Roles of and in the decays

Zhong-Yu Wang; Wei Liang

doi:10.1140/epjc/s10052-025-14372-x

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 644
https://doi.org/10.1140/epjc/s10052-025-14372-x

Regular Article - Theoretical Physics

Roles of $f_{0} (500)$ $f_{0}(500)$ and $f_{0} (980)$ $f_{0}(980)$ in the $D_{(s)}^{+} \to π^{+} π^{+} π^{-}$ $D_{(s)}^{+}\rightarrow \pi ^{+}\pi ^{+}\pi ^{-}$ decays

Zhong-Yu Wang¹ and Wei Liang²^a

¹ College of Physics, Guizhou University, 550025, Guiyang, China
² School of Physics, Central South University, 410083, Changsha, China

^a 212201014@csu.edu.cn

Received: 19 January 2025
Accepted: 26 May 2025
Published online: 11 June 2025

Abstract

With the recent measurements of the $D_{s}^{+} \to π^{+} π^{+} π^{-}$ $D_{s}^{+}\rightarrow \pi ^{+}\pi ^{+}\pi ^{-}$ and $D^{+} \to π^{+} π^{+} π^{-}$ $D^{+}\rightarrow \pi ^{+}\pi ^{+}\pi ^{-}$ decays by the LHCb Collaboration, we study these two decay processes by considering the final state interaction formalism. Taking into account the external and internal W-emission dominant mechanisms at the quark level, our model can naturally explain why the $D_{s}^{+}$ $D_{s}^{+}$ decay only has a contribution from the $f_{0} (980)$ $f_{0}(980)$ resonance, while the $D^{+}$ $D^{+}$ decay has contributions from both the $f_{0} (500)$ $f_{0}(500)$ and $f_{0} (980)$ $f_{0}(980)$ states. The magnitudes and phases of $π^{+} π^{-}$ $\pi ^{+}\pi ^{-}$ for S-wave amplitudes in our model are in agreement with the experimental measurements. These results support the interpretations of $f_{0} (500)$ $f_{0}(500)$ and $f_{0} (980)$ $f_{0}(980)$ as the $π π$ $\pi \pi$ and $K \bar{K}$ $K\bar{K}$ resonances, respectively, where they are dynamically generated from the S-wave pseudoscalar-pseudoscalar meson interactions within the chiral unitary approach.

© The Author(s) 2025

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Funded by SCOAP³.

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Roles of f0(500) and f0(980) in the D(s)+→π+π+π- decays

Conference announcements

Roles of $f_{0} (500)$ $f_{0}(500)$ and $f_{0} (980)$ $f_{0}(980)$ in the $D_{(s)}^{+} \to π^{+} π^{+} π^{-}$ $D_{(s)}^{+}\rightarrow \pi ^{+}\pi ^{+}\pi ^{-}$ decays