$D^{+}{D}^{-}$ hadronic atom and its production in $pp$ and $p\bar{p}$ collisions

Abstract

There must be Coulomb bound states of a pair of hadrons, which are stable against the strong interaction, with opposite electric charges. Such bound states are hadronic atoms. We study the properties and the production of the ground-state $D^{+}{D}^{-}$ hadronic atom $A_{D^{+}{D}^{-}}$, called dionium, with quantum numbers $J^{PC}=0^{++}$. Using a nonrelativistic effective field theory for the $D^0{\bar{D}}^0$-$D^{+}{D}^{-}$ coupled-channel system, the mass of the ground-state dionium is predicted to be $(3739.3\pm 0.1)\text{MeV}$, with the binding energy reduced by about 10% compared to the Coulomb binding energy due to the strong interaction. Its width for the decay into the neutral $D^0{\bar{D}}^0$ channel is predicted to be $1.8_{-0.6}^{+1.4}$ keV using lattice inputs for the $D\bar{D}$ strong interaction. The cross section for the inclusive prompt production of the dionium at CMS and LHCb and that for the direct production $p\bar{p}\to A_{D^{+}{D}^{-}}$ at PANDA are estimated at an order-of-magnitude level. In particular, we expect that $\mathcal{O}(10^3\sim 10^5)$ events of the reaction chain $p\bar{p}\to A_{D^{+}{D}^{-}}\to D^0{\bar{D}}^0\to K^{-}\ddot{I}{€}^{+}{K}^{+}\ddot{I}{€}^{-}$ can be collected at PANDA, and valuable information on the charmed meson interaction and on understanding charmoniumlike states will be obtained.

25 pages, 5 figures. Version to appear in Phys. Rev. D