$D^0 D^0 pi^+$ mass distribution in the production of the $T_{cc}$ exotic state

We perform a unitary coupled channel study of the interaction of the $D^{*+} D^0, D^{*0} D^+$ channels and find a state barely bound, very close to isospin $I=0$. The width obtained is small, of the order of $80 ;{rm keV}$, tied to the width of the $D^*$ states, short of the experimental one, but which would certainly be bigger upon consideration of the experimental resolution. We perform a detailed study of the $D^0 D^0 pi^+$ spectrum and compare with experiment, suggesting that the investigation of this state in other decay channels would bring additional new information concerning the nature of this state.