Signatures of the two

We analyze theoretically the $$D^+\rightarrow \nu e^+ \rho \bar{K}$$ and $$D^+\rightarrow \nu e^+ \bar{K}^* \pi $$ decays to see the feasibility to check the double pole nature of the axial-vector resonance $$K_1(1270)$$ predicted by the unitary extensions of chiral perturbation theory (UChPT). Indeed, within UChPT the $$K_1(1270)$$ is dynamically generated from the interaction of a vector and a pseudoscalar meson, and two poles are obtained for the quantum numbers of this resonance. The lower mass pole couples dominantly to $$K^*\pi $$ and the higher mass pole to $$\rho K$$, therefore we can expect that different reactions weighing differently these channels in the production mechanisms enhance one or the other pole. We show that the different final VP channels in $$D^+\rightarrow \nu e^+ V P$$ weigh differently both poles, and this is reflected in the shape of the final vector-pseudoscalar invariant mass distributions. Therefore, we conclude that these decays are suitable to distinguish experimentally the predicted double pole of the $$K_1(1270)$$ resonance