Name: Jongping Hsu (email_not_shown)
Date: 01/22/17-04:12:35 PM Z

I have finished a paper on 'Confining Quark Model with General Yang-Mills Symmetry and Inadequate Faddeev-Popov Ghost'. It includes an acknowledgement:" The author would like to thank V. Shtabovenko and R. Mertig for help and for providing a `super-Feynman-toolbox' to shed light on complicated one-loop amplitudes and to do 'computer experiments'. " JP

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 Yangâ€“Mills Gravity (https://sites.google.com/site/yangmillsgravity123/)

----- Original Message -----

From: "Jongping Hsu" <jhsu@umassd.edu>
To: feyncalc@feyncalc.org
Cc: "Mehbub R Khan" <mkhan4@umassd.edu>
Sent: Sunday, November 13, 2016 9:20:58 PM
Subject: ?

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.

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 Yangâ€“Mills Gravity (https://sites.google.com/site/yangmillsgravity123/)

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