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It is well know that the precise measurement of $H\to\gamma\gamma$ cangenerate two degenerate parameter spaces of $H\gamma\gamma$ anomalous coupling.We propose to utilize the exclusive Higgs rare decays $H\to\Upsilon(ns)+\gamma$to break above mentioned degeneracy and further to constrain the$H\gamma\gamma$ anomalous coupling at the HL-LHC. We demonstrate that thebranching ratios of $H\to\Upsilon(ns)+\gamma$ can be significantly enhanced inthe non-SM-like parameter space from $H\to\gamma\gamma$ measurement, due to thedestructive interference between the direct and indirect production of$\Upsilon(ns)$ in the SM. By applying the NRQCD factorization formalism, wecalculate the partial decay widths of $H\to\Upsilon(ns)+\gamma$ at the NLOaccuracy of $\alpha_s$. We show that it is hopeful to break such degenerateparameter space at the HL-LHC if we can further highly suppress the backgroundand enhance the signal efficiency compared to the ATLAS preliminary simulation.

Probing the $H\gamma\gamma$ coupling via Higgs exclusive decay into quarkonia plus a photon at the HL-LHC