Could the $X(3915)$ and the $X(3930)$ Be the Same Tensor State?

Abstract

By using a combined amplitude analysis of the $\gamma \gamma \to D\bar{D}$ and $\gamma \gamma \to J/\psi \omega$ data, we demonstrate that the $X(3915)$, which is quoted as a $J^{PC}=0^{++}$ state in the Particle Data Group table, is favored by the data to be a $J^{PC}=2^{++}$ state appearing in both channels, which means that the $X(3915)$ and the $X(3930)$ can be regarded as the same $J^{PC}=2^{++}$ state. Meanwhile, the data also prefer a large helicity-0 contribution of this tensor resonance to the amplitudes instead of the helicity-2 dominance assumed by {\it BABAR}, which may indicate a sizable portion of non-$q\bar{q}$ components in this state. Identifying the $X(3915)$ with the $X(3930)$ and abandoning the helicity-2 dominance for this tensor state are helpful for the further understandings of the properties of this state and also of the mysterious "$XYZ$" charmoniumlike resonances.

Comments: 5 pages, 1 table, 3 figures, version accepted for publication in Phys. Rev. Lett.; Title changed, significantly improved discussions, minor corrections to formulas and figures, main framework and results not changed