Informal High Energy Theory Seminar

We continue a program of developing a new method for computing two-loop amplitudes based on generalized unitarity. In this approach, the two-loop amplitude is expanded in a basis of integrals, and the coefficients of the integrals are computed from tree amplitudes by performing generalized cuts. These cuts are defined as multidimensional contour integrals. The contours are particular linear combinations of tori encircling the leading singularities of the integrand. In contrast to the situation in one-loop generalized unitarity where such contours are unique, the analogous two-loop contours found in arXiv:1108.1180 were observed to depend on 6 free parameters. In this talk, we explain how these free parameters are related to the sharing of two-loop leading singularities between Riemann surfaces naturally associated with the solutions to the on-shell constraints. In doing so, we point out a natural relation of the leading singularities to the IR divergences of the integral. We give a complete classification of the solutions to the maximal cut of the general double-box integral, culminating in an elliptic curve. We discuss the relation of this elliptic curve to the appearance of non-polylogarithm-type functions in the analytical expression for a particular two-loop integral. In addition, we point out that the chiral integrals recently introduced by Arkani-Hamed et al. can be used as master integrals for the double-box contributions to the two-loop amplitudes in any gauge theory. The IR finiteness of these integrals allow for their coefficients as well as their integrated expressions to be evaluated in strictly four dimensions, providing significant technical simplification. We evaluate these integrals at four points and obtain remarkably compact results.