Molecular interpretation of X(3960) as D_s^+ D_s^- state

Abstract

We study D_s^+ D_s^- and D bar{D} states assuming that they are hadronic molecules with J^{PC}=0^{++} quantum number. We use two-point QCD sum rule formalism and extract the mass and decay constant values of these states. We take into account contributions of various quark, gluon, and mixed vacuum condensates up to dimension eight. The extracted mass and decay constant values of D bar{D} and D_s^+ D_s^- states read as M_{D bar{D}} = 3795^{+85}_{-82}~{textrm{MeV}} , f_{D bar{D}} = 1.70^{+0.33}_{-0.29} times 10^{-2} ~{textrm{GeV}}^5, and M_{D_s^+ D_s^-} = 3983^{+93}_{-88} ~{textrm{MeV}}, f_{D_s^+ D_s^-} = 2.52^{+0.64}_{-0.54} times 10^{-2} ~{textrm{GeV}}^5, respectively. The predicted mass of D_s^+ D_s^- state is in good agreement with the recent LHCb observation and supports quantum number and molecular picture assignments. A possible observation of D bar{D} state would help for establishing the lowest four-quark state in charmonium sector.