Can a femtoscopic correlation function shed light on the nature of the lightest charm axial mesons?

We present a coupled channel treatment of meson-meson dynamics, for systems with spin-parity $1^{+}$, and determine the corresponding amplitudes by solving the Bethe-Salpeter equations, which lead to the generation of two axial resonances when mesons are considered as the degrees of freedom in the model. One of them is narrow and has properties in good agreement with those of $D_1\left(2420\right)$. The other pole is wider, but its real and imaginary parts do not match well with the mass and width of $D_1\left(2430\right)$. The situation improves when a bare quark-model state is included, indicating that the dynamics at the quark level as well as among hadrons can describe the two states simultaneously. Further, we discuss that there exists a divergence in the value of the $D^{*}\pi$ scattering length determined through data coming from lattice QCD calculations and from heavy ion collisions. Such different values can be accommodated in the model by making small changes in the parameters while producing two poles having properties compatible with the two lightest $D_1$ states. With these results, we proceed to calculate the correlation function for the $D^{*+\left(0\right)}{\pi }^{0(+)}$ system for different sizes of the source. We discuss which scenarios can be useful to shed some light on the issue.