Phase-constrained ${\Sigma }^{\ast }$ spectroscopy in the pure-$I=1$ reactions $K_{L}p\to {\pi }^{+}{\Sigma }^0$ and $K_{L}p\to {\pi }^{+}\Lambda$

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 $K_{L}p$ reactions, we present, to our knowledge, the first simultaneous analysis of the pure-$I=1$ reactions $K_{L}p\to {\pi }^{+}{\Sigma }^0$ and $K_{L}p\to {\pi }^{+}\Lambda$ 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 ${\chi }^2/d.o.f.=1.604$. We find clear channel complementarity: the $t$-channel $K^{\ast }$ 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 ${\Lambda }^{\ast }$ spectrum.

Comments: 6+8 pages, 3+4 figures