Isospin-conserving hadronic decay of the $D_{s1}(2460)$ into $D_s{\pi }^{+}{\pi }^{-}$

Abstract

The internal structure of the charm-strange mesons $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ are subject of intensive studies. Their widths are small because they decay dominantly through isospin-breaking hadronic channels $D_{s0}^{\ast }(2317{)}^{+}\to D_s^{+}{\pi }^0$ and $D_{s1}(2460{)}^{+}\to D_s^{\ast +}{\pi }^0$. The $D_{s1}(2460)$ can also decay into the hadronic final states $D_s^{+}\pi \pi$, conserving isospin. In that case there is, however, a strong suppression from phase space. We study the transition $D_{s1}(2460{)}^{+}\to D_s^{+}{\pi }^{+}{\pi }^{-}$ in the scenario that the $D_{s1}(2460)$ is a $D^{\ast }K$ hadronic molecule. The $\pi \pi$ final state interaction is taken into account through dispersion relations. We find that the ratio of the partial widths of the $\Gamma (D_{s1}(2460{)}^{+}\to D_s^{+}{\pi }^{+}{\pi }^{-})/\Gamma (D_{s1}(2460{)}^{+}\to D_s^{\ast +}{\pi }^0)$ obtained in the molecular picture is consistent with the existing experimental measurement. More interestingly, we demonstrate that the ${\pi }^{+}{\pi }^{-}$ invariant mass distribution shows a double bump structure, which can be used to disentangle the hadronic molecular picture from the compact state picture for the $D_{s1}(2460{)}^{+}$. Predictions on the $B_{s1}^0\to B_s^0{\pi }^{+}{\pi }^{-}$ are also made.

Comments: 16 pages, 5 figures; the published version