Letter
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Complete determination of $S U (3)_{F}$ amplitudes and strong phase in $Λ_{c}^{+} \to Ξ^{0} K^{+}$

Chao-Qiang Geng^1,*, Xiao-Gang He^2,3,†, Xiang-Nan Jin^1,‡, Chia-Wei Liu ^2,§, and Chang Yang ^2,∥

¹School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024
²Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240
³Department of Physics, National Taiwan University, Taipei 10617

^*cqgeng@ucas.ac.cn
^†hexg@sjtu.edu.cn
^‡xnjin@ucas.ac.cn
^§chiaweiliu@sjtu.edu.cn
^∥15201868391@sjtu.edu.cn

Phys. Rev. D 109, L071302 – Published 29 April, 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L071302

Abstract

The BESIII collaboration has recently reported the first time measurement of the decay asymmetry $α (Λ_{c}^{+} \to Ξ^{0} K^{+}) = 0.01 \pm 0.16 (stat) \pm 0.03 (syst)$ and also a sizable phase shift of $δ_{P} - δ_{S} = - 1.55 \pm 0.25$ or $1.59 \pm 0.25$ between S- and P-wave amplitudes. This implies significant strong phase shifts in the decay amplitudes. The strong phases indicate the existence of rescattering or loop effects, which are challenging to calculate due to nonperturbative effects. By employing the flavor $S U (3)_{F}$ symmetry and applying the Körner-Pati-Woo theorem to reduce the number of parameters, we find that the current data already allow us to obtain, for the first time, model-independent decay amplitudes and their strong phases. The establishment of the existence of sizable strong phases opens a window for future investigations into $C P$ violation. In our fit, a notable discrepancy emerges in the branching ratio of $Ξ_{c}^{0} \to Ξ^{-} π^{+}$ . The direct relationship between $Γ (Λ_{c}^{+} \to Λ e^{+} ν_{e})$ and $Γ (Ξ_{c}^{0} \to Ξ^{-} e^{+} ν_{e})$ , along with newly discovered $S U (3)_{F}$ relations, collectively suggests an underestimation of $B (Ξ_{c}^{0} \to Ξ^{-} π^{+})$ in experimental findings.

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References (28)

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Phys. Rev. D 109, L071302– Published 29 April, 2024

Vol. 109, Iss. 7 — 1 April 2024

Received 16 October 2023
Revised 9 November 2023
Accepted 27 March 2024

DOI: https://doi.org/10.1103/PhysRevD.109.L071302

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Complete determination of $S U (3)_{F}$ amplitudes and strong phase in $Λ_{c}^{+} \to Ξ^{0} K^{+}$

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Complete determination of SU(3)F amplitudes and strong phase in Λc+→Ξ0K+

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Complete determination of $S U (3)_{F}$ amplitudes and strong phase in $Λ_{c}^{+} \to Ξ^{0} K^{+}$