Employing the relativized quark model and the quark-interchange model, we investigate the decay of the charged heavy quarkonium-like states Z c (3900), Z c (4020), Z c (4430), Z b (10610) and Z b (10650) into the ground and radially excited heavy quarkonia via emitting a pion meson. The Z c and Z b states are assumed to be hadronic molecules composed of open-flavor heavy mesons. The calculated decay ratios can be compared with the experimental data, which are useful in judging whether the molecule state assignment for the corresponding Z c or Z b state is reasonable or not. The theoretical framework constructed in this work will be helpful in revealing the underlying structures of some exotic hadrons. Yan-Rui Liu, Jia-Jun Wu, and Yuan Song. We also thank Prof. Ulf-G. Meißner for a careful reading and helpful suggestions.

We investigate the ratio of the branching fractions of the molecular candidates decaying into the ground and radially excited states within the quark-interchange model. Our numerical results suggest that these molecular candidates are more likely to decay into the radially excited states than into ground states. In particular, the ratio Γ½Z c ð4430Þ → πψð2SÞ=Γ½Z c ð4430Þ → πJ=ψ ∼ 9.9 is close to the experimental measurement, which supports the interpretation of Z c ð4430Þ as theDD Ã ð2SÞ molecular state. The ratios of the branching fractions of Z b ð10610Þ and Z b ð10650Þ to πϒð2S; 3SÞ and πϒð1SÞ agrees very well with the Belle Collaboration's measurement. We also predict the similar ratios for Z c ð3900Þ, Z c ð4020Þ, R Z c ð3900Þ ≈ 1.4, and R Z c ð4020Þ ≈ 4.8. Hopefully, the πψð2SÞ mode and the ratios R Z c ð3900Þ and R Z c ð4020Þ will be measured by the BESIII and Belle collaborations in the near future, which shall be very helpful for understanding the underlying dynamics of these exotic states.

The magnetic moment of a baryon state is an equally important dynamical observable as its mass, which encodes crucial information of its underlying structure. According to the different color-flavor structure, we have calculated the magnetic moments of the hidden-charm pentaquark states with the isospin (I, I 3 ) = ( + in the molecular model, the diquark-triquark model, and the diquark-diquark-antiquark model, respectively. Although a good description for the pentaquark mass spectrum and decay patterns has been obtained in all three models, different color-flavor structures lead to different magnetic moments, which can be used to pin down their inner structures and distinguish various models.

In the framework of the one boson exchange model, we have calculated the effective potentials between two heavy mesons BB * and DD * from the t-and u-channel π, η, ρ, ω and σ meson exchange with four kinds of quantum number: I = 0, J PC = 1 ++ ; I = 0, J PC = 1 +− ; I = 1, J PC = 1 ++ ; I = 1, J PC = 1 +− . We keep the recoil corrections to the BB * and DD * system up to O( 1 M 2 ). The spin orbit force appears at O( 1 M ), which turns out to be important for the very loosely bound molecular states. Our numerical results show that the momentum-related corrections are unfavorable to the formation of the molecular states in the I = 0, J PC = 1 ++ and I = 1, J PC = 1 +− channels in the DD * systems.

Through the spin rearrangement scheme in the heavy quark limit, we have performed a comprehensive investigation of the decay pattern and production mechanism of the hidden beauty di-meson states, which are either composed of a P-wave bottom meson and an S-wave bottom meson or two S-wave bottom mesons. We further extend the corresponding formula to discuss the decay behavior of some charmonium-like states by combining the experimental information with our numerical results. The typical ratios presented in this work can be measured by future experiments like BESIII, Belle, LHCb and the forthcoming BelleII, which shall provide important clues to the inner structures of the exotic states.

In this work, we have adopted the spin rearrangement scheme in the heavy quark limit and extensively investigated three classes of the radiative decays: M → (bb) + γ, (bb) → M + γ, M → M ′ + γ, corresponding to the electromagnetic transitions between one molecular(resonant) state and bottomonium, one bottomonium and molecular(resonant) state, and two molecular(resonant) states respectively. We also extend the same formalism to study the radiative decays of the molecular(resonant) states with hidden charm. We have derived some model independent ratios when the initial or final states belong to the same spin flavor multiplet. Future experimental measurement of these ratios will test the molecular picture and explore the underlying structures of the XYZ states.

The number of exotic candidates which are beyond the conventional quark model has grown dramatically during the last decades. Some of them could be viewed as analogues of the deuteron. Similarly, the existence of the triton indicates that bound states formed by three hadrons could also exist. To illustrate this possibility, we study the DD * K and BB * K systems by using the Born-Oppenheimer Approximation. To leading order, only one-pion exchange potentials are considered, which means that the three constitutes share one virtual pion. That is similar to the role of the delocalized π bond for the formation of Benzene in chemistry. After solving the Schrödinger equation, we find two three-body DD * K and BB * K bound states with masses 4317.92 +3.66 −4.32 MeV and 11013.65 +8.49 −8.84 MeV, respectively. The masses of their DD * K and BB * K analogues are 4317.92 +6.13 −6.55 MeV and 11013.65 +8.68 −9.02 MeV. From the experimental side, the DD * K bound state could be found by analyzing the current world data of the B → J/ψππK process by focusing on the J/ψπK channel. Its confirmation could also help to understand the formation of kaonic nuclei in nuclear physics.

Strong decay patterns of the hidden-charm pentaquark states P c (4380) With the heavy quark symmetry and spin rearrangement scheme, we study the strong decay behavior of the hidden-charm pentaquark states with J P = 3 2 ± , 5 2 ± assuming they are molecular candidates composed ofD ( * ) andc . We obtain several typical ratios of the partial decay widths of the hidden-charm pentaquarks. For the three S-wave (DΣ * c I. INTRODUCTIONRecently, the LHCb Collaboration announced the observation of two hidden-charm resonances, P c (4380) and P c (4450), in the J/ψp invariant mass spectrum in the process Λ b → J/ψpK [1]. The masses and widths of P c (4380) and P c (4450) are [1] M P c (4380) = (4380 ± 8 ± 29) MeV, Γ P c (4380) = (205 ± 18 ± 86) MeV, M P c (4450) = (4449.8 ± 1.7 ± 2.5) MeV, Γ P c (4450) = (39 ± 5 ± 19) MeV.Since they are observed in the final state J/ψp, the isospin of P c (4380) and P c (4450) is I = 1/2. According to LHCb's analysis, their angular momentum and the parity of the two Pc states are either J P = 3 2 ± or 5 2± . At present the spin and parity of each Pc state cannot be determined. In the literature there exist some theoretical discussions of the possible hidden-charm pentaquark states [2][3][4][5][6]. Specifically, the possibility of hidden-charm molecular pentaquarks composed of an anticharmed meson and a charmed baryon was studied systematically in the framework of the one boson exchange model in Ref. [4]. In fact, the existence of the hidden-charm molecular pentaquarks was predicted [4].Let us take the deuteron, which is an extremely loosely bound molecular state composed of one proton and a neutron with a binding energy around 2 MeV, as an example. Generally speaking, the binding energy of the hadronic molecular state is around several to several tens of MeV. Within the molecular scheme, it is quite natural to understand the masses of P c (4380) Within the molecular scheme, the P-wave, D-wave or even higher orbital excitations may also exist if the binding energy of the lowest S-wave hadronic molecule reaches several tens of MeV. For example, the P-wave state may lie slightly above the S-wave ground state with an excitation energy around several to tens of MeV. In other words, the S-wave and P-wave states may completely overlap with each other. There may exist two or more resonant signals around 4380 MeV which are close to each other but may carry different parity. If the P-wave or higher excitation is very broad with a width around 600 MeV, such a state may easily be mistaken as the background. On the other hand, if the excitation lies several MeV within 4380 MeV but with a width as narrow as several MeV, then this state may probably be buried by the Pc(4380) resonance with a width around 205 MeV. The same situation may also occur around 4450 MeV. The above speculation may partly explain why the different assignment of the spin and parity of these two Pc states yields roughly the same good fit [1]. The identification of the nearly degenerate resonances with different parities and ...