Scattering Amplitudes in Gauge Theories by Johannes M. Henn & Jan C. Plefka

Author:Johannes M. Henn & Jan C. Plefka
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(3.37)

As the u i and v j are independent of the loop momentum l μ we see that the integrand Eq. (3.35) with N≥5 can be completely reduced to a sum of scalar integrands with N′≤N points by inserting the above identity. We have thus shown that tensor integrals with N>4 points can be reduced to scalar integrals with up to N points.

3.4.2.2 Scalar Integrals with N>5 Points

Let us start out with a scalar integrand of the form

(3.38)

The goal is to reduce this integrand to a sum of lower-point scalar integrands with maximally five points. For this consider the following five equations for N unknowns α i

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