The relativistic three-body scattering and the $D^0{D}^{\ast +}-D^{+}{D}^{\ast 0}$ 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 $D^0{D}^{\ast +}-D^{+}{D}^{\ast 0}$, where the $D^{\ast +}$ $(D^{\ast 0})$ enters as a $p$-wave $D^{+}\ddot{I}{€}^0$ or $D^0\ddot{I}{€}^{+}$ ($D^0\ddot{I}{€}^0$ or $D^{+}\ddot{I}{€}^{-}$) resonance. The interaction potentials in the coupled-channel $D^0{D}^{\ast +}-D^{+}{D}^{\ast 0}$ system contain the $\ddot{I}ƒ$, $\ddot{I}$, $\ddot{I}‰$ and $\ddot{I}€$-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 $D^{\ast +}$ $(D^{\ast 0})$ is a complex two-body unitarity cut, through which one can further analytically continue into another unphysical Riemann sheet. Dynamical singularities emerged from the $\ddot{I}€$-exchange potential are stressed. The pole generated from the $D^0{D}^{\ast +}-D^{+}{D}^{\ast 0}$ interaction and its line shape in $D^0{D}^0\ddot{I}{€}^{+}$ break-up production are in agreement with double-charmed tetraquark $T_{cc}^{+}$ observed by the LHCb Collaboration.