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 $D^0{D}^{*+}-D^{+}{D}^{*0}$, 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 $D^0{D}^{*+}-D^{+}{D}^{*0}$ 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 $D^0{D}^{*+}-D^{+}{D}^{*0}$ interaction and its line shape in $D^0{D}^0{\pi }^{+}$ break-up production are in agreement with double-charmed tetraquark $T_{cc}^{+}$ observed by the LHCb Collaboration.

• Received 12 February 2024
• Accepted 9 April 2024

DOI:https://doi.org/10.1103/PhysRevD.109.094010

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Published by the American Physical Society