Off-shell Chiral Dynamics in the $\Lambda(1405)$ Resonance and $K^-p$ Femtoscopic Correlations

We present the first systematic investigation of the $S=-1$ meson--baryon interaction within a fully off-shell covariant unitarized chiral effective field theory framework up to next-to-leading order. In particular, we perform a detailed comparison with the widely used on-shell approximation. We find that the resulting scattering observables are very similar, thereby confirming the validity of key results obtained within the on-shell scheme. A notable advantage of the off-shell treatment, however, is the absence of unphysical left-hand cuts induced by the on-shell approximation. Employing the off-shell amplitudes, we compute the femtoscopic correlation functions for $K^-p$ and $\pi^\pm\Sigma^\mp$ pairs. The $K^-p$ correlation functions are found to be consistent with previously published results based on the on-shell approximation, with marginal differences attributed to slight variations in the descriptions of the scattering data. The $\pi^\pm\Sigma^\mp$ correlation functions are predicted for the first time, and are expected to provide valuable constraints on the nature of the $\Lambda(1405)$ resonance and the coupled-channel chiral dynamics of the $K^-p$ system.