Signatures of the two $K_1(1270)$ poles in $D^{+}\to \nu e^{+}VP$ decay

Abstract

We analyze theoretically the $D^{+}\to \nu e^{+}\rho \bar{K}$ and $D^{+}\to \nu e^{+}{\bar{K}}^{\ast }\pi$ 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 $K^{\ast }\pi$ 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 $D^{+}\to \nu e^{+}VP$ 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.

Comments: 7 pages, 3 figures