Understanding the newly observed Y (4008) by Belle

Very recently a new enhancement around 4.05 GeV was observed by the Belle experiment. We discuss some possible assignments for this enhancement, i.e. the ψ(3S) and DD̄ molecular states. In these two assignments, Y (4008) can decay into J/ψππ with a branching ratio comparable with that of Y (4008) → J/ψππ. Thus, one suggests high energy experimentalists to look for Y (4008) in J/ψππ channel. Furthermore one proposes further experiments to search for the missing channels DD̄, DD̄ +h.c. and especially χcJπ ππ and ηcπ ππ, which will be helpful to distinguish the ψ(3S) and DD̄ molecular state assignments for this new enhancement. PACS. 13.30.Eg 13.75.Lb Very recently the Belle Collaboration observed an enhancement with mass m = 4008±40 −28 MeV and width Γ = 226± 44± 87MeV besides confirming Y (4260) by studying the initial state radiation (ISR) process e+e− → γISRJ/ψπ π [1]. The Belle experiment also indicated that a fit using two interfering Breit–Wigner shapes describes the data better than one that uses only Y (4260) [1]. In this work, we called this new structure Y (4008). Recently, a series of observations of charmonium like states X, Y , Z [2–21] has challenged our understanding of non-perturbative QCD. At present how to understand this new structure is one of the intriguing and challenging topics. This short note is dedicated to a discussion of the possible interpretations for Y (4008). 1 A possible candidate for ψ(3S)? In the known charmonium states listed in the Particle Data Book, only the mass of ψ(4040) is close to that of Y (4008) [22]. At present ψ(4040) is usually considered as the candidate for ψ(3S). The central value of the width of Y (4008) is larger than that of ψ(4040) around 100MeV. However, due to the large error given by the Belle experiment, the mass and width of this new enhancement are consistent with that of ψ(4040). For Y (4008), the Belle experiment also gave B(J/ ψπ+π−) ·Γe+e− = 5.0± 1.4 +6.1 −0.9 eV and 12.4± 2.4 +14.8 −1.1 eV, corresponding to two solutions in fitting the data [1]. As a e-mail: [email protected] a candidate of ψ(3S), the decay width of ψ(4040)→ e+e− is 0.86± 0.07 keV [22]. Using the above values, we can roughly estimate B[Y (4008) → J/ψπ+π−] = 5.8×10−3 and 1.4×10−2 for the above two solutions if Y (4008) is the ψ(3S) state. Due to the large experimental errors, the central value of the former one does not contradict the upper limit of the branching ratio of ψ(4040)→ J/ψπ+π− (B[ψ(4040)→ J/ψπ+π−] < 4×10−3), though the former one is slightly larger than the upper limit of the branching ratio of ψ(4040)→ J/ψπ+π−. At present, only Y (4008)→ J/ψπ+π− values are reported by Belle [1]. If Y (4008) is ψ(3S), B[Y (4008)→ J/ψππ] is comparable with B[Y (4008)→ J/ψπ+π−]. Thus Y (4008) can be found in the J/ψππ channel. Although at present the experiments did not give a measurement for ψ(3S)→ J/ψππ, ψ(2S)ππ, the transition of ψ(3S) to lower states, ψ(nS) (n < 3), with two pions being emitted can be solved by the QCD multipole expansion (QCDME) method proposed by Gottfried, Yan and Kuang [23–27], which is depicted by Fig. 1. In a recent work [28], Ke et al. calculated the transitions of ψ(3S)→ ψ(nS)ππ to obtain Γ [ψ(3S)→ J/ψππ] = 589.91 keV , (1) Γ [ψ(3S)→ ψ(2S)ππ] = 14.96 keV (2) by adopting the Cornell potential V (r) =−κr + br [29, 30] and Γ [ψ(3S)→ J/ψππ] = 12.38 keV, (3) Γ [ψ(3S)→ ψ(2S)ππ] = 8.84 keV (4) 472 X. Liu: Understanding the newly observed Y (4008) by Belle Fig. 1. The transition of ψ(3S) to lower states ψ(nS) (n < 3) with two pions being emitted by adopting a modified Cornell potential, which includes a spin-related term [31]