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

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 $1.8^{+1.4}_{-0.6}$ 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 $p\bar p\to A_{D^+D^-}\to D^0\bar D^0 \to K^-π^+K^+π^-$ can be collected at PANDA, and valuable information on the charmed meson interaction and on understanding charmoniumlike states will be obtained.