We present the first fully off-shell covariant investigation of the $S=-1$ meson-baryon interaction within the 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 ${\pi }^{\pm }{\mathrm{\Sigma }}^{\mp }$ pairs. The $K^{-}p$ correlation functions are found to be consistent with previously published results based on the on-shell approximation, with marginal differences arising from slightly different descriptions of scattering data. The ${\pi }^{\pm }{\mathrm{\Sigma }}^{\mp }$ correlation functions are predicted for the first time and are expected to provide valuable constraints on the nature of the $\mathrm{\Lambda }(1405)$ resonance and the coupled-channel chiral dynamics of the $\overline{K}N-\pi \mathrm{\Sigma }$ system.

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• Chiral perturbation theory
• Hadron-hadron interactions
• Hyperons