The $Dπ$ and $D^*π$ femtoscopy puzzle
We present a relativistic momentum-space framework for femtoscopic correlation functions including strong and Coulomb interactions in coupled channels. The approach extends the Vincent--Phatak prescription to the three-dimensional Bethe--Salpeter equation, combining a fully relativistic treatment with the correct Coulomb asymptotics through wave-function matching. We apply it to the $Dπ$ system using a coupled-channel heavy-meson chiral interaction that reproduces the established two-pole structure of the $D_0^*(2300)$. Our correlation functions agree with previous theoretical calculations but differ significantly from those extracted by the ALICE Collaboration. We trace this tension to the assumption made in the experimental analysis that the genuine correlation function reaches unity above a relative momentum of $100$ MeV, whereas this region remains affected by the lower $D_0^*(2300)$ pole. Repeating the extraction over different fitting windows reveals a strong dependence of the extracted signal on the chosen range, demonstrating that the resulting $Dπ$ scattering parameters are not robust and motivating a dedicated reanalysis of the experimental data. We extend the analysis to the $D^*π$ system, where the same issue arises in close connection with heavy-quark spin symmetry. Together with the unresolved tension between theoretical calculations and the ALICE $Kπ$ femtoscopic measurements, this highlights the need to clarify the origin of this puzzle, with the aim of establishing femtoscopy as a reliable quantitative tool for precision studies of low-energy hadron interactions.