Weak lensing deflection of three-point correlation functions

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.