We present a next-to-leading-order (NLO) analysis of the rare radiative decay ηb→J/ψγ, a flavor-changing transition between bottomonium and charmonium, within the framework of non-relativistic QCD (NRQCD). We systematically compute the complete O(αs) 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 2.06−1.32+2.82×10−7 at LO to 7.53−1.16+5.67×10−7 at NLO, representing an increase by a factor of about 3.65. The theoretical uncertainties caused by renormalization scale and mb/c masses are also discussed. Furthermore, the renormalization scale dependence is reduced at NLO.
@article{arxiv.2603.14847,
title = {Two-loop QCD corrections to $\eta_b \to J/\psi + \gamma$},
author = {Hao Yang and Lin Zuo and Bingwei Long},
journal= {arXiv preprint arXiv:2603.14847},
year = {2026}
}