Fate of the Tetraquark Candidate Zc(3900) from Lattice QCD

Abstract

The possible exotic meson Zc(3900), found in e + e − reactions, is studied by the method of coupledchannel scattering in lattice QCD. The interactions among πJ/ψ, ρηc andDD * channels are derived from (2+1)-flavor QCD simulations at mπ = 410-700 MeV. The interactions are dominated by the off-diagonal πJ/ψ-DD * and ρηc-DD * couplings, which indicates that the Zc(3900) is not a usual resonance but a threshold cusp. Semiphenomenological analyses with the coupled-channel interaction are also presented to confirm this conclusion.PACS numbers: 12.38. Gc, 14.40.Rt, 13.75.Lb One of the long-standing problems in hadron physics is to identify the existence of exotic hadrons different from the quark-antiquark states (mesons) and three-quark states (baryons). Candidates of such exotic hadrons include the pentaquark states P In particular, Z c (3900) appears as a peak in both the π ± J/ψ and DD * invariant mass spectra in the reaction,Its quantum numbers are then identified as I G (J P C ) = 1 + (1 +− ), so that at least four quarks, ccud (or its isospin partners), are involved. (See the level structure and the decay scheme in Fig.1.) So far, there have been various phenomenological attempts to characterize the Z c (3900) as a hadrocharmonium, a compact tetraquark, a hadronic molecule (e.g., Refs. [5,6]) as well as a kinematical threshold effect (e.g., Refs. [7,8]). However, due to the lack of information of the diagonal and off-diagonal interactions among different channels (such as πJ/ψ, ρη c , andDD * ), the predictions of those models are not well under theoretical control. On the other hand, the direct lattice QCD studies with the standard method of temporal correlations show no candidate for the Z c (3900) eigenstate [9,10], which indicates that the Z c (3900) may not be an ordinary resonance state. Under these circumstances, it is most desirable to carry out manifestly coupled-channel analyses with the first-principles QCD inputs.The purpose of this Letter is to report a first attempt to determine the nature of the Z c (3900) on the basis of the HAL QCD method [11][12][13][14]. We consider three two-body channels below Z c (3900) (πJ/ψ, ρη c andDD * ) which couple with each other. The interactions among these channels faithful to the QCD S matrix are derived from the equal-time Nambu-Bethe-Salpeter (NBS) wave functions on the lattice according to the coupled-channel formulation of the HAL QCD method [15][16][17]. The s-wave interactions and the S matrix thus obtained are used to search for the complex poles in the πJ/ψ andDD * scattering amplitudes to unravel the nature of the Z c (3900). We note here that the conventional resonances such as the ρ meson and the ∆ baryon have not yet been analyzed in the HAL QCD method, and the comparison with the Lüscher's method [18] in these channels is one of the important future subjects. (Such comparison in the nonresonant ππ channel has been done in Refs. [19,20]; See also Ref. [21]). Note also that the coupled-channel HAL QCD method has not been experimentally tested in othe...

$$Z_c(3900)/Z_c(3885)$$ Z c ( 3900 ) / Z c ( 3885 ) as a virtual state from $$\pi J/\psi -\bar{D}^*D$$ π J / ψ - D ¯ ∗ D interaction

“…However, in theses studies, all coupling constants of the interactions were chosen as free parameters. A recent lattice work suggests that the off-diagonal π J/ψ −D D * coupling is more important than theD D * interaction, and a semiphenomenological analysis was adopted to study the invariant mass spectrum [32]. In their comparison with data, two general free parameters were adopted to π J/ψ andD D * channel, respectively, which smeared an important experiment results about the relative magnitudes of decays in these two channels.…”

Heavy-hadron interactions from Lattice QCD

“…Coupled-channel S-wave potentials from the HALQCD method. Figure taken from [45]. Figure 11 shows the resulting diagonal and off-diagonal potentials and illustrates their pattern: While not much is happening for the diagonal, some of the off-diagonal potentials are quite strong.…”

“…A different approach is pursued in [45,46], where a coupled channel extension of the HALQCD method (for the original method see [47]) is used to investigate coupled-channel scattering J/Ψπ, η c ρ,DD * with quantum numbers I G (J PC ) = 1 + 1 +− (same as above). In the HALQCD method potentials V(r), functions of the distance r, are calculated as an intermediate quantity.…”

Hadron spectroscopy and interactions from lattice QCD

“…First the potential V πJ/ψ−πJ/ψ (r) related to Nambu-Bethe-Salpeter equation is determined between the J/ψ and π as a function of their separation r [17]. This is presented in Fig.…”

“…The off-diagonal potential between channels πJ/ψ and DD * is larger than other potentials, which seems to indicate a sizable coupled channel effect near DD * threshold. The potentials render 3 × 3 scattering matrix for three coupled channels [17]. This is then used to determine the three body decay Y(4260) → J/ψππ and Y(4260) → DD * π in a semi-phenomenological way.…”