$$D_s \rightarrow f_0(980)$$ form factors and the $$D_s^+ \rightarrow (f_0(980) \rightarrow )\left[ \pi \pi \right] _{S}^{\textrm{I} = 0} e^+ \nu _e$$ decay from light-cone sum rules

Abstract

AbstractIn this paper we revisit $$D_s \rightarrow f_0(980)$$ D s → f 0 ( 980 ) form factors from the light-cone sum rules based on the $${\bar{q}}q$$ q ¯ q picture of $$f_0(980)$$ f 0 ( 980 ) . The main motivation of this study is the decay width of $$D_s^+ \rightarrow \left[ \pi \pi \right] _{S}^{\textrm{I} = 0} e^+ \nu _e$$ D s + → π π S I = 0 e + ν e measured recently by BESIII collaboration and the $$D_s \rightarrow f_0(980)$$ D s → f 0 ( 980 ) form factor extracted under the resonant model, here the subscript S and superscript $$\textrm{I}=0$$ I = 0 indicate the S-wave isoscalar dipion system. Our result of the differential width of $$D_s^+ \rightarrow f_0(980) (\rightarrow \left[ \pi \pi \right] _{S}^{\textrm{I} = 0}) e^+ \nu _e$$ 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 $$\sim 20^{\circ }$$ ∼ 20 ∘ between $${\bar{s}}s$$ s ¯ s and $${\bar{u}}u+{\bar{d}}d$$ u ¯ u + d ¯ d of $$f_0$$ f 0 . In order to get a model independent prediction, we suggest to calculate $$D_s \rightarrow \left[ \pi \pi \right] ^{\textrm{I} = 0}$$ D s → π π I = 0 form factors with the isoscalar dipion light-cone distribution amplitudes. Our calculation of $$D_s \rightarrow \left[ \pi \pi \right] ^{\textrm{I} = 0}$$ 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 $$D_s \rightarrow f_0(980)$$ 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.