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

TL;DR

This study provides a detailed theoretical analysis of Higgs boson decays into various bottomonium states using nonrelativistic QCD, highlighting significant higher-order corrections and feeddown effects that impact decay predictions.

Contribution

The paper presents the first complete $ ext{O}( ext{α} ext{α}_s^2)$ calculation of inclusive bottomonium production via Higgs decay, including new NLO QCD corrections and detailed feeddown effects.

Findings

NLO QCD corrections significantly enhance decay width predictions.

Feeddown effects from higher excited states are substantial.

Predicted branching ratios are close to current LHC experimental sensitivities.

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.