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Abstract
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.
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