$J\mathrm{/}\psi$ associated production with a bottom quark pair from the Higgs boson decay in next-to-leading order QCD

In this work, we investigate the next-to-leading order (NLO) QCD correction to $J\mathrm{/}\psi$ associated production with a bottom quark pair from the Higgs boson decay within the nonrelativistic QCD framework. From numerical results, {we find that the decay width of process $H\to b+J\mathrm{/}\psi +\bar{b}$ at leading order (LO) mainly comes from the contribution of the Fock state ${}^3{S}_1^{(8)}$, and the NLO QCD corrections significantly enhance the decay width at LO accuracy by about 2 times. At NLO accuracy, the Fock states ${}^3{S}_1^{(8)}$ and ${}^3{P}_J^{(8)}$ channels give the main contribution, accounting for about $68\mathrm{\%}$ and $29\mathrm{\%}$ of the total decay width of $J\mathrm{/}\psi$ associated production with a bottom quark pair at NLO accuracy from the Higgs boson decay, respectively. Considering the dominant contribution of color octet (CO) channels at NLO accuracy, the inclusive decay process $H\to b+J/\psi+\bar b + X$ has the potential to be found in future colliders with high energy/luminosity.} The study of $J\mathrm{/}\psi$ associated production with a bottom quark pair from the Higgs boson decay is not only useful to study the mechanism of color-octet, but also to assist in the investigation of the coupling for the Higgs boson with the bottom quark.