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Definition of Matter Fields

Posted: 25. Sep 2018, 13:46
by saiyad
Respected Sir, I am a new user of SARAH. I have some questions regarding the model file in SARAH.

Q.1. Is it necessary to define all the matter fields as left-handed? (e.g., we have e_R in the SM. Is it necessary to define conj[eR]? or, it is just okay to define e_R?)
Q.2. Suppose, there is an SU(2) triplet fermion T (with hypercharge +1) field in my model. Should I define the triplet fermion as T^a_b or T^{ab}?
where,

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 T^a_b = {{Tp/Sqrt[2], Tpp}, {T0, -Tp/Sqrt[2]}} 

and

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 T_{ab} = {{Tpp, Tp/Sqrt[2]}, {Tp/Sqrt[2], T0}} 

Q.3. Suppose we have a vector like fermion T=T_L+T_R. How should I define T_L and T_R?

Hope for your reply. Thanks in advance.

Re: Definition of Matter Fields

Posted: 25. Sep 2018, 20:57
by FStaub
Hi,

1/2: at the end, you must be sure that everything is consistent (charge assignments, contractions, mixings )
3: sorry, but I don't get the question

In general: there are many public models with Triplets and vectorlike states. Going through them should be helpful.

Cheers

Re: Definition of Matter Fields

Posted: 25. Sep 2018, 21:17
by saiyad
Regarding Q.2. When I am defining the triplet as T^{ab}, I am getting some charge violating (two fermion-one vector boson) vertices, and except that everything is fine. I am unable to trace where this error is coming. (and yes, charge assignments, contractions, mixings are defined correctly).

Does the structure of a multiplet (whether T^{ab} or T^a_b) matter, while the kinetic terms

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 bar[T] i slash[D] T 
are being calculated?

Re: Definition of Matter Fields

Posted: 26. Sep 2018, 07:32
by FStaub
Sorry yes, that's correct.
The indices in the kinetic terms are derived automatically and for the adjoint always an upper and a lower index is used.

Cheers,
Florian

Re: Definition of Matter Fields

Posted: 26. Sep 2018, 12:05
by saiyad
Thanks for the reply.

So, for an SU(2) triplet, one should define it as T^a_b. What about an SU(2) 4-plet or an SU(2) 5-plet?
[ An SU(2) 4-plet is a rank 3 tensor with three indices. How should one define it ? as

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 4^{abc} or 4^a_{bc} or 4^{ab}_c ? 
]

Re: Definition of Matter Fields

Posted: 26. Sep 2018, 16:25
by FStaub
Hi,

For the adjoint always a lower and upper index is used. All other cases can be checked via

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CheckIrrepSUN[d,N]
With N=2 and d=4,5,10...

The number of upper/lower indices are the 3./4. entry

Cheers
Florian