Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium

Abstract

Abstract Within the framework of nonrelativistic QCD (NRQCD) factorization, we calculate the next-to-leading-order (NLO) perturbative corrections to the radiative decay Υ → η c (χ cJ ) + γ. Both the helicity amplitudes and the helicity decay widths are obtained. It is the first computation for the processes involving both bottomonium and charmonium at two-loop accuracy. By employing the Cheng-Wu theorem, we are able to convert most of complex-valued master integrals (MIs) into real-valued MIs, which makes the numerical integration much efficient. Our results indicate the O α s $$ \mathcal{O}\left({\alpha}_s\right) $$ corrections are moderate for η c and χ c2 production, and are quite marginal for χ c0 and χ c1 production. It is impressive to note the NLO corrections considerably reduce the renormalization scale dependence in both the decay widths and the branching fractions for χ cJ , and slightly improve that for η c . With the NRQCD matrix elements evaluated via the Buchmüller-Tye potential model, we find the decay width for η c production is one-order-of-magnitude larger than χ cJ production, which may provide a good opportunity to search for Υ → η c + γ in experiment. In addition, the decay width for χ c1 production is several times larger than those for χ c0,2. Finally, we find the NLO NRQCD prediction for the branching fraction of Υ → χ c1 + γ is only half of the lower bound of the experimental data measured recently by Belle. Moreover, there exists serious contradiction between theory and experiment for Υ → η c + γ. The discrepancies between theory and experiment deserve further research efforts.

Keywords

• NLO Computations
• QCD Phenomenology