Role of the $\Sigma(1430)(1/2^-)$ in the $J/\psi \to \Lambda \bar{\Lambda} \pi^0$ reaction

Abstract

We study the $J/\psi \to \bar{\Lambda} \Lambda \pi^0$ reaction, an isospin violating reaction, by looking at the trios of baryon-antibaryon-pseudoscalar meson that conform a singlet of $\text{SU}(3)$ in the $u, d, s$ quarks. These terms conserve isospin; however, once the final-state interactions of meson-baryon and meson-antibaryon are taken into account, isospin is violated due to the different masses of particles within the same isospin multiplets. Since the reaction is tied to the interaction of particles, only resonances that are dynamically generated by these interactions show up in the reaction. In this sense, our approach produces the $\Sigma(1430)(1/2^-)$ state, but not the $\Sigma(1385)(3/2^+)$. Comparing with the BESIII data we observe that, within the limited statistics of the experiment, the data show a structure {around $M_{\pi\Lambda} = 1430$ MeV} that is reproduced by the theory, and no signal is seen for the $\Sigma(1385)(3/2^+)$ as the theory predicts. We call for a future update of the experiment once better statistics become available.