Understanding the 0++ and 2++ charmonium(-like) states near 3.9 GeV.

We propose that the X(3915) observed in the J/ψω channel is the same state as the χc2(3930), and the X(3960), observed in the Ds+Ds- channel, is an S-wave Ds+Ds- hadronic molecule. In addition, the JPC=0++ component in the B+→D+D-K+ assigned to the X(3915) in the current Review of Particle Physics has the same origin as the X(3960), which has a mass around 3.94 GeV. To check the proposal, the available data in the DD¯ and Ds+Ds- channels from both B decays and γγ fusion reaction are analyzed considering both the DD¯-DsD¯s-D*D¯*-Ds*D¯s* coupled channels with 0++ and a 2++ state introduced additionally. It is found that all the data in different processes can be simultaneously well reproduced, and the coupled-channel dynamics produce four hidden-charm scalar molecular states with masses around 3.73, 3.94, 3.99 and 4.23 GeV, respectively. The results may deepen our understanding of the spectrum of charmonia as well as of the interactions between charmed hadrons.