Global Symmetries SUSY

Z_N and U(1) global symmetries can be defined. For this purpose, a new array Global has been introduced:

Global[[/1|1]] = {Z[2], RParity};
Global[[/2|2]] = {U[1], PecceiQuinn};

First, the kind of the symmetry is defined and afterwards a name is given to the symmetry. In principle, up to 99 different global symmetries can be defined for one model. Note, Z_N symmetries are always understood as multiplicative symmetries. The second entry gives a name to the symmetry. For the U(1) there is one specific name which can be used to define R-symmetries: RSymmetry. In that case, the R charges of the SUSY coordinates are considered as well. There are two possibilities to define the charges of SUSY fields with respect to a global symmetry:

1. if in the definition of the vector or chiral superfields, which will be explained below, only one quantum number is given per superfield per global symmetry this number is used for the superfield itself but also for component fields.
2. if a list with three entries is given as charge for a vector or chiral superfield the following convention applies: for chiral superfields, the first entry is the charge for the superfield, the second one for the scalar component, the third one for the fermionic component. For vector superfield, the second entry refers to the gaugino, the third to the gauge boson.

With these conventions a suitable definition of the global symmetries for states with R-parity ±1 would be

RpM = {-1, -1,  1};
RpP = { 1,  1, -1};

In some cases, like for a gauged B − L symmetry no global symmetry is present but R-parity is just a remnant of the broken U(1)_B − L. However, it turns out to be helpful to keep the standard definition for R-parity: we can use this Z₂ to get the relic density with MicrOmegas. Sometimes, one uses also matter parities to have an additional Z₂ in models with gauged B − L .

See also