Three-baryon femtoscopy as an effective 3$\rightarrow$3 scattering experiment

Scattering experiments have long been the gold standard for constraining hadron$-$hadron interactions, providing direct information on the angular momentum and spin dependence over a wide range of kinematic configurations. However, experimental constraints on three-body dynamics remain limited, specifically for unbound systems and systems involving short-lived hadrons. In this work, the three-proton correlation function is measured in pp collisions at $\sqrt{s}=13.6$ TeV with ALICE at the LHC and presented as a novel approach to access hadronic interactions in three-body systems. A new analysis strategy is employed to isolate the p$-$p$-$p contribution to the correlation function by correcting for background channels and experimental effects, and enabling a direct comparison with state-of-the-art three-body continuum calculations. The extracted correlation function provides the first direct access to the isospin $3/2$ three-body system. The measured observable is found to be sensitive to the partial-wave structure of the nucleon$-$nucleon interaction and indicates that the nuclear interaction acts even at high angular momentum and parity states of the three-body system, revealing an effective long-range attractive component, observed experimentally for the first time in a three-proton continuum system. Hence, three-hadron femtoscopy emerges as an effective 3$\rightarrow$3 scattering experiment with three unbound hadrons in initial and final states. The copious production of hyperons at the modern high-energy colliders ensures the possibility of extending such measurements beyond nucleons, opening a new avenue for future precision studies of three-body dynamics in the strangeness sector.