Two-loop QCD corrections to $\eta_b \to J/\psi + \gamma$

TL;DR

This paper calculates next-to-leading-order QCD corrections to the rare decay of eta_b into J/psi and a photon, significantly refining the predicted branching ratio and reducing theoretical uncertainties within the NRQCD framework.

Contribution

It provides the first complete NLO QCD correction calculation for the eta_b to J/psi gamma decay, including both one-loop and two-loop contributions, enhancing theoretical precision.

Findings

Branching ratio increases by a factor of about 3.65 at NLO.

Renormalization scale dependence is reduced at NLO.

Theoretical uncertainties from scale and mass variations are discussed.

Abstract

We present a next-to-leading-order (NLO) analysis of the rare radiative decay $\eta_b \to J/\psi\gamma$, a flavor-changing transition between bottomonium and charmonium, within the framework of non-relativistic QCD (NRQCD). We systematically compute the complete $\mathcal{O}(\alpha_s)$ corrections, which include the one-loop QCD corrections to the QED-initiated amplitudes and the two-loop corrections to the QCD-initiated ones. The branching ratio is enhanced from $2.06^{+2.82}_{-1.32}\times10^{-7}$ at LO to $7.53^{+5.67}_{-1.16}\times10^{-7}$ at NLO, representing an increase by a factor of about 3.65. The theoretical uncertainties caused by renormalization scale and $m_{b/c}$ masses are also discussed. Furthermore, the renormalization scale dependence is reduced at NLO.