Incorporating $DD\pi$ effects and left-hand cuts in lattice QCD studies of the $T_{cc}(3875{)}^{+}$

We generalize the relativistic field-theoretic three-particle finite-volume scattering formalism to describe generic $DD\pi$ systems in the charm $C=2$ sector. This includes the isospin-0 channel, in which the recently discovered doubly-charmed tetraquark $T_{cc}(3875{)}^{+}$ is expected to manifest as a pole in the $DD\pi \to DD\pi$ scattering amplitude. The formalism presented here can also be applied to lattice QCD settings in which the $D^{\ast }$ is bound and, in particular, remains valid below the left-hand cut in $D{D}^{\ast }$ scattering, thus resolving an issue in previous analyses of lattice-determined finite-volume energies.