha_s(m_Z) = \pm 0.0009\), \(\Delta\Gamma_{J/\psi\to e^+e^-} = \pm 0.10\ \text{GeV}\), \(\Delta\overline{m}_c(\overline{m}_c) = \pm 0.0046\ \text{GeV}\), 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.