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We study the doubly charmed tetraquark state $T_{cc}^+$ by the HAL QCD methodapplied to the $D^*D$ system in $(2+1)$ flavor lattice QCD at nearly physicalpion mass, $m_\pi= 146$ MeV. We obtain the attractive potential at alldistances in the $S$-wave of the isoscalar $D^* D$ system, whose long distancebehavior is well described by the two-pion exchange (TPE), and it generates avirtual pole near $D^* D$ threshold with a pole position $E_{\rm pole} = -59(^{+53}_{-99}) (^{+2}_{-67})$ keV and an inverse scattering length$1/a_0=0.05(5)(^{+2}_{-2})$ fm$^{-1}$. The virtual pole turns into a looselybound state pole if the pion mass in the TPE potential is extrapolated to thephysical value, $m_\pi =135$ MeV. The potential at the physical pion mass isshown to give a semi-quantitative description of the $D^0 D^0\pi^+$ massspectrum at the LHCb.

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