Inclusive productions of ϒ(1S,2S,3S) and χb(1P,2P,3P) via the Higgs boson decay

In this paper, we carry out the complete $\mathcal{O}(\ensuremath{\alpha}{\ensuremath{\alpha}}_{s}^{2})$-order study on the inclusive productions of $\mathrm{\ensuremath{\Upsilon}}(nS)$ and ${\ensuremath{\chi}}_{b}(nP)$ ($n=1$, 2, 3) via the Standard Model Higgs boson decay, within the framework of nonrelativistic QCD. The feeddown effects via the higher excited states are found to be substantial. The color-octet ${^{3}S}_{1}^{[8]}$ state related processes consisting of ${H}^{0}\ensuremath{\rightarrow}b\overline{b}[{^{3}S}_{1}^{[8]}]+g$ and ${H}^{0}\ensuremath{\rightarrow}b\overline{b}[{^{3}S}_{1}^{[8]}]+Q+\overline{Q}$ ($Q=c$, $b$) play a vital role in the predictions on the decay widths. Moreover, our newly calculated next-to-leading order QCD corrections to ${H}^{0}\ensuremath{\rightarrow}b\overline{b}[{^{3}S}_{1}^{[8]}]+g$ can enhance its leading-order result by 3-4 times, subsequently magnifying the total ${^{3}S}_{1}^{[8]}$ contributions by about 40%. Such a remarkable enhancement will to a large extent influence the phenomenological conclusions. For the color-singlet ${^{3}P}_{J}^{[1]}$ state, in addition to ${H}^{0}\ensuremath{\rightarrow}b\overline{b}[{^{3}P}_{J}^{[1]}]+b+\overline{b}$, the newly introduced light hadrons associated process, ${H}^{0}\ensuremath{\rightarrow}b\overline{b}[{^{3}P}_{J}^{[1]}]+g+g$, can also provide non-negligible contributions, especially for ${^{3}P}_{2}^{[1]}$. Summing up all the contributions, we have ${\mathcal{B}}_{{H}^{0}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{b}(nP)+X}\ensuremath{\sim}{10}^{\ensuremath{-}6}--{10}^{\ensuremath{-}5}$ and ${\mathcal{B}}_{{H}^{0}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}(nS)+X}\ensuremath{\sim}{10}^{\ensuremath{-}5}--{10}^{\ensuremath{-}4}$, which meets marginally nowadays LHC experimental data and can help in understanding the heavy quarkonium production mechanism as well as the Yukawa couplings.