Reconstructing rare particle source by femtoscopic correlations

Measurement of particle emission source is a fundamental objective of femtoscopy in high-energy nuclear collisions. Conventional analyses rely on Gaussian parameterizations of pair emission sources, which makes the extraction of single-particle emission sources challenging, particularly for rare particles. Here, we introduce a novel Statistical Reconstruction method that allows extracting information of target single-particle sources relative to a data-constrained reference source instead of the Gaussian assumption. The correlation function is expressed as an ensemble average over single-particle-conditioned correlation kernel, defined as the particle-by-particle contribution to the correlation function conditioned by the target particles. For particles with rare yeilds, the particle-by-particle distribution of this kernel can be transformed into event-by-event extraction and becomes experimentally accessible, enabling a direct statistical reconstruction of the single-particle emission source, instead of inferring a pair source. We apply this method to reconstruct $J/\psi$ source via $p-J/\psi$ correlations, using HAL QCD-derived $NJ/\psi$ potentials in $\sqrt{s}=13.6$~TeV $pp$ collisions simulated with EPOS4HQ. The reconstructed source reproduces the key characteristics and this new approche achieves a systematic uncertainty of approximately $13\%$ based on EPOS4 simulation.