Name: Jongping Hsu Date: 11/14/16-03:20:58 AM Z
Dear Dr. Mertig:
Could you please help to resolve a puzzling result that the OneLoop
FeynCalc calculation leads to incorrect results (in comparison with my
hand-calculations and those in the literature (e.g.,Politzer’s) for the
3rd. order Feynman diagram involving 3 ghost propagators and 3 external
gluon lines [with one external gluon momentum set to be zero for
simplicity] in the calculation of the asymptotic freedom)? Thank you
very much for your help.
I used Mathematica 11 for calculations(with SU(2) in mind). My short program is attached for your reference.
Comments (do not run the .nb before reading these comments):
1. The vertices g1*g2*g3 contains 2 terms. For clarity, I first
calculate the first term by using the vertex g1*g2*g3t. The
OneLoop[…] gives the result A1, which is only half of the
correct result A10 (see In[2182]).
2. I calculate the second term by using g1*g2*g3tt, which lead to the
oneloop result A2. Only when it is multiplied by(3/2), one gets the
correct result. See In[2198].
3. In[2198]: By observation, A1*(4/2)+A2*(3/2) give the
correct result.
4. For the crossed diagram (of external gluons with non-zero momenta),
a similar corrections for the one-loop results (T1 and T) are done for
the 2 terms: B1=2*T1, B2=(3/2)*T.
5. The corrected result, {A1*2 + A2*(3/2)}+{2*T1 + (3/2)*T}, leads
to the correct structure and magnitude of the diagram involving 3 ghost
internal lines, as shown in the coefficient of B0 in Out[2231]
and in Out[2232].
HSU Jongping,
Chancellor Professor
Department of Physics
Univ. of Massachusetts Dartmouth,
North Dartmouth, MA 02747. FAX (508)999-9115
http://www.umassd.edu/engineering/phy/people/facultyandstaff/jong-pinghsu/
recent monograph: Space-Time Symmetry and Quantum Yang–Mills Gravity
(https://sites.google.com/site/yangmillsgravity123/)