Name: Lingxiao Xu Date: 11/05/14-03:46:47 PM Z
Dear developers:
SUNSimplify[SUNTrace[SUNT[i, j, i, j]], Explicit ->
True] just gives -2/3;
while SUNSimplify[SUNT[i, j, i, j], Explicit -> True]
gives -2/9.
why these two differ by a factor “3”?
In what conditions should I have to use SUNTrace when evaluating QCD
processes?
For example, when calculating an scalar QCD process(gluon
gluon–>q0,q0bar),I just evaluate the color factor at last, before that
I just have the squared matrix element equals (\!\(
\*SubsuperscriptBox[\(g\), \(s\), \(4\)]\ \((
\*SuperscriptBox[\(t\), \(2\)]\
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`i\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`j\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`j\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`i\)\)] + t\ u\
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`i\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`j\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`i\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`j\)\)] + t\ u\
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`j\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`i\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`j\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`i\)\)] +
\*SuperscriptBox[\(u\), \(2\)]\
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`i\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`j\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`j\)\)] .
\*SubscriptBox[\(T\),
\(TraditionalForm\`\(TraditionalForm\`i\)\)])\)\))/(32
s^2)
At this momente, I just wonder whether I have to use SUNTrace before
SUNSimplify. The answer is yes, only by that can the result match the
correct one. But I don’t know why I have to?
Thanks for the help!
Best Regards!
Lingxiao Xu