Exclusive decay of the upsilon into $h_c$, the $X(3940)$ and $X(4160)$

摘要: In this paper, we study double charmonia production in Upsilon peaks, especially, a S-wave charmonium ηc and a P-wave charmonium hc(1P1), or a S-wave charmonium J/ψ 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 JPC=1−− state Υ(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 ΛQCD. Explanation of the X(3940) and X(4160) as the 31S0 and 41S0 states, respectively, are compatible with the observed upper limits for the branching fractions of Υ(1S,2S)→J/ψ+X, where X=X(3940), X(4160) by the Belle Collaboration. The branching fractions of Υ(1S,2S,3S)→ηc+hc(1P1) are predicted to be around 10−6, which shall be tested in Belle-II experiments.