Bispectrum BAO and the baryon-dark matter relative velocity

We evaluate the Baryon Acoustic Oscillation (BAO) signal in the bispectrum as a tool to detect and characterize the relative velocity effect. We extend the existing framework by presenting an updated model for the redshift-space tree-level bispectrum that comprehensively incorporates all relative velocity terms. We introduce a novel, unbiased technique to extract the isotropic BAO dilation parameter (alpha iso) solely from the bispectrum monopole. Validated against N-body simulations, this template-based extraction successfully recovers the acoustic scale and enhances the statistical constraining power by about30%, when analyzed in tandem with the pre-reconstruction power spectrum, offering a powerful complement to standard post-reconstruction pipelines. We quantify how individual relative velocity components distort both two- and three-point statistics. We find that these effects induce distinct systematic shifts in the extracted alpha iso between the two probes. We find systematic discrepancies of up to 2% for b v squared= plus or minus0.05 and up to 20% for b delta bc-2. This differences demonstrate that a direct comparison of independent power spectrum and bispectrum BAO measurements can break parameter degeneracies and isolate the amplitude of these biases. Finally, we provide a concrete prescription to detect and constrain the three associated relative velocity bias parameters, showing that a joint analysis is highly sensitive to the b v squared and b delta bc amplitudes. This establishes the bispectrum BAO as a robust cosmological probe for current and next-generation galaxy surveys, serving both as a cross-check for standard analyses and a crucial diagnostic tool against systematic biases.