Color factor

Asked by Safinaz

Dear Calchep authors,

I read at the manual (3.3.6. p:150) about the color factor evaluation that is used by CalcHEP ..
Where the ggg vertex can be expressed in terms of the gqq vertex, where f_abc
 substituted by 2i [ tr (t^b t^a t^c) - tr (t^a t^b t^c)] ..
My question is:

This substitution for f_abc is hidden in Calchep .. I can see only in the lgrn.mdl
file the GG factor and the Lorentz part ..

If I have a new vertex of one gluon and two octet scalars : G S S and
and I wrote their vertex as tr [t^a t^b t^c] .. do Calchep now
interpret this color factor or define it implicitly because I still see
in the lgrn.mdl file for this vertex only GG and the Lorentz part ?


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Alexander Belyaev
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Neil Christensen (neil-christensen-qft) said :

Dear Safinaz,

All color factors are implicit in CalcHEP. They are the same as in the SM QCD vertices. That is, all vertices with three color octets are assumed to have the color structure of the three-gluon vertex. All vertices with a fundamental, an anti fundamental and a octet are assumed to have the same structure as the usual q,qbar,gluon vertex. If you want a different vertex, you have to split it using an auxiliary field. At this point, explicit color structures are not supported.

Best wishes,

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Safinaz (sramadan) said :

Hi Dr. Neil,

Thanks, I will try this.


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Best Alexander Belyaev (alexander.belyaev) said :

Dear Safinaz,
please let us know if you still have your question?
Again, any

ggg vertex has a hidden f^a^b^c structure which always substituted for
3 particles with 8 colours i.e. for 8-8-8 color structurem
q-bar q g vertex always has a hidden lambda^a^b^c martix in the vertex
which is automatically substituted for
3-3-8 colour structure

Do you have any other questions or we can close this topic?

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Safinaz (sramadan) said :

Thanks Alexander Belyaev, that solved my question.

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Safinaz (sramadan) said :

Hi Dr. Sasha,

I were trying to define a new vertex for Calchep as Tr[T^a T^b T^c] but I understood now Calc. get
any 8,8,8 vertex as f^a^b^c and as also I understood I can only define this new coupling
"Tr[T^a T^b T^c]" with the vertex g SS when introducing some auxiliury filed ..

So thanks,

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Alexander Pukhov (pukhov) said :

In principle we can implement new color factors like tr() or d_abc . But here some ambiguity appears and we need a column in Lagrangian table for color factors.