Phase-constrained $\Sigma^*$ spectroscopy in the pure-$I=1$ reactions $K_Lp\to\pi^+\Sigma^0$ and $K_Lp\to\pi^+\Lambda$

Abstract

Low-energy $\bar K N$ scattering provides direct access to strange-baryon spectroscopy, but conventional charged-kaon reactions mix the $I=0$ and $I=1$ amplitudes. Motivated by the isospin-selective nature of the $K_Lp$ reactions, we present, to our knowledge, the first simultaneous analysis of the pure-$I=1$ reactions $K_Lp\to\pi^+\Sigma^0$ and $K_Lp\to\pi^+\Lambda$ in which a common set of resonance parameters and a fixed relative-phase convention are imposed on both final states. Within an effective-Lagrangian model, a joint fit of available differential cross sections and recoil polarizations yields $\chi^2/\mathrm{d.o.f.}=1.604$. We find clear channel complementarity: the $t$-channel $K^*$ exchange is more important in $K_L p\to \pi^+\Lambda$, especially at forward angles, whereas $K_L p\to \pi^+\Sigma^0$ is more sensitive to the contribution of $\Sigma(1620)\,1/2^-$. At the same time, $\Sigma(1660)\,1/2^+$ remains important through interference effects in both channels. These results demonstrate the importance of multichannel, phase-constrained analyses for establishing the $I=1$ hyperon spectrum and provide timely phenomenological input for future high-precision measurements by the KLF program at JLab. Once the pure $I=1$ amplitudes are reliably determined, they will also enable the separation of the $I=0$ component in the much more abundant $K^- p\to \pi^\pm\Sigma^\mp$ data, opening a path toward a more quantitative study of the $\Lambda^*$ spectrum.