Signatures of the two $$K_1(1270)$$ poles in $$D^+\rightarrow \nu e^+ V P$$ decay

Abstract

We analyze theoretically the $$D^+\rightarrow \nu e^+ \rho \bar{K}$$ D + → ν e + ρ K ¯ and $$D^+\rightarrow \nu e^+ \bar{K}^* \pi $$ D + → ν e + K ¯ ∗ π decays to see the feasibility to check the double pole nature of the axial-vector resonance $$K_1(1270)$$ K 1 ( 1270 ) predicted by the unitary extensions of chiral perturbation theory (UChPT). Indeed, within UChPT the $$K_1(1270)$$ 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 $$K^*\pi $$ K ∗ π and the higher mass pole to $$\rho K$$ ρ 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 $$D^+\rightarrow \nu e^+ V P$$ D + → ν 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 $$K_1(1270)$$ K 1 ( 1270 ) resonance.

Combined theoretical study of the $$D^+ \rightarrow \pi ^+ \eta \eta $$ and $$D^+ \rightarrow \pi ^+ \pi ^0 \eta $$ reactions

“…In view of the impossibility to obtain a ratio R bigger than 0.5 with A = 1, we take now A = −1 with the other parameters in the same range of Eq. (31). In this case we can obtain bigger ratios than before.…”

“…It is then quite customary in this kind of problems to assume SU(3) symmetry except in terms which involve directly the masses of the particles. Some tests of SU(3) breaking have been done in other weak decays hadronizing withūu +dd + (1 − α)ss, finding that even a 20 % breaking of SU(3) symmetry, taking α = 0.20, leads only to 5 % changes in the decay widths [31]. For all these reasons we keep these terms, but we also perform a study removing them and discuss the consequence on the mass distributions.…”

Analysis of the $$ \varvec{e^+ e^- \rightarrow J/\psi D{\bar{D}}}$$ reaction close to the threshold concerning claims of a $$\chi _{c0}(2P)$$ state

“…[24,25] (see also Refs. [44][45][46][47]). We should also note the strong Flatté effect in the coupled channels amplitudes in Fig.…”

Tau decay into $$\nu _\tau $$ and $$a_1(1260)$$, $$b_1(1235)$$, and two $$K_1(1270)$$

“…As far as the two K 1 (1270) states is concerned, as in [7] and other works that studied the separation of these two states using different reactions [48][49][50], the suggestion is always the same: to measure the K * π decay mode to see the K 1 (A) state and ρ K to measure the K 1 (B) state. So far experiments look at theK ππ invariant mass distribution, which contains both K * π and ρ K .…”