PaXEvaluateUV
PaXEvaluateUV[expr,q]
is like PaXEvaluate
but with the difference that it returns only the UV-divergent part of
the result.
The evaluation is using H. Patel’s Package-X.
See also
Overview, PaXEvaluateIR, PaXEvaluate, PaXEvaluateUVIRSplit.
Examples
int = -FAD[{k, m}] + 2*FAD[k, {k - p, m}]*(m^2 + SPD[p, p])
k2.((k−p)2−m2)2(m2+p2)−k2−m21
PaXEvaluateUV[%, k, PaXImplicitPrefactor -> 1/(2 Pi)^D, FCE -> True]
16π2εUVim2+8π2εUVip2
Notice that with PaVeUVPart
one can get the same
result
res = PaVeUVPart[ToPaVe[int, k], Prefactor -> 1/(2 Pi)^D]
−D−4i21−2Dπ2−2D(2D+1πDm2−(2π)Dm2+2D+1πDp2)
Series[FCReplaceD[res, D -> 4 - 2 EpsilonUV], {EpsilonUV, 0, 0}] // Normal // SelectNotFree2[#, EpsilonUV] & // ExpandAll
16π2εUVim2+8π2εUVip2
int2 = TID[FVD[2 k - p, mu] FVD[2 k - p, nu] FAD[{k, m}, {k - p, m}] - 2 MTD[mu, nu] FAD[{k, m}], k]
(1−D)p2(k2−m2).((k−p)2−m2)−(1−D)p2pmupnu−Dp2pmupnu−4m2p2gmunu+p4gmunu+4m2pmupnu+(1−D)p2(k2−m2)2(−(1−D)p2gmunu−Dpmupnu−p2gmunu+2pmupnu)
PaXEvaluateUV[int2, k, PaXImplicitPrefactor -> 1/(2 Pi)^D, FCE -> True]
48π2εUVipmupnu−48π2εUVip2gmunu