title: Gauge Symmetries SUSY
permalink: /Gauge_Symmetries_SUSY/
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:

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 
Dimension
: This defines the dimension of the S**U(N) gauge group:U[1]
for an Abelian gauge group orSU[N]
with integer N for a nonAbelian gauge group. 
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. 
Coupling
: The name of the coupling constant, e.g.g1

Expand
: Values can beTrue
orFalse
. If it is set toTrue
, 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)_{L} in the MSSM. 
Global
: Transformation under global symmetries
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
 Gluon, its ghost and gluino are named
VG
,gG
andfG
 The S**U(3) generators, the GellMann matrices, are used
 The color index is abbreviated
colX
(forX
= 1,2, ...)  The strong coupling constant is named
g3
 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.
SARAH uses
D_{μ} = ∂_{μ} − i(ḡ_{a}Q_{a} + ḡ_{b**a})Ā_{μ}^{a} − i(ḡ_{a**b}Q_{a} + ḡ_{b}Q_{b})Ā_{μ}^{b}
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
∑_{i}∑_{j}M_{i**j}λ_{i}λ_{j} + 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