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.

arXiv comment7 pages, 3 figures

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• Two-pole structures in QCD: Facts, not fantasy!
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• Combined theoretical study of the $D^{+}\to {\pi }^{+}\eta \eta$ and $D^{+}\to {\pi }^{+}{\pi }^0\eta$ reactions
• Unveiling the $a_0(1710)$ nature in the process $J/\psi \to {\bar{K}}^0{K}^{+}{\rho }^{-}$
• Tau decay into ${\nu }_{\tau }$ and $a_1(1260)$, $b_1(1235)$, and two $K_1(1270)$
• Muon mass correction in partial wave analyses of charmed meson semi-leptonic decays
• Study of the axial-vector and tensor resonant contributions to the $D\to VP{\ell }^{+}{\nu }_{\ell }$ decays based on SU(3) flavor analysis
• Inconsistency of the data on the $K_1(1270)\to \pi K_0^{\ast }(1430)$ decay width
• Observation of $D\to {\bar{K}}_1(1270){\mu }^{+}{\nu }_{\mu }$ and test of lepton flavor universality with $D\to {\bar{K}}_1(1270){\ell }^{+}{\nu }_{\ell }$