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

TL;DR

This paper uses nonrelativistic QCD to study double charmonia production in Upsilon decays, predicting branching fractions and explaining the nature of certain exotic states, with implications for future experiments.

Contribution

It provides a theoretical analysis of Upsilon decay channels into double charmonia, including explanations for X(3940) and X(4160) as specific S-wave states, and predicts measurable branching fractions for future experiments.

Findings

X(3940) and X(4160) are compatible with being 3S and 4S charmonium states.

Predicted branching fractions for certain decay channels are around 10^{-6}.

The study offers testable predictions for Belle-II experiments.

Abstract

In this paper, we study double charmonia production in Upsilon peaks, especially, a S-wave charmonium $\eta_c$ and a P-wave charmonium $h_c(^1P_1)$, 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 $\Upsilon(nS)$ 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 $3 ^1S_0$ and $4 ^1S_0$ states, respectively, are compatible with the observed upper limits for the branching fractions of $\Upsilon(1S,2S)\to J/\psi+X$, where $X=X(3940)$, $X(4160)$ by the Belle Collaboration. The branching fractions of $\Upsilon(1S,2S,3S)\to \eta_c+h_c(^1P_1)$ are predicted to be around $10^{-6}$, which shall be tested in Belle-II experiments.