Feasibility Study of Measuring $\Lambda^0\to n\pi^{0}$ Using a High-Granularity Zero-Degree Calorimeter at the Future Electron-Ion Collider

Key measurements at the future Electron-Ion Collider (EIC), including first-of-their-kind studies of kaon structure, require the detection of $\Lambda^0$ at forward angles. We present a feasibility study of $\Lambda^0 \to n\pi^0$ measurements using a high-granularity Zero Degree Calorimeter to be located about 35 m from the interaction point. We introduce a method to address the unprecedented challenge of identifying $\Lambda^0$s with energy $O(100)$ GeV that produce displaced vertices of $O(10)$ m. In addition, we present a reconstruction approach using graph neural networks. We find that the energy and angle resolution for $\Lambda^0$ is similar to that for neutrons, both of which meet the requirements outlined in the EIC Yellow Report.Furthermore, we estimate performance for measuring the neutron's direction in the $\Lambda^0$ rest frame, which reflects the $\Lambda^0$ spin polarization. We estimate that the neutral-decay channel $\Lambda^0 \to n\pi^0$ will greatly extend the measurable energy range for the charged-decay channel $\Lambda^0 \to p\pi^-$, which is limited by the location of small-angle trackers and the accelerator magnets. This work paves the way for EIC studies of kaon structure and spin phenomena.