Lensing corrections on galaxy-lensing cross correlations and
  galaxy-galaxy auto correlations
  We study the impact of lensing corrections on modeling cross correlations
between CMB lensing and galaxies, cosmic shear and galaxies, and galaxies in
different redshift bins. Estimating the importance of these corrections becomes
necessary in the light of anticipated high-accuracy measurements of these
observables. While higher order lensing corrections (sometimes also referred to
as post Born corrections) have been shown to be negligibly small for lensing
auto correlations, they have not been studied for cross correlations. We
evaluate the contributing four-point functions without making use of the Limber
approximation and compute line-of-sight integrals with the numerically stable
and fast FFTlog formalism. We find that the relative size of lensing
corrections depends on the respective redshift distributions of the lensing
sources and galaxies, but that they are generally small for high
signal-to-noise correlations. We point out that a full assessment and judgement
of the importance of these corrections requires the inclusion of lensing
Jacobian terms on the galaxy side. We identify these additional correction
terms, but do not evaluate them due to their large number. We argue that they
could be potentially important and suggest that their size should be measured
in the future with ray-traced simulations. We make our code publicly available.
