FeynCalc manual (development version)

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

PaVeUVPart[A0[m^2]]

−2m2D−4-\frac{2 m^2}{D-4}

PaVeUVPart[x + y B0[SPD[p, p], 0, M^2]]

Dx−4x−2yD−4\frac{D x-4 x-2 y}{D-4}

PaVe[0, 0, {p10, p12, p20}, {m1^2, m2^2, m3^2}] 
 
PaVeUVPart[%]

C00(p10,p12,p20,m12,m22,m32)\text{C}_{00}\left(\text{p10},\text{p12},\text{p20},\text{m1}^2,\text{m2}^2,\text{m3}^2\right)

−12(D−4)-\frac{1}{2 (D-4)}

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)\text{D}_{000000}\left(0,\text{p10},\text{p12},\text{p23},\text{p13},\text{p20},\text{m4}^2,\text{m1}^2,\text{m2}^2,\text{m3}^2\right)

−5  m12−5  m22−5  m32−5  m42+p10+p12+p13+p20+p23480(D−4)\frac{-5 \;\text{m1}^2-5 \;\text{m2}^2-5 \;\text{m3}^2-5 \;\text{m4}^2+\text{p10}+\text{p12}+\text{p13}+\text{p20}+\text{p23}}{480 (D-4)}

int = FVD[k + p, rho] FVD[k + p, si] FAD[k, {k + p, 0, 2}] 
 
TID[int, k, UsePaVeBasis -> True] 
 
% // PaVeUVPart[#, FCE -> True] &

(k+p)rho(k+p)sik2.(k+p)4\frac{(k+p)^{\text{rho}} (k+p)^{\text{si}}}{k^2.(k+p)^4}

iπ2grho  si  C00(0,p2,p2,0,0,0)+iπ2prhopsi  C11(p2,p2,0,0,0,0)i \pi ^2 g^{\text{rho}\;\text{si}} \;\text{C}_{00}\left(0,p^2,p^2,0,0,0\right)+i \pi ^2 p^{\text{rho}} p^{\text{si}} \;\text{C}_{11}\left(p^2,p^2,0,0,0,0\right)

−iπ2grho  si2(D−4)-\frac{i \pi ^2 g^{\text{rho}\;\text{si}}}{2 (D-4)}