Where are $$\chi _{cJ}(3P)$$ χ c J ( 3 P ) ?

Abstract

In the present work, we propose Y (4140) as the χ c1 (3P) state by studying the χ c1 π + π − invariant mass spectrum of the B → K χ c1 π + π − process. In the DD invariant mass spectrum of the B → K DD process, we find a new resonance with the mass and width to be (4083.0 ± 5.0) and (24.1 ± 15.4) MeV, respectively, which could be a good candidate of the χ c0 (3P) state. The theoretical investigations on the decay behaviors of the χ cJ (3P) in the present work support the assignments of the Y (4140) and Y (4080) as the χ c1 (3P) and χ c0 (3P) states, respectively. In addition, the χ c2 (3P) state is predicted to be a very narrow state. The results in the present work could be tested by further experiments in the LHCb and forthcoming Belle II.When checking the mass spectrum of the charmonia, one can find the charmonia above 4 GeV are not abundant and our understanding of these states is not comprehensive. In the past decade, a number of the charmonium-like states around 4 GeV have been observed experimentally (see Ref.[1] for details), which provides us a good opportunity to expand our knowledge of the charmonia spectrum. For the P wave spintriplet, the ground states have been well established a long time ago, which are χ c0 (3414), χ c1 (3510), and χ c2 (3556) [2]. For the first excitation of the P wave state, the χ c2 (2P) state has been confirmed, which was successively discovered in the γ γ → DD process by Belle and Babar Collaborations [3,4]. X (3915) observed in the γ γ → J/ψω [5,6] and B → K J/ψω [7,8] processes is a candidate of χ c0 (2P), and X (3872) first observed in the B → K J/ψπ + π − process by the Belle Collaboration in 2003 [9], was supported to be χ c1 (2P) [10][11][12][13][14].The mass gap of χ c2 (2P) and χ c2 (1P) is about 370 MeV. By adding this mass gap to the mass of χ c2 (2P), we can roughly estimate that the χ c2 (3P) states should be below 4.3 GeV, since the mass gaps become smaller with the radial quantum number increasing. Thus, the masses of the a e-mail: chendy@impcas.ac.cn χ cJ (3P) state should be smaller than 4.3 GeV, which indicates that the charmonium-like states below 4.3 GeV with the positive C parity could be the candidates of the χ cJ (3P) states. Very recently, the LHCb Collaboration has confirmed the existence of the Y (4140) and the J PC quantum numbers were determined to be 1 ++ [15,16], so it could be a candidate of the χ c1 (3P) state.Y (4140) was first observed by the CDF Collaboration in the J/ψφ invariant mass spectrum in the exclusive B + → J/ψφ K + decays with a statistical significance of the signal being 3.8σ [17]. The mass and width of the structure were 4143.0 ± 2.9(stat.) ± 1.2(syst.) MeV and 11.7 +8.3 −5.0 (stat.) ± 3.7(syst.) MeV, respectively [17]. Later, the Belle Collaboration measured the cross sections for the γ γ → J/ψφ and found no evidence of Y (4140) [22], which would rule out the J PC = 0 ++ , 2 ++ assignment for the Y (4140). In 2011, the CDF Collaboration reanalyzed the process B ± → J/ψφ K ± with a larger data sample [18]. The obtained ...

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