The relativistic three-body scattering and the $D^0D^{*+}-D^+D^{*0}$ system

Abstract: Scattering amplitudes involving three-particle scattering processes are investigated within the isobar approximation which respects constraints from two- and three-body unitarity. The particular system considered is the $D^0D^{*+}-D^+D^{*0}$, where the $D^{*+}$ $(D^{*0})$ enters as a $p$-wave $D^+\pi^0$ or $D^0\pi^+$ ($D^0\pi^0$ or $D^+\pi^-$) resonance. The interaction potentials in the coupled-channel $D^0D^{*+}-D^+D^{*0}$ system contain the $\sigma$, $\rho$, $\omega$ and $\pi$-exchange. The analytic continuation of the amplitudes across the three-body unitary cuts is investigated to search for poles on the unphysical Riemann sheets. Associated with an unstable particle $D^{*+}$ $(D^{*0})$ is a complex two-body unitarity cut, through which one can further analytically continue into another unphysical Riemann sheet. Dynamical singularities emerged from the $\pi$-exchange potential are stressed. The pole generated from the $D^0D^{*+}-D^+D^{*0}$ interaction and its line shape in $D^0D^0\pi^+$ break-up production are in agreement with double-charmed tetraquark $T_{cc}^+$ observed by the LHCb Collaboration.