Title: Weak lensing deflection of three-point correlation functions,
Abstract: Weak gravitational lensing alters the apparent separations between observed
sources, potentially affecting clustering statistics. We derive a general
expression for the lensing deflection which is valid for any three-point
statistic, and investigate its effect on the three-point clustering correlation
function. We find that deflection of the clustering correlation function is
greatest at around $z=2$. It is most prominent in regions where the correlation
function varies rapidly, in particular at the baryon acoustic oscillation scale
where it smooths out the peaks and troughs, reducing the peak-to-trough
difference by about 0.1 percent at $z=1$ and around 2.3 percent at $z=10$. The
modification due to lensing deflection is typically at the per cent level of
the expected errors in a Euclid-like survey and therefore undetectable.