Name: Nefedov Maxim Date: 05/11/13-07:25:08 PM Z
-——— ðÅÒÅÎÁÐÒÁ×ÌÅÎÎÏÅ ÓÏÏÂÝÅÎÉÅ ———-
ïÔ: *Nefedov Maxim*
äÁÔÁ: ÓÕÂÂÏÔÁ, 11 ÍÁÑ 2013 Ç.
ôÅÍÁ: Box-diagrams, rational parts and OneLoop
ëÏÍÕ:
[feyncalc_at_HIDDEN-E-MAIL]
Hi!
Trying to calculate box diagrams with OneLoop (Mathematica 7 + FC
8.2.0)
I obtained the different results in the seemingly equivalent
calculations:
-—————————————————————–
ScalarProduct[q1, q1] = 0;
ScalarProduct[q2, q2] = 0;
ScalarProduct[q3, q3] = 0;
den = FAD[{q, 0}, {q - q1, 0}, {q - q1 - q2, 0}, {q - q1 - q2 -
q3,
0}];
(*Doing OneLoop with q^2*q^mu*q^nu in numerator and then contracting
with
g_munu*)
ex1 = PaVeReduce[
Contract[OneLoop[q, den*SP[q,
q]*FV[q,mu]*FV[q, nu]]*
MT[mu, nu]]]
(*Doing OneLoop with q^4 in numerator*)
ex2 = PaVeReduce[OneLoop[q, den*SP[q, q]^2]]
-—————————————————————–
The results are different:
ex1-ex2=I*Pi^2/2
It looks like that in this two cases, the rational part of the answer
(the
part which is finite in the limit D->4, but not proportional to the
basis
scalar integrals) is treated in a different way, and I can not guess how
to
use OneLoop to obtain always the correct answers.
Thanks in advance for any help.
Maxim Nefedov