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On the $π^+π^-$ and $D^+_sπ^{\pm}$ mass spectra in the $D_{s1}(2536) \to D^+_sπ^+π^-$ decays

Jorgivan Morais Dias, Yi-Yao Li, Eulogio Oset

TL;DR

The paper tests the molecular interpretation of $D_{s1}(2536)$ by treating it as a pure $K^*D$ state and computing the decay $D_{s1}(2536) o D_s^+π^+π^-$ via triangle-loop diagrams with intermediate $D$, $K^*$, and $K$ mesons. Using the Local Hidden Gauge formalism, it derives the triangle amplitudes for two diagrams, regulated with $q_{ ext{max}}=1025$ MeV and $\\Lambda=600$ MeV, to predict the $π^+π^-$ and $D_s^+π^\

Abstract

We have carried out an evaluation of the $π^+ π^-$ and $D_s^+ π^+$ mass distributions in the $D_{s1}(2536)$ decay to $D_s^+ π^+ π^-$, from the perspective that the $D_{s1}(2536)$ is a molecular state, mostly made from $K^*D$ in $I=0$. We are able to obtain, not only the mass distributions, but the branching ratio of this decay. The shape of the mass distributions differ appreciably from those of the analogous reaction $D_{s1}(2460)\to D_s^+ π^+ π^-$, which has been measured by the LHCb collaboration and analyzed theoretically from the perspective that the $D_{s1}(2460)$ is a molecular state of $D^*K$, showing a good agreement with the data. In spite of the analogy with the $D_{s1}(2460)$ decay, the dynamical differences in the decay mechanism are important, since now the $f_0(500)$ resonance is not generated, while it was the dominant mechanism in the $D_{s1}(2460)\to D_s^+ π^+ π^-$ decay. Nonetheless, we find striking differences in the mass distributions compared with phase space as a consequence of the decay mechanism. The branching ratio obtained is an order of magnitude bigger than the one of the $D_{s1}(2460)\to D_s^+ π^+ π^-$ reaction, mostly due to the larger available phase space. We also show that the shape of the distributions obtained from the molecular picture are quite different from those obtained based on a $q\bar{q}$ picture. We conclude that measuring the shape of the mass distributions and the total strength of the decay mode, should be very valuable to learn about the structure of the $D_{s1}(2536)$.

On the $π^+π^-$ and $D^+_sπ^{\pm}$ mass spectra in the $D_{s1}(2536) \to D^+_sπ^+π^-$ decays

TL;DR

The paper tests the molecular interpretation of by treating it as a pure state and computing the decay via triangle-loop diagrams with intermediate , , and mesons. Using the Local Hidden Gauge formalism, it derives the triangle amplitudes for two diagrams, regulated with MeV and MeV, to predict the and $D_s^+π^\

Abstract

We have carried out an evaluation of the and mass distributions in the decay to , from the perspective that the is a molecular state, mostly made from in . We are able to obtain, not only the mass distributions, but the branching ratio of this decay. The shape of the mass distributions differ appreciably from those of the analogous reaction , which has been measured by the LHCb collaboration and analyzed theoretically from the perspective that the is a molecular state of , showing a good agreement with the data. In spite of the analogy with the decay, the dynamical differences in the decay mechanism are important, since now the resonance is not generated, while it was the dominant mechanism in the decay. Nonetheless, we find striking differences in the mass distributions compared with phase space as a consequence of the decay mechanism. The branching ratio obtained is an order of magnitude bigger than the one of the reaction, mostly due to the larger available phase space. We also show that the shape of the distributions obtained from the molecular picture are quite different from those obtained based on a picture. We conclude that measuring the shape of the mass distributions and the total strength of the decay mode, should be very valuable to learn about the structure of the .

Paper Structure

This paper contains 8 sections, 40 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Formalism
  3. Numerical Results
  4. Consideration of $\varepsilon^0(K^*)$ and negative energy parts of the propagators
  5. Consideration of $\varepsilon^0(K^*)$
  6. Consideration of negative energy component of the propagators
  7. Discussion
  8. Summary

Figures (3)

  • Figure 1: $D_{s1}$ decay mechanism: (a) Decay through the $K^{*+}D^0$ component, while in (b), the $D_{s1}$ meson decays through the $K^{*0}D^+$ component.
  • Figure 2: $\pi^+\pi^-$ invariant mass spectrum and phase space.
  • Figure 3: $D^+_s\pi^{+}$ invariant mass spectrum and phase space.