T-matrix analysis of pion-proton femtoscopy

The observed shift of the $\Delta(1232)$ resonance peak in $\pi$-$p$ femtoscopic correlations challenges the conventional Breit-Wigner description of resonances in femtoscopy. We revisit the Koonin-Pratt framework by formulating femtoscopy in the momentum-space representation and employing the T-matrix approach to disentangle on-shell and off-shell contributions. By employing a Friedrichs-Lee model constrained by low-energy scattering data, we demonstrate that the finite spatial extent of the emission source induces sensitivity to off-shell dynamics, which leads to a peak shift accompanied by a dip on the high-momentum side of the peak. The resulting correlation strength, however, does not fully reproduce the measured amplitude, and a high-momentum side dip is not observed in experiments. The remaining discrepancies may be attributed to the structural complexity of the emission source beyond a simple spherical Gaussian approximation.