Roles of $$a_0(980)^+ f_0(500,980)$$ and $$a_1(1260)^+\eta $$ production mechanisms in decay $$D_s^+ \rightarrow \pi ^+ \pi ^0 \pi ^0 \eta $$

Abstract

In this work, we theoretically investigate the decay mechanism of

based on BESIII data, considering two mechanisms: the production of two dynamically generated resonances,

$$D_s^+ \rightarrow a_0(980)^+ f_0(500,980)$$ D s + → a 0 ( 980 ) + f 0 ( 500 , 980 )

, and a process with one dynamically generated resonance,

$$D_s^+ \rightarrow a_1(1260)^+\eta $$ D s + → a 1 ( 1260 ) + η

. In the first mechanism, the interactions

$$\pi ^+\eta $$ π + η

and

$$K^+\bar{K}^0$$ K + K ¯ 0

are included to generate the

$$a_0(980)^+$$ a 0 ( 980 ) +

, while coupled-channel interactions involving

$$\pi ^+\pi ^-$$ π + π -

,

$$\pi ^0\pi ^0$$ π 0 π 0

,

$$K^+K^-$$ K + K -

,

$$K^0\bar{K}^0$$ K 0 K ¯ 0

,

$$\eta \eta $$ η η

, and

$$\pi ^0\eta $$ π 0 η

are adopted to generate the

$$f_0(500)$$ f 0 ( 500 )

as well as the

$$f_0(980)$$ f 0 ( 980 )

. For the second mechanism, the

$$\pi \rho $$ π ρ

and

$$\bar{K}^*{K} - K^*\bar{K}$$ K ¯ ∗ K - K ∗ K ¯

channels are included to generate the

$$a_1(1260)$$ a 1 ( 1260 )

. With these interactions, the amplitudes are calculated in the chiral unitary approach and used to compute the invariant mass spectra of

$$D_s^+ \rightarrow \pi ^+ \pi ^0 \pi ^0 \eta $$ D s + → π + π 0 π 0 η

. The results suggest that the peak near 1000 MeV in the

$$\pi ^+\eta $$ π + η

invariant mass spectrum can be well interpreted as the

$$a_0(980)^+$$ a 0 ( 980 ) +

arising from a cusp effect. The

$$f_0(980)$$ f 0 ( 980 )

, generated together with the

$$f_0(500)$$ f 0 ( 500 )

, is responsible for the small structure near 1000 MeV in the

$$\pi ^0\pi ^0$$ π 0 π 0

spectrum. The

$$a_1(1260)^+$$ a 1 ( 1260 ) +

and its decay to

$$\rho ^+\pi ^0$$ ρ + π 0

followed by the subsequent

$$\rho ^+$$ ρ +

decay provide a good description of the

$$\pi ^+\pi ^0\pi ^0$$ π + π 0 π 0

and

$$\pi ^+\pi ^0$$ π + π 0

mass spectra. The inclusion of an additional resonance near 800 MeV in the

$$\pi ^+\eta $$ π + η

spectrum leads to only a marginal improvement of the fit.