Dₛ f₀ (980) form factors and the Dₛ^+ (f₀ (980) ) ₒ^I = 0 e^+ ₑ decay from light-cone sum rules

Abstract In this paper we revisit Dₛ f₀ (980) D s → f 0 (980) form factors from the light-cone sum rules based on the qq q ¯ q picture of f₀ (980) f 0 (980). The main motivation of this study is the decay width of Dₛ^+ ₒ^I = 0 e^+ 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) (ₒ^I = 0) e^+ 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 ss s ¯ s and uu+dd u ¯ u + d ¯ d of f₀ f 0. In order to get a model independent prediction, we suggest to calculate Dₛ ^I = 0 D s → π π I = 0 form factors with the isoscalar dipion light-cone distribution amplitudes. Our calculation of Dₛ ^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.