Doubly Charmed Tetraquark $T_{cc}^{+}$ from Lattice QCD near Physical Point

Abstract

The doubly charmed tetraquark $T_{cc}^{+}$ recently discovered by the LHCb Collaboration is studied on the basis of $(2+1)$-flavor lattice QCD simulations of the $D^{\ast }D$ system with nearly physical pion mass $m_{\pi }=146$ MeV. The interaction of $D^{\ast }D$ in the isoscalar and $S$-wave channel, derived from the hadronic spacetime correlation by the HAL QCD method, is attractive for all distances and leads to a near-threshold virtual state with a pole position $E_{\text{pole}}=-59\left({}_{-99}^{+53}\right)\left({}_{-67}^{+2}\right)$ keV and a large scattering length $1/a_0=0.05(5)\left({}_{-2}^{+2}\right){\text{fm}}^{-1}$. The virtual state is shown to evolve into a loosely bound state as $m_{\pi }$ decreases to its physical value by using a potential modified to $m_{\pi }=135$ MeV based on the pion-exchange interaction. Such a potential is found to give a semiquantitative description of the LHCb data on the $D^0{D}^0{\pi }^{+}$ mass spectrum. Future study is necessary to perform physical-point simulations with the isospin-breaking and open three-body-channel effects taken into account.

Comments: 7 pages, 4 figures + supplemental material; v3, match the published version in PRL