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 studies on the inclusive productions of $\\Upsilon(nS)$ and $\\chi_b(nP)$ ($n=1,2,3$) via the 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, we find that the 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 enlarging 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 nonnegligible 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 clearly indicates the abilities of these processes to be detected at the high energy colliders.