Error in Invariant Y2S

[TomSt]

Hi Florian,

I am trying to implement some SU(N)_C x SU(2)_L x SU(2)_R model, but unfortunately I am running into problems when adding a Yukawa term with a charge conjugated Higgs:

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LagYukawa = + yc FR.conj[H].FL Delta[col1, col3] epsTensor[rig1, rig2] epsTensor[lef2, lef3];

Whenever I choose N > 2 and to expand the SU(N) subgroup, calculation of the anomalous dimension fails with Part::partw, since in the invariant Y2S elements greater than the matrix are accessed.

If the subgroup is not expanded, the problem disappears, but I need to break it. Can you reproduce this error?
Thanks for your time.

cheers,
Tom

[FStaub]

Hi Tom,

yes, there is a problem. However, it doesn't come from the RGE routines themselves, but from contractions used in the RGEs: since the RGEs are calculated for unbroken gauge groups and since non-fundamental irreps are taken as vectors, not tensors, one needs to translate the clebsch-gordan coefficients between both representations. And something goes wrong. It's weird that this is the case for your term because it involves only fundamental fields. I would need to dig deeper what goes on. A quick fix for you is to give the contractions also for the RGEs explicitly in the model file via

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ContractionRGE[yc]=Delta[col1, col3] epsTensor[rig1, rig2] epsTensor[lef2, lef3];

Cheers
Florian

[TomSt]

Hi Florian,

please let us know as soon as you can identify the problem, since the quick fix does not seem to work. Thanks for digging into this.

Cheers,
Tom

[FStaub]

Hi,

well, that's strange. If this doesn't help, there must be another problem. Even if I find the problem with generating the correct CGCs automatically, the result should be equivalent to putting them by hand. Are you sure that this is the only term making problems?

Cheers,
Florian

[TomSt]

Hi Florian,

yes, this is the only term causing trouble, I just tested with this as the only interaction. When including the ContractionRGE[...] statement, the output changes however - there is no immediate error, but unresolved expressions with ContractionRGE[...] remain in the anomalous dimensions, causing more problems in the follow-up.

Cheers,
Tom

[FStaub]

Hi,

yes, sorry. The problem is that I used that option so far only for interaction which involve fields which only appear with one generation, i.e. the coupling doesn't carry any index. That's not the case here and not all appearances are replaces. So, you need to do

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ContractionRGE[yc]=Delta[col1, col3] epsTensor[rig1, rig2] epsTensor[lef2, lef3];
ContractionRGE[yc[a__]]=ContractionRGE[yc];

Cheers,
Florian