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

TL;DR

This work develops a generalized femtoscopic correlation framework that includes arbitrary partial waves through the Lippmann-Schwinger equation to probe hadron–hadron interactions. It applies the formalism to the $K^-p$ system in the $d$-wave sector using a coupled-channel, chiral-unitary approach that dynamically generates the $\Lambda(1520)$ resonance and yields its pole position, couplings, and compositeness. The analysis reproduces the measured $K^-p$ correlation function, reveals a $d$-wave–driven peak near $p_{K^-}\sim 240$ MeV, and provides a consistent set of branching ratios with the PDG, together with a pole at $\sqrt{s_{\rm pole}}=1519.75 - i6.57$ MeV and sizable molecular components. This demonstrates that femtoscopy with higher partial waves can tightly constrain hadron-hadron dynamics and the internal structure of high-spin resonances, offering a new tool for low-energy QCD studies.

Abstract

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 $\bar K N \to πΣ$ processes, from which the properties of $Λ(1520)$ 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.

Figures (2)

• Figure 1: The fitted result of the $K^-p$ correlation functions. The experimental data are taken from Ref. ALICE:2022yyh.
• Figure 2: Fitted results of the $D_{03}$ scattering amplitudes $T_{\bar{K}N \to \bar{K}N}$ and $T_{\bar{K}N \to \pi\Sigma}$. The data are taken from Ref. Zhang:2013cua.