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Nomenclature_for_fields_in_supersymmetric_models

Last edited by Martin Gabelmann
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Nomenclature for fields in supersymmetric models

In general, the names of the component fields which are used to express the SUSY Lagrangian for the gauge eigenstates are derived from the names of the vector and chiral superfields. All gauge eigenstates are named as follows:

ParticleType <> Basis <> [Indices]

With

  • Type: this is just one letter and indicates the type of a field. The convention is as follows:
  1. F for fermionic component of chiral superfield
  2. S for scalar component of chiral superfield
  3. f for fermionic component of vector superfield
  4. V for bosonic component of vector superfield
  5. g for ghost field

In addition, there are two types of auxiliary fields. This auxiliary field are not related in any way to the auxiliary components of the superfields in SUSY theories, but they are needed only for writing a CalcHep / CompHep model file. The type indicating letters are:

  1. A for an auxiliary scalar
  2. a for an auxiliary vector boson
  • Basis: this is for any gauge eigenstates the name of the underlying superfield.
  • Indices: this is alist of the indices which the particle carries. There are three different kinds of indices:
  1. generation: For all particles which appear in more than one generation
  2. lorentz: For all particles carrying a Lorentz index
  3. charge: For all components of a chiral superfield charged under a non-Abelian gauge group if this indices are not implicit

Examples

To clarify the above definitions, here some examples:

  1. VB[{lorentz}]: B-Boson with one Lorentz index
  2. fB: Bino
  3. SHd0: Neutral down Higgs
  4. FHd0: Neutral down Higgsino
  5. VG[{color,Lorentz}]: Gluon with one index for the adjoint of the color group and one Lorentz index
  6. fG[{color}]: Gluino with one adjoint index
  7. gG[{color}]: Gluon ghost with one adjoint index
  8. SdL[{generation,color}]: Left handed d-squark with one generation and one color index
  9. FdL[{generation,color}]: Left handed d-quark with one generation and one color index
  10. hh[{generation}]: Neutral, CP-even Higgs (light and heavy Higgs) after EWSB

Antiparticles

There are two functions to assign antiparticles: depending on the type of the particle conj or bar are used.

  1. Scalar, vector boson and Weyl spinor: conj, e.g. conj[SdR] or conj[VWm].
  2. Dirac fermion and ghost: bar, e.g bar[Fd] or bar[gG].

SARAH checks if a particle is a real scalar or vector bosons respectively a Majorana fermion. In these cases it simplifies the expressions by using

conj[RP] := RP
bar[MF] := MF

for a real particle RP or also real parameter, and for a Majorana fermion MF. The names of all Majorana fermions of the current model are saved in the list MajoranaPart, and all real parameters and particles are listed in realVar. Note, that the head bar is overloaded: it is either interpreted as hermitian or complex conjugated depending on the position of the fermions in a Dirac chains in order to build up Lorentz scalars.

See also