Femtoscopic correlation functions for general partial waves: Application to the $\Lambda(1520)$ resonance

The femtoscopic correlation function has been established in recent years as a high-precision tool for investigating hadron-hadron interactions and exotic states, providing stringent constraints on the dynamics of low-energy strong interactions. However, current research has been predominantly focused on the $s$-wave interaction between hadrons, while studies of higher partial waves remain scarce. We present a general analytical expression for the femtoscopic correlation function in an arbitrary partial wave using the Lippmann-Schwinger equation. This formalism is applied to constrain the $d$-wave $K^-p$ scattering through a combined study of the $K^-p$ correlation function and the $D_{03}$ scattering amplitude of $\bar K N \to \bar K N$ and $\bar K N \to \pi\Sigma$ processes, from which the properties of $\Lambda(1520)$ are extracted and found to be in good agreement with the experimental results. These findings demonstrate the feasibility of determining dynamics between hadrons through femtoscopic correlation functions and scattering amplitudes with higher partial waves.