  Correlation functions of gauge-invariant composite operators in N=4 super
Yang-Mills theory can be computed by integrability using triangulations. The
elementary tile in this process is the hexagon, which should be glued by
appropriately inserting resolutions of the identity involving virtual
("mirror") magnons. We consider this problem for five-point functions of
protected operators. At one-loop in the 't Hooft coupling, it is necessary to
glue three adjacent tiles which involves two virtual magnons scattering among
each other. We show that the result can be simplified by using an adapted
mirror rotation and employing appropriate summation techniques. The
mirror-particle contributions then yield hyperlogarithms of weight two.
Finally, we use these results to investigate braiding prescriptions introduced
in earlier work on the problem.
