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We consider Wilson loops in planar N=4 SYM for null polygons in the limit oftwo crossing edges. The analysis is based on a renormalisation group technique.We show that the previously obtained result for the leading and next-leadingdivergent term of the two loop hexagon remainder is in full agreement with theappropriate continuation of the exact analytic formula for this quantity.Furthermore, we determine the coefficients of the leading and next-leadingsingularity for the three loop remainder function for null n-gons with n >= 6.

Hexagon remainder function in the limit of self-crossing up to three loops