Validation of the Hybrid Bias Expansion model for the galaxy bispectrum
The Hybrid Bias Expansion model (also known as Hybrid Effective Field Theory, HEFT) provides a promising way to extend the range of validity of perturbative large-scale structure modelling by replacing perturbative gravitational evolution with the nonlinear displacement field measured from $N$-body simulations. While this approach has already been shown to improve the modelling of the power spectrum, its validity at the bispectrum level has not yet been established. In this work we perform a first systematic real-space validation of the Hybrid bispectrum model using DESI-like LRG and ELG mock catalogues constructed at fixed cosmology on volumes similar to those of DESI's LRG samples. We find that the model remains self-consistent up to $k_{\rm max}^B \simeq 0.25\,h\,{\rm Mpc}^{-1}$, while clear signs of breakdown appear for a similar EFT tree-level bispectrum approach at $k_{\rm max}^B \gtrsim 0.13\,h\,{\rm Mpc}^{-1}$. We also show that adding matter cross-statistics significantly improves the precision of the recovered bias parameters, while a partial third-order extension including only the $\delta^3$ operator does not extend the validity range. Finally, we find a strong hierarchy among the bispectrum basis terms when grouped by total bias-operator order, with the lowest-order sectors dominating the total amplitude, which has important implications in emulation strategies.