PaVeUVPart
PaVeUVPart[expr]
replaces all occurring Passarino-Veltman functions by their explicit values, where only the UV divergent part is preserved, while possible IR divergences and the finite part are discarded. The function uses the algorithm from arXiv:hep-ph/0609282 by G. Sulyok. This allows to treat Passarino-Veltman of arbitrary rank and multiplicity
See also
Overview, PaVe, PaVeReduce.
Examples
−D−42m2
PaVeUVPart[x + y B0[SPD[p, p], 0, M^2]]
D−4Dx−4x−2y
PaVe[0, 0, {p10, p12, p20}, {m1^2, m2^2, m3^2}]
PaVeUVPart[%]
C00(p10,p12,p20,m12,m22,m32)
−2(D−4)1
PaVe[0, 0, 0, 0, 0, 0, {p10, p12, p23, 0, p20, p13}, {m1^2, m2^2, m3^2, m4^2}]
PaVeUVPart[%]
D000000(0,p10,p12,p23,p13,p20,m42,m12,m22,m32)
480(D−4)−5m12−5m22−5m32−5m42+p10+p12+p13+p20+p23
int = FVD[k + p, rho] FVD[k + p, si] FAD[k, {k + p, 0, 2}]
TID[int, k, UsePaVeBasis -> True]
% // PaVeUVPart[#, FCE -> True] &
k2.(k+p)4(k+p)rho(k+p)si
iπ2grhosiC00(0,p2,p2,0,0,0)+iπ2prhopsiC11(p2,p2,0,0,0,0)
−2(D−4)iπ2grhosi