In this work, we study the πJ/ψ andD * D invariant mass spectra of the Y (4260) decay to find out the origin of the Z c (3900) and Z c (3885) structures. The πJ/ψ − D * D interaction is studied in a coupled-channel quasipotential Bethe-Saltpeter equation approach, and embedded to the Y (4260) decay process to reproduce both π − J/ψ and D * − D 0 invariant mass spectra observed at BESIII simultaneously. It is found out that a virtual state at energy about 3870 MeV is produced from the interaction when both invariant mass spectra are comparable with the experiment. The results support that both Z c (3900) and Z c (3885) have the same origin, that is, a virtual state from πJ/ψ −D * D interaction, in which theD * D interaction is more important and the coupling betweenD * D and πJ/ψ channels plays a minor role.
IntroductionIn recent years, many exotic resonance structures were observed near the threshold of two hadrons, which are difficult to put into the conventional quark model. The exotic resonance structures near theD * D threshold (in this work we will remark hidden charmed system with a vector D * /D * meson and a pseudoscalarD/D meson asD * D if the explicit is not necessary) are good examples of such phenomena. The first XY Z particle, X (3872) is almost on theD * D threshold, which was interpreted as aD * D hadronic molecular state immediately after its observation [1,2]. Later, an isovector resonant structure named Z ± c (3900) was observed in 2013 at BESIII and Bell in the π ± J/ψ invariant mass spectrum of e + e − → π + π − J/ψ at √ s = 4.26 GeV [3,4], and further confirmed at CLEO-c in the same channel at √ s = 4.17 GeV [5]. The observed Z c (3900) is also near theD * D threshold, thus, it is natural to explain it as an isovector partner of X (3872) in theD * D molecular scenario and expected to be observed in the (D * D) I =1 channel. It was confirmed by the a e-mail: junhe@njnu.edu.cn observation of Z c (3885) in the DD * invariant mass spectrum of Y (4260) decay in process e + e − → π ± (DD * ) ∓ [6]. Recently, the neutral partners of Z ± c (3900) and Z ± c (3885) were also observed at BESIII [7,8]. Besides, the spin parity of these state has been determined as J P = 1 + by a partial wave analysis [9].Thanks to the experiments at BESIII, Belle and CLEOc, the isovector Z c (3900)/Z c (3885) has been established. Since the Z ± c (3900)/Z ± c (3885) carries a charge, it cannot be explained as a cc state, which must be neutral. After the observation at BESIII, many interpretations of the origin of Z c (3900)/Z c (3885) have been proposed, which includes the hadronic molecular state [10][11][12][13][14], tetraquark state [15][16][17], initial-single-pion-emission mechanism [18,19], cusp effect from triangle singularity [20]. And its decays were also studied though intermediate meson loop [21][22][23]. Due to its closeness to theD * D threshold, the hadronic molecular state is an important picture to explain the Z c (3900)/Z c (3885) structure. In Refs. [24,25], theD * D interaction as well as the...