Dₛ → f₀(980) form factors and the Dₛ⁺ → (f₀(980) → )[ π π ] SI = 0 e⁺ ν ₑ decay from light-cone sum rules

In this paper we revisit Dₛ → f₀(980) D s → f 0 ( 980 ) form factors from the light-cone sum rules based on the q̄q q ¯ q picture of f₀(980) f 0 ( 980 ) . The main motivation of this study is the decay width of Dₛ⁺ → [ π π ] SI = 0 e⁺ ν ₑ D s + → π π S I = 0 e + ν e measured recently by BESIII collaboration and the Dₛ → f₀(980) D s → f 0 ( 980 ) form factor extracted under the resonant model, here the subscript S and superscript I=0 I = 0 indicate the S -wave isoscalar dipion system. Our result of the differential width of Dₛ⁺ → f₀(980) (→ [ π π ] SI = 0) e⁺ ν ₑ D s + → f 0 ( 980 ) ( → π π S I = 0 ) e + ν e decay obtained under the narrow width approximation is lower than the data, the result obtained under the resonant Flatté model is consistent with the data, indicating a sizable mixing ~ 20∘ ∼ 20 ∘ between s̄s s ¯ s and ūu+d̄d u ¯ u + d ¯ d of f₀ f 0 . In order to get a model independent prediction, we suggest to calculate Dₛ → [ π π ] I = 0 D s → π π I = 0 form factors with the isoscalar dipion light-cone distribution amplitudes. Our calculation of Dₛ → [ π π ] I = 0 D s → π π I = 0 form factors is carried out at leading twist level due to the finite knowledge of dipion system, the differential width shows a moderate evolution in contrast to that obtained from the narrow width approximation and the Flatté model. Since the Dₛ → f₀(980) D s → f 0 ( 980 ) form factors is dominated by the twist three contribution, further measurements on four-body semileptonic charm decays would help us to study the dimeson light-cone distribution amplitudes, especially for the subleading twist one.