Studying the $K\Lambda$ strong interaction with femtoscopic correlation functions and the $N^*(1535)$

We investigate the $K \Lambda$ strong interaction dynamics around the energy region of $N^*(1535)$ resonance through femtoscopic correlation functions within the Koonin-Pratt formalism, where coupled-channel effects of $\pi N$, $K\Lambda$, $K \Sigma$ and $\eta N$ channels are taken into account, by means of which the $N^*(1535)$ resonance can be dynamically generated in the chiral unitary approach. Two-body scattering amplitudes are calculated using the chiral unitary approach, and the corresponding wave functions and correlation functions are obtained. Our analysis shows that the $\pi N$ channel becomes important to the $K^+\Lambda$ correlation function through coupled channel effects, even if its mass threshold is far from the energy region of the $N^*(1535)$. Furthermore, with the picture that the $N^*(1535)$ is a dynamically generated state, we can get a good reproduction of the experimental data on the $K^+\Lambda$ correlation function. This work establishes femtoscopic correlation functions as a sensitive probe for coupled-channel dynamics and validates the Koonin-Pratt framework in multi-channel hadronic systems, offering critical insights into some exotic hadron states and strong interaction mechanisms.