Inclusive productions of $\Upsilon(1S,2S,3S)$ and $\chi_b(1P,2P,3P)$ via the Higgs boson decay

Abstract

In this paper, we carry out the complete $\mathcal O(\alpha\alpha_s^{2})$-order study on the inclusive productions of $\Upsilon(nS)$ and $\chi_b(nP)$ ($n=1,2,3$) 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 $^3S_1^{[8]}$ state related processes consisting of $H^0 \to b\bar{b}[^3S_1^{[8]}]+g$ and $H^0 \to b\bar{b}[^3S_1^{[8]}]+Q+\bar{Q}$ ($Q=c,b$) play a vital role in the predictions on the decay widths. Moreover, our newly calculated next-to-leading order QCD corrections to $H^0 \to b\bar{b}[^3S_1^{[8]}]+g$ can enhance its leading-order result by 3-4 times, subsequently magnifying the total $^3S_1^{[8]}$ contributions by about $40\%$. Such a remarkable enhancement will to a large extent influence the phenomenological conclusions. For the color-singlet $^3P_J^{[1]}$ state, in addition to $H^{0} \to b\bar{b}[^3P_J^{[1]}]+b+\bar{b}$, the newly introduced light hadrons associated process, $H^{0} \to b\bar{b}[^3P_J^{[1]}]+g+g$, can also provide non-negligible contributions, especially for $^3P_2^{[1]}$. Summing up all the contributions, we have $\mathcal B_{H^0 \to \chi_b(nP)+X} \sim 10^{-6}-10^{-5}$ and $\mathcal B_{H^0 \to \Upsilon(nS)+X} \sim 10^{-5}-10^{-4}$, which meets marginally nowadays LHC experimental data and can help in understanding the heavy quarkonium production mechanism as well as the Yukawa couplings.