Direct Extraction Of One Loop Rational Terms

We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. Working in D = 4 − 2ǫ dimensions, we interpret the dependence on the additional dimensions as equivalent to introducing an internal mass. We combine this with the use of generalised unitarity to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in 4− 2ǫ dimensions can be determined from quadruple, triple and double cuts without the need for independent pentagon contributions using a massive integral basis. The additional mass-dependent integral coefficients may then be extracted analytically or numerically using discrete Fourier projections. We check the method by computing the rational parts of all gluon helicity amplitudes with up to six external legs.