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)(P-1(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(1)S(0) and 4(1)S(0) states, respectively, are compatible with the observed upper limits for the branching fractions of Upsilon(1S, 2S) -> J/psi + X, where X = X(3940), X(4160) by the Belle Collaboration. The branching fractions of Upsilon(1S, 2S, 3S) -> eta(c) + h(c)(P-1(1)) are predicted to be around 10(-6), which shall be tested in Belle-II experiments.
key laboratory grant from the Office of Science and Technology, Shanghai Municipal Government [11DZ2260700]
; Shanghai Natural Science Foundation [15ZR1423100]
; State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China [Y5KF111CJ1]