PaXEvaluate[expr, q] evaluates scalar 1-loop integrals
(up to 4-point functions) in expr that depend on the loop
momentum q in D dimensions.
The evaluation is using H. Patel’s Package-X.
Overview, PaXEvaluateIR, PaXEvaluateUV, PaXEvaluateUVIRSplit.
FAD[{q, m}]
PaXEvaluate[%, q, PaXImplicitPrefactor -> 1/(2 Pi)^(4 - 2 Epsilon)]\frac{1}{q^2-m^2}
\frac{i m^2}{16 \pi ^2 \varepsilon }-\frac{i m^2 \left(-\log \left(\frac{\mu ^2}{m^2}\right)+\gamma -1-\log (4 \pi )\right)}{16 \pi ^2}
FAD[{l, 0}, {q + l, 0}]
PaXEvaluate[%, l, PaXImplicitPrefactor -> 1/(2 Pi)^(4 - 2 Epsilon)]\frac{1}{l^2.(l+q)^2}
\frac{i}{16 \pi ^2 \varepsilon }+\frac{i \log \left(-\frac{4 \pi \mu ^2}{q^2}\right)}{16 \pi ^2}-\frac{i (\gamma -2)}{16 \pi ^2}
PaVe functions do not require the second argument
specifying the loop momentum
PaVe[0, {0, Pair[Momentum[p, D], Momentum[p, D]], Pair[Momentum[p, D], Momentum[p, D]]}, {0, 0, M}]
PaXEvaluate[%]\text{C}_0\left(0,p^2,p^2,0,0,M\right)
\frac{1}{\varepsilon M-\varepsilon p^2}-\frac{\gamma -\log \left(\frac{\mu ^2}{\pi M}\right)}{M-p^2}+\frac{\log \left(\frac{M}{M-p^2}\right)}{M-p^2}+\frac{M \log \left(\frac{M}{M-p^2}\right)}{p^2 \left(M-p^2\right)}