Eur. Phys. J. C (2023) 83: 954
https://doi.org/10.1140/epjc/s10052-023-12131-4

Regular Article - Theoretical Physics

Theoretical interpretation of the $\mathrm{\Xi }(1620)$ and $\mathrm{\Xi }(1690)$ resonances seen in ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^{-}{\pi }^{+}{\pi }^{+}$ decay

¹ Department of Physics, Guangxi Normal University, 541004, Guilin, China
² Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University, 541004, Guilin, China
³ Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC Institutos de Investigación de Paterna, Aptdo.22085, 46071, Valencia, Spain

^c liangwh@mailbox.gxnu.edu.cn

Received: 25 August 2023
Accepted: 9 October 2023
Published online: 24 October 2023

Abstract

We study the Belle reaction ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Xi }}^{-}{\pi }^{+}{\pi }^{+}$ looking at the mass distribution of ${\pi }^{+}\mathrm{\Xi }$, where clear signals for the $\mathrm{\Xi }(1620)$ and $\mathrm{\Xi }(1690)$ resonances are seen. These two resonances are generated dynamically from the interaction in coupled channels of $\pi \mathrm{\Xi },\overline{K}\mathrm{\Lambda },\overline{K}\mathrm{\Sigma }$ and $\eta \mathrm{\Xi }$ within the chiral unitary approach. Yet, the weak decay process at the quark level, together with the hadronization to produce pairs of mesons, does not produce the $\pi \pi \mathrm{\Xi }$ final state. In order to produce this state one must make transitions from the $\overline{K}\mathrm{\Lambda },\overline{K}\mathrm{\Sigma }$ and $\eta \mathrm{\Xi }$ components to $\pi \mathrm{\Xi }$, and this interaction is what produces the resonances. So, the reaction offers a good test for the molecular picture of these resonances. Adding the contribution of the ${\mathrm{\Xi }}^{\ast }(1530)$ and some background we are able to get a good reproduction of the mass distribution showing the signatures of the two resonances as found in the experiment.