On the signature of the baryon-dark matter relative velocity in the two
  and three-point galaxy correlation functions
  We develop a configuration-space picture of the relative velocity between
baryons and dark matter that clearly explains how it can shift the BAO scale in
the galaxy-galaxy correlation function. The shift occurs because the relative
velocity is non-zero only within the sound horizon and thus adds to the
correlation function asymmetrically about the BAO peak. We further show that in
configuration space the relative velocity has a localized, distinctive
signature in the three-point galaxy correlation function (3PCF). In particular,
we find that a multipole decomposition is a favorable way to isolate the
relative velocity in the 3PCF, and that there is a strong signature in the l=1
multipole for triangles with 2 sides around the BAO scale. Finally, we
investigate a further compression of the 3PCF to a function of only one
triangle side that preserves the localized nature of the relative velocity
signature while also nicely separating linear from non-linear bias. We expect
that this scheme will substantially lessen the computational burden of finding
the relative velocity in the 3PCF. The relative velocity's 3PCF signature can
be used to correct the shift induced in the galaxy-galaxy correlation function
so that no systematic error due to this effect is introduced into the BAO as
used for precision cosmology.
