Speaker
Description
While various theoretical studies have been performed for the excited $\Xi(1620)$ and $\Xi(1690)$ states, their nature was not well understood due to the lack of experimental data. Recently, the invariant mass distribution of the $\Xi_c\rightarrow\pi\pi\Xi$ decay was observed by the Belle collaboration. [1]
By fitting the invariant mass spectrum with the Breit-Wigner distribution, the mass and decay width of the $\Xi(1620)$ were obtained as $M_R=1610 $ MeV and $\Gamma_R=30 $ MeV, respectively. This result provides precise spectra of the $\Xi(1620)$ and $\Xi(1690)$ resonances, and therefore it is desired to perform detailed theoretical analysis.
In this talk, we study the excited $\Xi$ states as dynamically generated resonances in the meson-baryon scattering amplitude using the the chiral unitary approach. In the previous study [2], the mass and width of the $\Xi(1620)$ were predicted to be $M_R=1607$ MeV and $\Gamma_R=280$ MeV, with the natural values of the subtraction constants.
Because of the difference between the results of Ref. [2] and those by Belle, it is required to improve the model of $\Xi(1620)$. By adjusting the subtraction constants of $\pi\Xi$ and $\bar{K}\Lambda$ channels, we successfully reproduce the mass and width of $\Xi(1620)$ by Belle. We, however, find that the threshold effect shifts the resonance peak near the threshold, by comparing the coupled channels meson-baryon scattering amplitude with the Breit-Wigner distribution. We conclude that the cation must be paid to determine the resonance pole near the threshold.
While there is one threshold $\bar{K}^0\Lambda$ near the $\Xi(1620)$, there are two thresholds $\bar{K}^0 \Sigma^0$ and $K^- \Sigma^+$ near the $\Xi(1690)$ due to the isospin symmetry breaking.
Here, we analyze the $\Xi(1690)$ using the model in Ref. [3], which is based on the Belle data of the $\Lambda_c$ decay, and includes the isospin symmetry breaking effect. Then, we show that the $\Xi(1690)$ spectrum is affected by two thresholds $\bar{K}^0 \Sigma^0$ and $K^- \Sigma^+$ due to the isospin symmetry breaking.
In future, studying the invariant mass distribution of the $\Xi_c\rightarrow\pi\pi\Xi$ decay in comparison with the Belle data, we aim at the determination of the spin and parity of the $\Xi$ resonances.
References
[1]Belle collaboration, M.Sumihama et al., Phys. Rev. Lett. 122, 072501 (2019).
[2] A. Ramos, E. Oset and C. Bennhold, Phys. Rev. Lett. 89, 252001 (2002).
[3] T. Sekihara, PTEP 2015, no.9, 091D01 (2015).
