SARAH function to obtain Clebsch-Gordan coefficients

[AlexanderVoigt]

Dear Florian,

in a model I'm using there exists a vertex which contains the symbol (the Clebsch-Gordan coefficient)

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CG[SU[3], {{0, 1}, {1, 0}, {0, 1}, {1, 0}}][ct2, ct1, ct3, ct4]

Is there a SARAH function to obtain the numerical value of this Clebsch-Gordan coefficent, given specific values for the indices c1, c2, c3 and c4?

Many thanks and best regards,
Alex

[FStaub]

Hi,

this particular CG is just a product of two Kroneckers. No idea, why it is written in this form. In general, you can see that CG is associated with a invariant matrix (which usually comes from Susyno up to some special, hardcoded cases):

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?CG
?InvMat

Thus, as soon as you plug in integers as argument, you get back the numerical value.

Cheers,
Florian

[AlexanderVoigt]

Dear Florian,

many thanks for your fast answer. As you say, CG is already defined for a couple of groups and a couple of given indices. However, this particular Clebsch-Gordan coefficent

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CG[SU[3], {{0, 1}, {1, 0}, {0, 1}, {1, 0}}][ct2, ct1, ct3, ct4]

is not defined in SARAH, even if one inserts numbers for ct1, ..., ct4. (It may be missing because the model is too exotic.)

If I remember correctly, Susyno is included in SARAH. Do you know by heart how to calculate SARAH's CG symbols from Susyno functions?

Best regards,
Alex

[FStaub]

Hi,

you have just a quartic interaction of four colour triplets, or? Doesn't sound too exotic to me.

SARAH takes the Invariants command of Susyno. However, there should also be a check for a ter abcd if (ab)(cd) are already gauge invariant. In that case it should factor the CGs.

I would need to dig into the code at some point what goes wrong, but right now I'm on parental leave and busy with other things. So, this might need some time. An simple try to circumvent the problem is attached: hardcoding the CGs for this case.

Cheers,
Florian

[AlexanderVoigt]

Hi Florian,

many thanks for having a look at this! Please take your time! For now FlexibleSUSY has implemented the explicit form of these CGs, as you suggested.

Best regards,
Alex