





title: Gauge Symmetries SUSY



permalink: /Gauge_Symmetries_SUSY/










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






Definition of Vector Superfields










The vector superfields are defined by the array `Gauge`. An entry reads






Gauge[[/ii]]={Superfield Name, Dimension, Name of Gauge Group, Coupling, Expand, Global};






The different parts have the following meaning:






1. `Superfield name`:



This is the name for the vector superfield and also the basis of the names for vector bosons, ghosts and gauginos [as explained here](/Nomenclature_for_fields_in_supersymmetric_models "wikilink")



2. `Dimension`:



This defines the dimension of the *S**U*(*N*) gauge group: `U[1]` for an Abelian gauge group or `SU[N]` with integer N for a nonAbelian gauge group.



3. `Name of Gauge Group`:



This is the name of the gauge group, e.g. hypercharge, color or left. This choice is import because all matter particles charged under a nonAbelian gauge group carry an corresponding index. The name of the index consists of the first three letter of the name plus a number. Hence, it must be taken care that the first three letters of different gauge group names are not identical. Also the name for the indices in the adjoint representation are derived from this entry.



4. `Coupling`: The name of the coupling constant, e.g. `g1`



5. `Expand`: Values can be `True` or `False`. If it is set to `True`, all sums over the corresponding indices are evaluated during the calculation of the Lagrangian. This is normally done nonAbelian gauge groups which get broken like the *S**U*(2)<sub>*L*</sub> in the MSSM.



6. `Global`: Transformation under [global symmetries](/Global_Symmetries_SUSY "wikilink")






SARAH adds for every vector superfield a softbreaking gaugino mass






Mass<>"Superfield Name"






##### Example: Standard model color group






Gauge[[/33]] = {G, SU[3], color, g3, False};






The consequence of this entry is






1. Gluon, its ghost and gluino are named `VG`, `gG` and `fG`



2. The *S**U*(3) generators, the GellMann matrices, are used



3. The color index is abbreviated `colX` (for `X` = 1,2, ...)



4. The strong coupling constant is named `g3`



5. The sums over the color indices are not evaluated






Models with several *U*(1) gauge groups










In the case of several Abelian gauge groups, there is an additional particulariyt: [Gauge kinetic mixing](/Supported_gauge_sectors#Gauge_kinetic_mixing "wikilink").






SARAH uses






*D*<sub>*μ*</sub> = ∂<sub>*μ*</sub> − *i*(*ḡ*<sub>*a*</sub>*Q*<sub>*a*</sub> + *ḡ*<sub>*b**a*</sub>)*Ā*<sub>*μ*</sub><sup>*a*</sup> − *i*(*ḡ*<sub>*a**b*</sub>*Q*<sub>*a*</sub> + *ḡ*<sub>*b*</sub>*Q*<sub>*b*</sub>)*Ā*<sub>*μ*</sub><sup>*b*</sup>






for the covariant derivatives to write the Lagrangian in that case. For that purposes, it generates new gauge couplings






g<>A<>B






for the offdiagonal couplings. Here `gA` and `gB` are the names for the diagonal gauge couplings defined in `Gauge`, i.e the first letter is always dropped. In addition, the gaugino mass terms are written as






∑<sub>*i*</sub>∑<sub>*j*</sub>*M*<sub>*i**j*</sub>*λ*<sub>*i*</sub>*λ*<sub>*j*</sub> + h.c..






The sum *i* and *j* runs over all Abelian gauge groups. The names for the offdiagonal gaugino mass are






Mass<>A<>B






Here, `A` and `B` are the names of the vector superfields defined in `Gauge`.






##### Example






In the case of a gauge sector containing






Gauge[[/11]] = {R, U[1], right, gR, False};



Gauge[[/22]] = {BL, U[1], bminusl, gBL, False};






the offdiagonal gauge couplings are called






gRBL



gBLR






and the offdiagonal gaugino masses are






MassRBL



MassBLR






See also



 


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