Progress towards 2 to 2 scattering at two-loops
E. W. N. Glover, M. E. Tejeda-Yeomans
TL;DR
The paper analyzes two-loop, massless 2→2 scattering amplitudes, focusing on the leading-colour, planar sector for qqbar→q' q'bar'. It develops a tensor-to-scalar reduction framework using master integrals, highlighting that 1/(D−4) factors arise with the Smirnov-Veretin basis (I1,I2) but can be avoided by using I3 as an irreducible-numerator basis, provided the ε-part of I1 is known. Through differential-equation techniques and IBP reductions, the authors express planar-box contributions in terms of I1 and I3, derive relations among master integrals, and demonstrate that the leading 1/ε^4 pole of the two-loop amplitude matches the square of the one-loop result. The results establish the ingredients to compute the leading-colour two-loop amplitude for massless 2→2 processes and validate the expected singular structure, paving the way for full NNLO predictions in this channel.
Abstract
We discuss the two-loop integrals necessary for evaluating massless 2 to 2 scattering amplitudes. As a test process, we consider the leading colour two-loop contribution to qqbar to q'qbar'. We show that for physical scattering processes the two Smirnov-Veretin planar box graphs I1 and I2 are accompanied by factors of 1/(D-4) thereby necessitating a knowledge of both I1 and I2 to O(epsilon). Using an alternative basis I1 and the irreducible numerator integral I3, the factors of 1/(D-4) disappear.