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

Abstract

We have carried out an evaluation of the ${\pi }^{+}{\pi }^{-}$ and $D_s^{+}{\pi }^{+}$ mass distributions in the $D_{s1}(2536)$ decay to $D_s^{+}{\pi }^{+}{\pi }^{-}$, from the perspective that the $D_{s1}(2536)$ is a molecular state, mostly made from $K^{\ast }D$ 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 $D_{s1}(2460)\to D_s^{+}{\pi }^{+}{\pi }^{-}$, which has been measured by the LHCb collaboration and analyzed theoretically from the perspective that the $D_{s1}(2460)$ is a molecular state of $D^{\ast }K$, 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 $D_{s1}(2460)\to D_s^{+}{\pi }^{+}{\pi }^{-}$ 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 $D_{s1}(2460)\to D_s^{+}{\pi }^{+}{\pi }^{-}$ 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 $D_{s1}(2536)$.

Comments: 21 pages, 3 figures. Revised version with further discussions and references