Three-loop leading singularities and Bern-Dixon-Smirnov ansatz for five particles

We use the leading singularity technique to determine the planar three-loop five-particle amplitude in N=4 super Yang-Mills in terms of a simple basis of integrals. We analytically compute the integral coefficients for both the parity-even and the parity-odd parts of the amplitude. The parity-even part involves only dual conformally invariant integrals. Using the method of obstructions we numerically evaluate two previously unfixed coefficients that appear in the three-loop Bern Dixon Smirnov ansatz.