## Contractions

Question how to implement a model or how to change a model implementation
antonioc
Posts: 11
Joined: 23. Nov 2016, 07:51

### Contractions

Dear Florian,
there is a way to check what kind of contractions are needed for a generic interaction term, e.g. Phi.Eta.Xi, if they belong to unusual representations of SU(2) and/or SU(3)?

Thanks

Antonio

FStaub
Posts: 785
Joined: 13. Apr 2016, 14:05

### Re: Contractions

Hi,

you can see the contractions used by SARAH for the given implementation via
1) Non-SUSY models

Code: Select all

`SA`LagrangianContractions`

2) SUSY models

Code: Select all

`ShowSuperpotentialContractions`

antonioc
Posts: 11
Joined: 23. Nov 2016, 07:51

### Re: Contractions

Dear Florian,
thanks for the answer. However I am still a bit confused. Concerning the model (SM+Triplet, Complex) I don't understand why the contraction of the term

KHT conj[H].trip.H

is

conj[H[{lef1}][{gen1}]] Delta[lef1, lef2] Delta[lef2b,lef3] H[{lef3}][{gen3}] trip[{lef2, lef2b}][{gen2}]

There shouldn't be a epsTensor[lef2b,lef3] instead of Delta[lef2b,lef3]?
The fields are

ScalarFields[[1]] = {H, 1, {Hp, H0}, 1/2, 2, 1};
ScalarFields[[2]] = {trip, 1, {{T0/Sqrt[2],Tp},{Tm,-T0/Sqrt[2]}}, 0, 3, 1};

Thank you.
With regards

Antonio

FStaub
Posts: 785
Joined: 13. Apr 2016, 14:05

### Re: Contractions

Hi,

I don't think so, because H^* has a lower index, H an upper index and the triplet one lower and one upper index, i.e. the term reads (H^*)_a T^b_c H^d. One lower and one upper index is contracted with Delta, while epsilon appears for two lower or two upper ones.

Cheers
Florian

antonioc
Posts: 11
Joined: 23. Nov 2016, 07:51

### Re: Contractions

Dear Florian,
I have another question regarding the contractions but for a different case. I've implemented a model with left-right symmetry with the following fileds

Gauge[[1]]={B, U[1], bminl, gBL,False};
Gauge[[2]]={WL, SU[2], left, g2,True};
Gauge[[3]]={WR, SU[2], right, gR,True};
Gauge[[4]]={G, SU[3], color, g3,False};

ScalarFields[[1]] = {Phi, 1, {{H0, Hp},{Hm, HPrime0}}, 0, -2, 2, 1};
ScalarFields[[3]] = {HR, 1, {hR0, hRm}, 1, 1, 2, 1};

In the potential I have these two terms (one of them need h.c. of course)

muPhi2 conj[Phi].Phi
and
mPhi2 Phi.Phi

The model seems to work fine but in the RG I got the "Still Entangled" error for muPhi2 and mPhi2. (By the way, the same error appear in the LRmodels-tripletLR where there are two similar terms)

Have I to specify the contractions for the RG equations? Are these contractions different from the potential ones (corresponding to the same coupling)?

Thanks

Antonio

FStaub
Posts: 785
Joined: 13. Apr 2016, 14:05

### Re: Contractions

Hi,

sorry for the delayed reply. I don't think that this is necessarily a problem with the contractions because they should be fine. The problem is that the RGEs are calculated in terms of real scalars, i.e. both terms involve the same external states. One needs to take the superposition of different field combinations to get the running of single parameters. And that seems to fail somehow.
I'll take a look at the LR models to see if I can find a solution.

Cheers,
Florian

FStaub
Posts: 785
Joined: 13. Apr 2016, 14:05

### Re: Contractions

Hi,

I found a potential problem in the routine and tried to patch it. However, I don't have time to test that in detail. I attach the file with changed. Maybe, you can give a try if it works for you. I'll try to come back to this problem when I have more time (what might be in about 2 weeks..)

Cheers,
Florian
Attachments
nonSUSYrges.m

antonioc
Posts: 11
Joined: 23. Nov 2016, 07:51

### Re: Contractions

Dear Florian,
thank You for the effort. I'll see if it works and I'll feedback You of course.
With regards

Antonio

antonioc
Posts: 11
Joined: 23. Nov 2016, 07:51

### Re: Contractions

Dear Florian,
Your solution works fine, at least for my model.
Thank You.

Antonio