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Dear Rolf and Vladyslav:

Thank you very much for your help.

Rolf has done works on qcd, could you please tell me whether there is a program related to the calculation of beta function or asymptotic freedom or third order vertex corrections (of pure gluons, without fermions)? If you have one, could you please send it to us for reference?

Vladyslav's answer regarding the relation between -p^2 Co and Bo for asymptotic property (or UV divergence) is interesting and puzzling. I have some related questions:

(1)Are there relations between p^4 Do(0,p^2,0,p^2,p^2,p^2,0,0,0,0) and Bo, and between

p^4 Do(0,0,p^2,p^2,0,p^2,0,0,0,0) and Bo for asymptotic property? If yes, please let me know.

(2)These relations are very intriguing. If one is interested in asymptotic freedom, one just calculate the UV divergent terms, which show up in Bo in the OneLoop calculations. One can do subtraction at finite p^2 to avoid IR divergence. Since Co is not a UV divergent integral(although it may have IR divergence), one does not expect it to contribute to the UV divergent amplitudes. So, why p^2 Co contribute to the asymptotic freedom in the OneLoopSimplify[...] and OneLoop[...]?

(3)How to avoid the error warning:".....FC Split: Error! Splitting 0 w,r,t, {PaVe, DenPaVe, Ao,........Co,Do} failed!"? I tried to introduce an artificial mass for massless gluon, it does not seem to work. This problem suddenly happened today and all calculations are aborted. 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/)

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