PaXEvaluate
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.
See also
Overview, PaXEvaluateIR, PaXEvaluateUV, PaXEvaluateUVIRSplit.
Examples
FAD[{q, m}]
PaXEvaluate[%, q, PaXImplicitPrefactor -> 1/(2 Pi)^(4 - 2 Epsilon)]
q2−m21
16π2εim2−16π2im2(−log(m2μ2)+γ−1−log(4π))
FAD[{l, 0}, {q + l, 0}]
PaXEvaluate[%, l, PaXImplicitPrefactor -> 1/(2 Pi)^(4 - 2 Epsilon)]
l2.(l+q)21
16π2εi+16π2ilog(−q24πμ2)−16π2i(γ−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[%]
C0(0,p2,p2,0,0,M)
εM−εp21−M−p2γ−log(πMμ2)+M−p2log(M−p2M)+p2(M−p2)Mlog(M−p2M)