The interaction between various charmed mesons and charmed baryons are studied within the framework of the coupled channel unitary approach with the local hidden gauge formalism. Several meson-baryon dynamically generated narrow N * and Λ * resonances with hidden charm are predicted with mass above 4 GeV and width smaller than 100 MeV. The predicted new resonances definitely cannot be accommodated by quark models with three constituent quarks and can be looked for at the forthcoming PANDA/FAIR experiments.PACS numbers: 14.20. Gk, 13.30.Eg, 13.75.Jz Up to now, all established baryons can be ascribed into 3-quark (qqq) configurations [1], although some of them were suggested to be meson-baryon dynamically generated states [2][3][4][5][6][7][8] or states with large (qqqqq) components [9][10][11]. A difficulty to pin down the nature of these baryon resonances is that the predicted states from various models are around the same energy region and there are always some adjustable ingredients in each model to fit the experimental data. In this letter, we report a study of the interactions between various charmed mesons and charmed baryons within the framework of the coupled channel unitary approach with the local hidden gauge formalism. Several meson-baryon dynamically generated narrow N * and Λ * resonances with hidden charm are predicted with mass above 4 GeV and width smaller than 100 MeV. The predicted new resonances can be looked for at the forthcoming PANDA/FAIR experiments [13]. If confirmed, they definitely cannot be accommodated by quark models with three constituent quarks.We follow the recent approach of Ref.[12] and extend it from three flavors to four. We consider the P B → P B and V B → V B interaction by exchanging a vector meson, as shown by the Feynman diagrams in Fig. 1.The effective Lagrangians for the interactions involved are [12]:where P and V stand for pseudoscalar and vector mesons of the 16-plet of SU(4), respectively. Under the low energy approximation, the three momentum versus the mass of the meson can be neglected. We can just take the γ 0 component of Eq. (1). The threemomentum and energy of the exchanged vector are both much smaller than its mass, so its propagator is approximately g µν /M 2 V . Then with g = M V /2f the transition potential corresponding to the diagrams of Fig. 1 are given bywhere the a, b stand for different channels of P 1 (V 1 )B 1 and P 2 (V 2 )B 2 , respectively. The E is the energy of corresponding particle. The ǫ is the polarization vector of the initial or final vector. And the ǫ 0 1,2 component is neglected consistently with taking p/M V ∼ 0, with p the momentum of the vector meson. The C ab coefficients can be obtained by the SU(4) Clebsch Gordan Coefficients which we take from Ref. [14]. We list the values of the C ab coefficients for P B → P B with isospin and strangeness (I, S) = (1/2, 0) and (0, -1) explicitly in Table I and Table II, respectively. With the transition potential, the coupled-channel scattering matrix can be obtained by solving the coupledc...

The interactions ofDΣ c -DΛ c ,D * Σ c -D * Λ c , and related strangeness channels, are studied within the framework of the coupled channel unitary approach with the local hidden gauge formalism. A series of meson-baryon dynamically generated relatively narrow N * and Λ * resonances are predicted around 4.3 GeV in the hidden charm sector. We make estimates of production cross sections of these predicted resonances inpp collisions for PANDA at the forthcoming FAIR facility. π 0 √ 2 + η 8

The BES-III Collaboration recently reported the observation of anomalously large isospin violations in J/ψ→γη(1405/1475)→γπ(0)f(0)(980)→γ+3π, where the f(0)(980) in the ππ invariant mass spectrum appears to be much narrower (~10 MeV) than the peak width (~50 MeV) measured in other processes. We show that a mechanism, named as triangle singularity (TS), can produce a narrow enhancement between the charged and neutral KK¯ thresholds, i.e., 2m(K(±))~2m(K(0)). It can also lead to different invariant mass spectra for η(1405/1475)→a(0)(980)π and KK ¯*+c.c., which can possibly explain the long-standing puzzle about the need for two close states η(1405) and η(1475) in ηππ and KK¯π, respectively. The TS could be a key to our understanding of the nature of η(1405/1475) and advance our knowledge about the mixing between a(0)(980) and f(0)(980).

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the BetheSalpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allow for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.

Isospin breaking and f 0 (980)-a 0 (980) mixing in the η(1405) → π 0 f 0 (980) reaction

The model dependence of the predictions of nucleon resonances with hidden charm is investigated. We consider several coupled-channel models which are derived from relativistic quantum field theory by using (1) a unitary transformation method and (2) the three-dimensional reductions of the Bethe-Salpeter equation. With the same vector-meson exchange mechanism, we find that all models give very narrow molecularlike nucleon resonances with hidden charm in the mass range of 4.3 < M R < 4.5 GeV, consistent with the previous predictions.

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Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order L −6 . Furthermore, assuming that a stable dimer exists in the infinite volume, the shift for the lowest particle-dimer scattering state is obtained up to and including order L −3 . The result for the lowest three-particle state agrees with the results from the literature, and the result for the lowest particle-dimer state reproduces the one obtained by using the Lüscher equation.