Can X(3915) be the tensor partner of the X(3872)?

It has been proposed recently (Phys. Rev. Lett. 115 (2015), 022001) that the charmoniumlike state named X(3915) and suggested to be a $0^{++}$ scalar, is just the helicity-0 realisation of the $2^{++}$ tensor state $\chi_{c2}(3930)$. This scenario would call for a helicity-0 dominance, which were at odds with the properties of a conventional tensor charmonium, but might be compatible with some exotic structure of the $\chi_{c2}(3930)$. In this paper, we investigate, if such a scenario is compatible with the assumption that the $\chi_{c2}(3930)$ is a $D^*\bar D^*$ molecular state - a spin partner of the $X(3872)$ treated as a shallow bound state. We demonstrate that for a tensor molecule the helicity-0 component vanishes for vanishing binding energy and accordingly for a shallow bound state a helicity-2 dominance would be natural. However, for the $\chi_{c2}(3930)$, residing about 100 MeV below the $D^*\bar D^*$ threshold, there is no a priori reason for a helicity-2 dominance and thus the proposal formulated in the above mentioned reference might indeed point at a molecular structure of the tensor state. Nevertheless, we find that the experimental data currently available favour a dominant contribution of the helicity-2 amplitude also in this scenario, if spin symmetry arguments are employed to relate properties of the molecular state to those of the X(3872). We also discuss what research is necessary to further constrain the analysis.Comment: LaTeX2e, 23 pages, 2 figures, version to appear in JHE

Charge symmetry breaking as a probe for the real part of eta--nucleus scattering lengths

We demonstrate that one can use the occurrence of charge symmetry breaking as a tool to explore the eta--nucleus interaction near the eta threshold. Based on indications that the cross section ratio of pi+ and pi0 production on nuclei deviates from the isotopic value in the vicinity of the eta production threshold, due to, e.g., pi0-eta mixing, we argue that a systematic study of this ratio as a function of the energy would allow to pin down the sign of the real part of the eta-nucleus scattering length. This sign plays an important role in the context of the possible existence of eta-nucleus bound states.Comment: 4 pages, 1 figur

Spin partners of the Zb(10610)Z_b(10610) and Zb(10650)Z_b(10650) revisited

We study the implications of the heavy-quark spin symmetry for the possible spin partners of the exotic states $Z_b(10610)$ and $Z_b(10650)$ in the spectrum of bottomonium. We formulate and solve numerically the coupled-channel equations for the $Z_b$ states that allow for a dynamical generation of these states as hadronic molecules. The force includes short-range contact terms and the one-pion exchange potential, both treated fully nonperturbatively. The strength of the potential at leading order is fixed completely by the pole positions of the $Z_b$ states such that the mass and the most prominent contributions to the width of the isovector heavy-quark spin partner states $W_{bJ}$ with the quantum numbers $J^{++}$ ($J=0,1,2$) come out as predictions. Since the accuracy of the present experimental data does not allow one to fix the pole positions of the $Z_b$'s reliably enough, we also study the pole trajectories of their spin partner states as functions of the $Z_b$ binding energies. It is shown that, once the heavy-quark spin symmetry is broken by means of the physical $B$ and $B^*$ masses, especially the pion tensor force has a significant impact on the location of the partner states clearly demonstrating the need of a coupled-channel treatment of pion dynamics to understand the spin multiplet pattern of hadronic molecules.Comment: 21 pages, 5 figures, 1 tabl