  Antiferromagnetic or charge density wave fluctuations couple with light
through the recently discovered {\pi}-ton contribution to the optical
conductivity, and quite generically constitute the dominant vertex corrections
in low-dimensional correlated electron systems. Here we study the arguably
simplest version of these $\pi$-tons based on the semi-analytical random phase
approximation (RPA) ladder in the transversal particle-hole channel. The vertex
corrections to the optical conductivity are calculated directly for real
frequencies. We validate that the RPA qualitatively reproduces the {\pi}-ton
vertex corrections to the Drude peak in the Hubbard model. Depending on the
temperature we find vertex corrections to broaden or sharpen the Drude peak.
