Prediction of a missing higher charmonium around 4.26 GeV in $$J/\psi $$ J / ψ family

Abstract

Inspired by the similarity between the mass gaps of the J/ψ and ϒ families, the prediction of a missing higher charmonium with mass 4,263 MeV and very narrow width is made. In addition, the properties of two charmonium-like states, X (3940) and X (4160), and charmonium ψ(4415) are discussed, where our calculation shows that X (3940) as η c (3S) is established, while the explanation of X (4160) to be η c (4S) is fully excluded and that η c (4S) is typically a very narrow state. These predictions might be accessible at BESIII, Belle, and BelleII in near future.Since the observation of J/ψ in 1974 [1,2], the charmonium family has become abundant with more and more such states announced by the experiments [3]. Especially in the past decade, a series of charmonium-like states have been observed, which have further stimulated theorists' extensive interest in revealing their underlying properties (see a recent review in Ref.[4]), since these novel phenomena reflect non-perturbative behavior of quantum chromodynamics (QCD). Among the studies on these states, it is an important research topic for the whole community of particle physics how to identify the exotic states, whose establishment is, of course, tied with our understanding of the charmonium family.When checking the mass spectra of the observed charmonia with spin-parity J PC = 1 −− and comparing them with those of the corresponding bottomonia, we notice that the mass gap between ψ(2S) and J/ψ is almost the same as that between ϒ(2S) and ϒ(1S). There also exist similar mass a e-mail: help08@lzu.edu.cn if ψ(4415) is ψ(4S), such a law is violated since the mass gap of ψ(4415) and ψ(3S) is much larger than that of ϒ(4S) and ϒ(3S).In fact, the properties of the charmonia above 4.1 GeV are still not understood well, which is the possible reason to result in the above puzzling mass gap. In general, compared with the J/ψ family, the bottomonia with the radial quantum numbers n = 1, 2, 3, 4 were well established both by experiment and theory. Thus, the study of the J/ψ family can be borrowed from ϒ family. If this law of mass gap relation still holds for states with n = 3, 4 in J/ψ and ϒ families, we find that the mass of ψ(4S) should be located at 4,263 MeV, where we add the mass gap between ϒ(4S) and ϒ(3S) to the mass of ψ(3S). In Fig. 1, we show the details of the mass gaps for J/ψ and ϒ families and compare the corresponding gaps with each other. After obtaining the above prediction, we notice the results of the mass spectra of charmonium family given in Ref. [5], where the screening potential was adopted in their calculation. They also found that the mass of ψ(4S) is about 4,273 MeV, which is consistent with our estimate of the mass for the missing charmonium ψ(4S). Additionally, another theoretical work [6] also supports existence of a missing ψ(4S). In Ref.[6], the color-screening effect was considered in the calculation of the mass spectrum of charmonium, where the mass of ψ(4S) was obtained as 4,247 MeV.If this predicted state exists in the J/ψ family,...

The hidden-charm pentaquark and tetraquark states

“…62 shows the details of the mass gaps for the J/ψ and Υ families. This simple estimate of the mass of the ψ(4S ) [834] is consistent with the results obtained with the screened potential in Refs. [838,601], where the mass of the ψ(4S ) was predicted to be 4247 MeV in Ref.…”

“…However, the η c (4S ) was predicted to lie higher than the X(4160) [813,601]. He et al indicated that the η c (4S ) may have a very narrow width according to their calculation [834].…”

“…In Ref. [834], He et al calculated the two-body open-charm decay widths of the X(3940) as the η c (3S ) charmonium state. However, a problem of the η c (3S ) interpretation of the X(3940) is that its mass is a bit lower than theoretical predictions [813,601].…”

“…[834], He et al noticed the similarity between vector charmonium and bottomonium families. The mass gap between the ψ(2S ) and J/ψ is almost the same as that between the Υ(2S ) and Υ(1S ) and M ψ(3S ) − M ψ(2S ) ≈ M Υ(3S ) − M Υ(2S ) , where the ψ(3686) and ψ(4040) are treated as the ψ(2S ) and ψ(3S ) charmonium states, respectively.…”

“…Until now the bottomonia with the radial quantum numbers n = 1, 2, 3, 4 have been established [1]. If this mass gap relation continues to hold for higher states with n = 3, 4 in J/ψ and Υ families, the mass of the ψ(4S ) should be located at 4263 MeV [834]. Within this framework, the ψ(4415) cannot be treated as the ψ(4S ).…”