Bottomonium production associated with a photon at a high luminosity $e^{+}{e}^{-}$ collider with next-to-leading order QCD corrections

Abstract

We make a detailed discussion on the one-loop QCD correction to the bottomonium production associated with a photon, i.e. via the channel $e^{+}{e}^{-}\to {\gamma }^{\ast }/Z^0\to |H_{b\bar{b}}⟩+\gamma$, where $|H_{b\bar{b}}⟩$ stands for the color-singlet bottomonium state as ${\eta }_b$, ${\rm Y}$, $h_b$ or ${\chi }_{bJ}$ ($J$=0, 1 or 2), respectively. At the super $Z$ factory with the collision energy $E_{cm}\sim m_Z$, by summing up the cross sections for all bottomonium states, we obtain a large one-loop QCD correction, i.e. $|R|\sim 30\%$. This ensures the necessity and importance of the one-loop QCD corrections for the present processes. Further more, for the ${\eta }_b$, $h_b$ and ${\chi }_{bJ}$ production, their cross sections are dominated by the $s$-channel diagrams and are enhanced by the $Z^0$ boson resonance effect when $E_{cm}\sim m_Z$. While, for the ${\rm Y}$ production, such resonance effect shall be smeared by a large $t(u)$-channel contribution that dominant over the $s$-channel one. Theoretical uncertainties caused by slight change of $E_{cm}$, the $b$-quark mass, the renormalization scale and etc. have been presented. At the super $Z$ factory with a high luminosity up to $\mathcal{L}=10^{36}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$, the bottomonium plus one photon events are sizable, especially for ${\eta }_b$ and ${\rm Y}$, which have large signal significance. Summing up all bottomonium states, we shall totally have $\sim 3.8\times 10^5$ bottomonium events in one operation year. So, the super $Z$ factory shall provide a good platform for studying the bottomonium properties.

15 pages, 9 figures. Discussions improved, to be published in Phys.Rev.D

References in corpus (8)

• Algorithm FIRE -- Feynman Integral REduction
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• $Apart: A Generalized Mathematica Apart Function
• QCD corrections to J/psi plus eta_c production in e+e- annihilation at sqrt{s}=10.6 GeV
• Spectrum for Heavy Quankonia and Mixture of the Relevant Wave Functions within the Framework of Bethe-Salpeter Equation
• Exclusive heavy quarkonium + gamma production from e+ e- annihilation into a virtual photon
• Production of a Heavy Quarkonium with a Photon or via ISR at $Z$ Peak in $e^{+}{e}^{-}$ Collider
• Next-to-leading order QCD corrections for the charmonium production via the channel $e^{+}{e}^{-}\to H(|c\bar{c}⟩)+\gamma$ round the $Z^0$ peak

Cited by in corpus (4)

• $Z$ boson radiative decays to a $S$-wave quarkonium at NNLO and NLL accuracy
• $Z$ boson radiative decays to a $P$-wave quarkonium at NNLO and LL accuracy
• Photoproduction of the $B_c$ meson at the future $e^{+}{e}^{-}$ colliders
• Inclusive productions of ${\rm Y}(1S,2S,3S)$ and ${\chi }_b(1P,2P,3P)$ via the Higgs boson decay