Hi Jongping,
many thanks.
Cheers,
Vladyslav
Am 22.01.2017 um 16:12 schrieb Jongping Hsu:
> Hi, Vladyslav and Rolf,
> 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 Yang–Mills Gravity
> (https://sites.google.com/site/yangmillsgravity123/)
>
> ------------------------------------------------------------------------
> *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.
>
> 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/)
>
>
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