form factors and the decay from light-cone sum rules

Shan Cheng; Shu-Lei Zhang

doi:10.1140/epjc/s10052-024-12734-5

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 379
https://doi.org/10.1140/epjc/s10052-024-12734-5

Regular Article - Theoretical Physics

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

Shan Cheng¹^,2^,3^a and Shu-Lei Zhang¹^,2^,3

¹ School of Physics and Electronics, Hunan University, 410082, Changsha, People’s Republic of China
² School for Theoretical Physics, Hunan University, 410082, Changsha, People’s Republic of China
³ Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, 410082, Changsha, People’s Republic of China

^a scheng@hnu.edu.cn

Received: 2 November 2023
Accepted: 29 March 2024
Published online: 9 April 2024

Abstract

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

Mathematics Subject Classification: 13.20.Fc Decays of charmed mesons || 11.55.Hx Sum rules

© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.