NPointTo4Point
NPointTo4Point[expr, q]
reduces scalar IR finite 5-point functions to scalar 4-point functions according to Eq. 4.52 in arXiv:0709.1075.
See also
Overview, PaVeReduce.
Examples
FCClearScalarProducts[]
SPD[p1] = 0;
SPD[p1, p4] = 0;
SPD[p3, p4] = 0;
SPD[p1, p2] = 0;
SPD[p2, p4] = 0;
int = FCI[FAD[{q, m0}, {q + p1, 0}, {q + p2, 0}, {q + p3, 0}, {q + p4, 0}]]
(q2−m02).(p1+q)2.(p2+q)2.(p3+q)2.(p4+q)21
NPointTo4Point[int, q, FCE -> True, FCVerbose -> -1]
FCClearScalarProducts[]
((q2−m02).(p1+q)2.(p2+q)2.(p4+q)28m02p22p42(p1⋅p3)+(q2−m02).(p1+q)2.(p3+q)2.(p4+q)28p42(p1⋅p3)(m02(p1⋅p3)−m02(p2⋅p3)+p22(p1⋅p3))+(q2−m02).(p2+q)2.(p3+q)2.(p4+q)28p42(m02p22(p1⋅p3)−m02(p1⋅p3)(p2⋅p3)−m02p22p32+m02(p2⋅p3)2−p22(p1⋅p3)(p2⋅p3)+p22p32(p1⋅p3))+(q2−m02).(p1+q)2.(p2+q)2.(p3+q)28p22(m02+p42)(p1⋅p3)2−(8(2m02p22p42(p1⋅p3)−2m02p42(p1⋅p3)(p2⋅p3)+m02p22(p1⋅p3)2+m02p42(p1⋅p3)2−m02p22p32p42+m02p42(p2⋅p3)2−p22p42(p1⋅p3)(p2⋅p3)+p22p32p42(p1⋅p3)))/(p1+q)2.(p2+q)2.(p3+q)2.(p4+q)2)/(16m04p22p42(p1⋅p3)−16m04p42(p1⋅p3)(p2⋅p3)+8m04p22(p1⋅p3)2+8m04p42(p1⋅p3)2−8m04p22p32p42+8m04p42(p2⋅p3)2−16m02p22p42(p1⋅p3)(p2⋅p3)+16m02p22p32p42(p1⋅p3)+8p22p44(p1⋅p3)2+8p24p42(p1⋅p3)2)