Low-lying $\Lambda$ and $\Sigma$ resonances studied with the forward $K^{\ast }$ productions off the proton induced by a high-momentum $\pi$ beam

Abstract

We develop a novel model utilizing the forward $K^{\ast }$ production reaction off the nucleon, $\pi N\to K^{\ast }MB$, induced by a high-momentum $\pi$ beam, as a tool to study low-lying $Y^{\ast }$ resonances below and just above the $\bar{K}N$ threshold. Because conventional $K^{-}p$ scattering experiments face difficulties in directly accessing this kinematic region, the proposed reaction offers a valuable complementary approach for $Y^{\ast }$ spectroscopy. The constructed model is based on the one-meson exchange mechanism, which is known to dominate forward-angle production at high energies, and the half-off-shell scattering amplitudes from the ANL-Osaka dynamical coupled-channels models (Model A and Model B). We predict various observables, including differential cross sections and angular distributions. Our results demonstrate significant enhancements in the subthreshold region of the invariant mass spectra. Notably, we show that overlapping resonances, such as a potential new $3/2^{+}$ $\Sigma$ state and the well-established $\Sigma (1385)3/2^{+}$, can constitute a single peak in the $\pi \Lambda$ mass spectrum, indicating that the existence of previously unconfirmed subthreshold states cannot be ruled out by analyzing only the existing mass spectrum data. Furthermore, we find that angular distributions provide strong discriminatory power to disentangle such overlapping states through partial-wave interference effects, while the $t^{\prime }$ and ${\varphi }_M^{\ast }$ dependencies provide crucial constraints on the high-energy production mechanisms. Our predictions for these highly sensitive observables can facilitate high-statistics measurements, which are accessible at modern hadron facilities such as J-PARC, to unravel the $S=-1$ $Y^{\ast }$ mass spectrum.

22 pages, 20 figures, published version

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