Boosting HI-Galaxy Cross-Clustering Signal through Higher-Order Cross-Correlations

After reionization, neutral hydrogen (HI) traces the large-scale structure (LSS) of the Universe, enabling HI intensity mapping (IM) to capture the LSS in 3D and constrain key cosmological parameters. We present a new framework utilizing higher-order cross-correlations to study HI clustering around galaxies, tested using real-space data from the IllustrisTNG300 simulation. This approach computes the joint distributions of $k$-nearest neighbor ($k$NN) optical galaxies and the HI brightness temperature field smoothed at relevant scales (the $k$NN-field framework), providing sensitivity to all higher-order cross-correlations, unlike two-point statistics. To simulate HI data from actual surveys, we add random thermal noise and apply a simple foreground cleaning model, filtering out Fourier modes of the brightness temperature field with $k_\parallel < k_{\rm min,\parallel}$. Under current levels of thermal noise and foreground cleaning, typical of a Canadian Hydrogen Intensity Mapping Experiment (CHIME)-like survey, the HI-galaxy cross-correlation signal in our simulations, using the $k$NN-field framework, is detectable at $>30\sigma$ across $r = [3,12] \, h^{-1}$Mpc. In contrast, the detectability of the standard two-point correlation function (2PCF) over the same scales depends strongly on the foreground filter: a sharp $k_\parallel$ filter can spuriously boost detection to $8\sigma$ due to position-space ringing, whereas a less sharp filter yields no detection. Nonetheless, we conclude that $k$NN-field cross-correlations are robustly detectable across a broad range of foreground filtering and thermal noise conditions, suggesting their potential for enhanced constraining power over 2PCFs.