The Exclusive Decay of Upsilon into $h_c$, the $X(3940)$ and $X(4160)$

Abstract

In this paper, we study double charmonia production in Upsilon peaks, especially, a S-wave charmonium ${\eta }_c$ and a P-wave charmonium $h_c{(}^1{P}_1)$, or a S-wave charmonium $J/\psi$ and the $X(3940)$ and $X(4160)$ within the nonrelativistic QCD (NRQCD) approach which is a powerful tool to realize the factorization of double charmonia production in electron-positron annihilation. The $J^{PC}=1^{--}$ state ${\rm Y}(nS)$ can provide an ideal laboratory for studying the properties of double-heavy quarkonium and also can separate the perturbative and nonperturbative parts due to the large heavy quark mass compared with the typical hadron scale ${\Lambda }_{QCD}$. Explanation of the $X(3940)$ and $X(4160)$ as the $3^1{S}_0$ and $4^1{S}_0$ states, respectively, are compatible with the observed upper limits for the branching fractions of ${\rm Y}(1S,2S)\to J/\psi +X$, where $X=X(3940)$, $X(4160)$ by the Belle Collaboration. The branching fractions of ${\rm Y}(1S,2S,3S)\to {\eta }_c+h_c{(}^1{P}_1)$ are predicted to be around $10^{-6}$, which shall be tested in Belle-II experiments.

8 pages, 1 figure and 2 tables, published version in PRD

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• Algorithm FIRE -- Feynman Integral REduction
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Cited by in corpus (11)

• Fully-heavy tetraquark spectra and production at hadron colliders
• Hidden charm octet tetraquarks from a diquark-antidiquark model
• Relativistic corrections to the form factors of $B_c$ into $S$-wave Charmonium
• Relativistic corrections to the form factors of $B_c$ into $P$-wave orbitally excited charmonium
• The Strong Decays of X(3940) and X(4160)
• Understanding close-lying exotic charmonia states within QCD sum rules
• Inclusive $h_c$ production and energy spectrum from $e^{+}{e}^{-}$ annihilation at Super $B$ factory
• Factorization for radiative heavy quarkonium decays into scalar Glueball
• Radiative $h_{c/b}$ decays to $\eta$ or ${\eta }^{\prime }$
• The Production of $X(3940)$ and $X(4160)$ in $B_c$ decays
• $X(3860)$ production in association with $J/\psi$ via $e^{+}{e}^{-}$ annihilation at Belle