Resolving the $T_{cc}^{+}$ with $\ddot{I}€$ Exchange from Lattice QCD

Abstract

We revisit the lattice QCD description of the doubly charmed tetraquark $T_{cc}^{+}$ using a finite-volume scattering formalism that incorporates one-pion exchange nonperturbatively, thereby making the nearest left-hand cut explicit while respecting unitarity and analyticity. We simultaneously determine the $D{D}^{\star }\ddot{I}€$ coupling and the isoscalar $D{D}^{\star }$ scattering amplitude by reanalyzing the previously computed finite-volume $D{D}^{\star }$ spectrum below the $D^{\star }{D}^{\star }$ threshold, on lattices with pion mass $m_{\ddot{I}}€\approx 391\mathrm{MeV}$. We find that the inclusion of pion exchange changes the $T_{cc}^{+}$ from a real-valued to a complex-valued pole in the second sheet of the $J^P=1^{+}$, $D{D}^{\star }$ amplitude below threshold. We further predict that the $T_{cc}^{+}$ pole will move closer to the real-energy axis as the pion mass approaches its physical value.