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

Abstract

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