Analysis of $H \to J/\psi+\gamma$ up to Next-to-Next-to-Leading Order QCD Corrections

Abstract

The rare exclusive decay of the Higgs boson $H \to J/\psi + \gamma$ is an important channel for measuring the Yukawa coupling of the charm quark. In this article, we analyze the process by employing the Principle of Maximum Conformality (PMC) up to the next-to-next-to-leading order (NNLO) in QCD. Conventional scale setting leads to theoretical predictions affected by errors dominated by renormalization scale uncertainty. The PMC provides a systematic method to eliminate this renormalization scale uncertainty by resumming non-conformal $\beta$ contributions into the QCD running coupling via renormalization group equation (RGE). We obtain a PMC scale result of $Q_\star = 3.29\ \text{GeV}$, which reflects the low virtuality of the underlying QCD dynamics for the $H \to J/\psi + \gamma$ process. In fact, this is an order of magnitude smaller than the guessed scale using the conventional method, i.e., $\mu_r = m_H/2$. By removing non-conformal $\{\beta_i\}$-terms from the perturbative QCD (pQCD) series, the PMC eliminates renormalization scale uncertainty. Comparing results, we find that the PMC NLO QCD correction term is significantly enhanced, while the PMC NNLO QCD correction is suppressed. This indicates improved convergence of the pQCD series up to NNLO. Finally, we determine the decay width $\Gamma(H \to J/\psi + \gamma) = 14.183^{+0.249}_{-0.347} \pm 0.022$ eV, where the first error arises from the factorization scale $\mu_\Lambda \in [1, 2]\ \text{GeV}$, and the second error from estimating unknown higher-order terms using the Pade approximant approach. The corresponding branching fraction is $\mathcal{B}(H \to J/\psi + \gamma) = 3.485_{-0.161}^{+0.152} \times 10^{-6}$.