Does the enhancement observed in $γγ\to D\bar{D}$ contain two $P$-wave higher charmonia?

Abstract

Solved is a new puzzle raised by the observation of an enhancement structure Z(3930) in $γγ\to D\bar{D}$. If categorizing Z(3930) as $χ_{c2}(2P)$ suggested by Belle and BaBar, we must explain why $χ_{c0}(2P)$ dominantly decaying into $D\bar{D}$ is missing in the $D\bar{D}$ invariant mass spectrum. In this work, we propose that the Z(3930) enhancement structure may contain two $P$-wave higher charmonia {$χ_{c0}(2P)$} and $χ_{c2}(2P)$. We show that this assumption is supported by our analysis of the $D\bar{D}$ invariant mass spectrum and $\cosθ^\ast$ distribution of $γγ\to D\bar{D}$. This observation would not only provide valuable information of two P-wave higher charmonia $χ_{c0}(2P)$ and $χ_{c2}(2P)$, but also serve as the crucial test of our novel proposal to the observed enhancement structure Z(3930), especially at the forthcoming BelleII and the approved SuperB.