Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-06-27
JHEP 0901:049,2009
Physics
High Energy Physics
High Energy Physics - Phenomenology
35 pages, 6 figures. Major revisions: new analytic results for gluon amplitudes and new section on treatment of massless fermi
Scientific paper
10.1088/1126-6708/2009/01/049
We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\e$ dimensions to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in $4-2\e$ 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 from the large mass limit which can be performed analytically or numerically. We check the method by computing the rational parts of all gluon helicity amplitudes with up to six external legs. We also present a simple application to amplitudes with external massless fermions.
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