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* (D) over bar* 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* (D) over bar* 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.