**Next message:**Pablo Sanchez Puertas: "Re: E0 scalar function"**Previous message:**Vladyslav Shtabovenko: "Re: E0 scalar function"**In reply to:**Jongping Hsu: "Re: thanks"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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 Yangâ€“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
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*> hand-calculations and those in the literature (e.g.,Politzer's) for the
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*> 3rd. order Feynman diagram involving 3 ghost propagators and 3 external
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*> gluon lines [with one external gluon momentum set to be zero for
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*> 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
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*> 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
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*> 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
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*> In[2182]).
*

*> 2. I calculate the second term by using g1*g2*g3tt, which lead to the
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*> 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
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*> similar corrections for the one-loop results (T1 and T) are done for the
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*> 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
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*> the correct structure and magnitude of the diagram involving 3 ghost
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*> internal lines, as shown in the coefficient of B0 in Out[2231] and in
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*> 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/)
*

*>
*

*>
*

**Next message:**Pablo Sanchez Puertas: "Re: E0 scalar function"**Previous message:**Vladyslav Shtabovenko: "Re: E0 scalar function"**In reply to:**Jongping Hsu: "Re: thanks"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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