Doubly charmed tetraquark $T_{cc}^{+}$ in (2+1)-flavor QCD near physical point

We study the doubly charmed tetraquark state $T_{cc}^{+}$ by the HAL QCD method applied to the $D^{\ast }D$ system in $(2+1)$ flavor lattice QCD at nearly physical pion mass, $m_{\pi }=146$ MeV. We obtain the attractive potential at all distances in the $S$-wave of the isoscalar $D^{\ast }D$ system, whose long distance behavior is well described by the two-pion exchange (TPE), and it generates a virtual pole near $D^{\ast }D$ threshold with a pole position $E_{\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{e}}=-59{(}_{-99}^{+53}){(}_{-67}^{+2})$ keV and an inverse scattering length $1\mathrm{/}{a}_0=0.05(5){(}_{-2}^{+2})$ fm${}^{-1}$. The virtual pole turns into a loosely bound state pole if the pion mass in the TPE potential is extrapolated to the physical value, $m_{\pi }=135$ MeV. The potential at the physical pion mass is shown to give a semi-quantitative description of the $D^0{D}^0{\pi }^{+}$ mass spectrum at the LHCb.