We 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.