Resonant $a_0(980)$ state in triangle rescattering $D_s^{+}\to {\pi }^{+}{\pi }^0\eta$ decays

Abstract

We study the $D_s^{+}\to {\pi }^{+}(a_0(980{)}^0\to ){\pi }^0\eta$, ${\pi }^0(a_0(980{)}^{+}\to ){\pi }^{+}\eta$ decays, which have been recently measured by the BESIII collaboration. We propose that $D_s^{+}\to {\pi }^{+(0)}(a_0(980{)}^{0(+)}\to ){\pi }^{0(+)}\eta$ receives the contributions from the triangle rescattering processes, where $M^0$ and ${\rho }^{+}$ in $D_s^{+}\to M^0{\rho }^{+}$, by exchanging ${\pi }^{0(+)}$, are formed as $a_0(980{)}^{0(+)}$ and ${\pi }^{+(0)}$, respectively, with $M^0=(\eta ,{\eta }^{\prime })$. Accordingly, we calculate that $\mathcal{B}(D_s^{+}\to a_0(980{)}^{0(+)}{\pi }^{+(0)})=(1.7\pm 0.2\pm 0.1)\times 10^{-2}$ and $\mathcal{B}(D_s^{+}\to {\pi }^{+(0)}(a_0(980{)}^{0(+)}\to ){\pi }^{0(+)}\eta )=(1.4\pm 0.1\pm 0.1)\times 10^{-2}$, being consistent with the data.

Comments: Title changed, 9 pages, 5 diagrams, version published in EPJC