Analysis of $\Sigma^*$ via isospin selective reaction $K_Lp \to \pi^+\Sigma^0$

The isospin-selective reaction $K_Lp \to \pi^+\Sigma^0$ provides a clean probe for investigating $I=1$ $\Sigma^*$ resonances. In this work, we perform an analysis of this reaction using an effective Lagrangian approach for the first time, incorporating the well-established $\Sigma(1189) 1/2^+$, $\Sigma(1385) 3/2^+$, $\Sigma(1670) 3/2^-$, $\Sigma(1775) 5/2^-$ states, while also exploring contributions from other unestablished states. By fitting the available differential cross section and recoil polarization data, adhering to partial-wave phase conventions same as PDG, we find that besides the established resonances, contributions from $\Sigma(1660) 1/2^+$, $\Sigma(1580) 3/2^-$ and a $\Sigma^*(1/2^-)$ improve the description. Notably, a $\Sigma^*(1/2^-)$ resonance with mass around 1.54 GeV, consistent with $\Sigma(1620)1/2^-$, is found to be essential for describing the data in this channel, a stronger indication than found in previous analyses focusing on $\pi\Lambda$ final states. While providing complementary support for $\Sigma(1660) 1/2^+$ and $\Sigma(1580) 3/2^-$, our results highlight the importance of the $\Sigma(1620) 1/2^-$ region in $K_Lp \to \pi^+\Sigma^0$. Future high-precision measurements are needed to solidify these findings and further constrain the $\Sigma^*$ spectrum.