FeynCalc manual (development version)

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}]]

\frac{1}{\left(q^2-\text{m0}^2\right).(\text{p1}+q)^2.(\text{p2}+q)^2.(\text{p3}+q)^2.(\text{p4}+q)^2}

NPointTo4Point[int, q, FCE -> True, FCVerbose -> -1] 
 
FCClearScalarProducts[]

\left(\frac{8 \;\text{m0}^2 \;\text{p2}^2 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3})}{\left(q^2-\text{m0}^2\right).(\text{p1}+q)^2.(\text{p2}+q)^2.(\text{p4}+q)^2}+\frac{8 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3}) \left(\text{m0}^2 (\text{p1}\cdot \;\text{p3})-\text{m0}^2 (\text{p2}\cdot \;\text{p3})+\text{p2}^2 (\text{p1}\cdot \;\text{p3})\right)}{\left(q^2-\text{m0}^2\right).(\text{p1}+q)^2.(\text{p3}+q)^2.(\text{p4}+q)^2}+\frac{8 \;\text{p4}^2 \left(\text{m0}^2 \;\text{p2}^2 (\text{p1}\cdot \;\text{p3})-\text{m0}^2 (\text{p1}\cdot \;\text{p3}) (\text{p2}\cdot \;\text{p3})-\text{m0}^2 \;\text{p2}^2 \;\text{p3}^2+\text{m0}^2 (\text{p2}\cdot \;\text{p3})^2-\text{p2}^2 (\text{p1}\cdot \;\text{p3}) (\text{p2}\cdot \;\text{p3})+\text{p2}^2 \;\text{p3}^2 (\text{p1}\cdot \;\text{p3})\right)}{\left(q^2-\text{m0}^2\right).(\text{p2}+q)^2.(\text{p3}+q)^2.(\text{p4}+q)^2}+\frac{8 \;\text{p2}^2 \left(\text{m0}^2+\text{p4}^2\right) (\text{p1}\cdot \;\text{p3})^2}{\left(q^2-\text{m0}^2\right).(\text{p1}+q)^2.(\text{p2}+q)^2.(\text{p3}+q)^2}-\left(8 \left(2 \;\text{m0}^2 \;\text{p2}^2 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3})-2 \;\text{m0}^2 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3}) (\text{p2}\cdot \;\text{p3})+\text{m0}^2 \;\text{p2}^2 (\text{p1}\cdot \;\text{p3})^2+\text{m0}^2 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3})^2-\text{m0}^2 \;\text{p2}^2 \;\text{p3}^2 \;\text{p4}^2+\text{m0}^2 \;\text{p4}^2 (\text{p2}\cdot \;\text{p3})^2-\text{p2}^2 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3}) (\text{p2}\cdot \;\text{p3})+\text{p2}^2 \;\text{p3}^2 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3})\right)\right)/(\text{p1}+q)^2.(\text{p2}+q)^2.(\text{p3}+q)^2.(\text{p4}+q)^2\right)/\left(16 \;\text{m0}^4 \;\text{p2}^2 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3})-16 \;\text{m0}^4 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3}) (\text{p2}\cdot \;\text{p3})+8 \;\text{m0}^4 \;\text{p2}^2 (\text{p1}\cdot \;\text{p3})^2+8 \;\text{m0}^4 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3})^2-8 \;\text{m0}^4 \;\text{p2}^2 \;\text{p3}^2 \;\text{p4}^2+8 \;\text{m0}^4 \;\text{p4}^2 (\text{p2}\cdot \;\text{p3})^2-16 \;\text{m0}^2 \;\text{p2}^2 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3}) (\text{p2}\cdot \;\text{p3})+16 \;\text{m0}^2 \;\text{p2}^2 \;\text{p3}^2 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3})+8 \;\text{p2}^2 \;\text{p4}^4 (\text{p1}\cdot \;\text{p3})^2+8 \;\text{p2}^4 \;\text{p4}^2 (\text{p1}\cdot \;\text{p3})^2\right)