





title: Particle Content nonSUSY



permalink: /Particle_Content_nonSUSY/










[Category:Model](/Category:Model "wikilink")






Defnition of scalars and fermions










The syntax for to define scalar and fermion fields in nonsupersymmetric models is as follows






FermionField[[/ii]]/ScalarField[[/ii]] = {Name, Generations, Components, Transformation Gauge 1,



Transformation Gauge 2..., Transformation Global 1, Transformation Global 2 };






1. `Name`: The name for the field



2. `Generations`: The number of generations



3. `Components`: The basis of the name for the components. Two cases are possible:



1. The field transforms only trivially under the gauge groups with expanded indices. In this case, the entry is one dimensional.



2. The field transforms nontrivially under gauge groups with expanded indices. In this case, the entry is a vector or higher dimensional tensor fitting to the dimension of the field. Note, representations larger than the fundamental one are written as tensor products



4. `Transformation Gauge X`: Transformation under the different gauge groups defined before. For *U*(1) this is the charge, for nonAbelian gauge groups the dimensions is given as integer respectively negative integer. The dimension D of an irreducible representation is not necessarily unique. Therefore, to make sure, SARAH uses the demanded representation, also the corresponding Dynkin labels have to be added.



5. `Transformation Global X`: Transformation under the different global symmetries.






### NonFundamental representations






More details about the [treatment of nonfundamental representations is given here](/Handling_of_nonfundamental_representations "wikilink").






### Real scalar






By default, scalars are taken to be complex. To define them as real, they must be added to the list






RealScalars






Examples










1. **Left handed Quarks and Higgs doublet in the SM**:



FermionFields[[/11]] = {q, 3, {uL, qL}, 1/6, 2, 3};



...



ScalarFields[[/11]] = {H, 1, {H0, Hm}, 1/2, 2, 1};






Here, we have not assumed any global symmetry.






2. **Inert Higgs doublet**



Global[[/11]] = {Z[2], Z2};



...



ScalarFields[[/11]] = {Hd, 1, {Hd0, Hdm}, 1/2, 2, 1, 1};



ScalarFields[[/22]] = {Hu, 1, {Hup, Hu0}, 1/2, 2, 1, 1};






One can see here the appearance of the transformation under the additionally defined *Z*<sub>2</sub> symmetry.






3. **Real singlets**: By default all scalars are taken to be complex. To define them as real the name of the field has to be added to the list <span>RealScalars</span>. For instance, a real singlet is added to the model by



ScalarFields[[/22]] = {S, 1, s, 0, 1, 1};



RealScalars = {S};






4. **Real triplets** One has to be a bit careful when defining real triplets. The correct way is



ScalarFields[[/22]] = {trip, 1, {{T0/Sqrt[2],conj[Tm]},{Tm,T0/Sqrt[2]}}, 0, 3, 1};



RealScalars = {T0};






Note, it would be wrong to define the entire triplet `trip` as real.






Remark










It is not possible to use <span>SuperFields</span> and <span>FermionFields</span> or <span>ScalarFields</span> at the same time. If the user wants to define scalars or fermions, all superfields have to be written as components.






See also



 


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