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

The internal structure of the charm-strange mesons $D_{s0}^*(2317)$ and $D_{s1}(2460)$ are subject of intensive studies. Their widths are small because they decay dominantly through isospin-breaking hadronic channels $D_{s0}^*(2317)^+\to D_s^+\pi^0$ and $D_{s1}(2460)^+\to D_s^{*+}\pi^0$. 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 $D^*K$ 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 $\Gamma(D_{s1}(2460)^+\to D_s^+\pi^+\pi^-)/\Gamma(D_{s1}(2460)^+\to D_s^{*+}\pi^0)$ 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.