Rotations in matter sector
General
The field rotations in the matter sector are defined via the list
DEFINITION[$EIGENSTATES][MatterSector] = { List of Rotations }
for each set of eigenstates. All possibilities to mix matter fields in the Lagrangian are briefly discussed here. One can see that there are in general two cases:
 The mass matrix is hermitian or symmetric. That's the case for scalars and Majorana fermions
 The mass matrix is not hermitian. That's the case for Dirac fermions
For both cases the entries in List of Rotations
look slightly different.
Hermitian or symmetric mass matrix
In this case one basis vector of the old eigenstates has to be defined which gets transformed to new mass eigenstates. Therefore, the general syntax is
{{List of Old Eigenstates},{Name of New Eigenstates, Name of Mixing Matrix}}
with
 A list of the names of old eigenstates
 The name of the new eigenstates
 The name of the mixing matrix
Note, while the list of the old eigenstates can be arbitrary long, just one name is defined for the new eigenstates. This eigenstates will appear automatically with the correct number of generations.
Examples

DownSquarks in the MSSM: the mixing of the three generations of d̃_{L} (
SdL
) and d̃_{R} (SdR
) to six generations of d̃ (Sd
) via the rotation matrix Z^{D} (ZD
) is defined by {{SdL, SdR}, {Sd, ZD}}This definition is interpreted as $\left(\begin{array}{c} \tilde{d}_L^i \\ \tilde{d}_R^i \end{array}\right)k = Z^{D,\dagger}{kj} \tilde{d}_j$

CPeven Higgs bosons in the MSSM: the mixing of ϕ_{d} (
phid
) and ϕ_{u} (phi_u
) to two generations of h (hh
) via the rotation matrix Z^{H} (ZH
) is defined by {{phid, phiu}, {hh, ZH}}This definition is interpreted as $\left(\begin{array}{c} \phi_d \\ \phi_u \end{array}\right)k = Z^{H,T}{kj} h_j$ Since
phid
andphiu
are real, SARAH automatically defineshh
as real as well. In addition, it is also possible to introduce a parametrisation forZH
via parameters.m. 
Charged Higgs bosons in the MSSM: the mixing of H_{d}^{−} (
SHdm
) and H_{u}^{+} (SHup
) to two generations of H^{±} (Hpm
) via the rotation matrix Z^{P} (ZP
) is defined by {{SHdm,conj[SHup]}, {Hpm, ZP}}This definition is interpreted as $\left(\begin{array}{c} H_d^ \\ (H_u^+)^* \end{array}\right)k = Z^{P,T}{kj} H^\pm_j$ Note the usage of
conj
in the above definition. 
Neutralinos in the MSSM: the mixing of B̃ (
fB
), W̃^{0} (fW0
), H̃_{d}^{0} (FHd0
) and H̃_{u}^{0} (FHu0
) to four generations of λ^{0} (L0
) via the rotation matrix Z^{N} (ZN
) is defined by {{fB, fW0, FHd0, FHu0}, {L0, ZN}}This definition is interpreted as $\left(\begin{array}{c} \tilde B \\ \tilde W^0 \\ \tilde H_d^0 \\ \tilde H_u^0 \end{array}\right)k = Z^{N,\dagger}{kj} \lambda^0_j$ One can form a Majorana spinor from the Weyl spinorsλ^{0} via
DEFINITION[EWSB][DiracSpinors]={ ... Chi >{ L0, conj[L0]}
Nonhermitian mass matrix
In that case two sets of old eigenstates (O_{1},O_{2}) are rotated to two new sets of mass eigenstates (N_{1}, N_{2}) via two rotation matrices (M_{1}, M_{2}). The general definition in SARAH is therefore
{{{First Basis},{Second Basis}},{{First States,First Matrix},{Second States,Second Matrix}}}
This is interpreted as
O_1 = M_1 N_1 \\ O_2 = M_2 N_2 \\
Examples

Up Quarks in the SM or MSSM: the definition {{{FuL},{conj[FuR]}},{{FUL,ZUL},{FUR,ZUR}}}
is equivalent to $U_{L,i} = Z^{U_L}{ij} u{L,j} \hspace{1cm} U^*{R,i} = Z^{U_R}{ij} u_{R,j}$ where the gauge eigenstates are u_{L} (
FuL
) and u_{R} (FuR
). 
Charginos in the MSSM: the definition {{{fWm, FHdm}, {fWp, FHup}}, {{Lm,Um}, {Lp,Up}}}
is interpreted as
$\left( \begin{array}{c} \tilde{W}^ \\ \tilde{H}_d^ \end{array} \right)i = U^{,\dagger}{ij} \lambda^_j, \hspace{1cm} \left( \begin{array}{c} \tilde{W}^+ \\ \tilde{H}u^+ \end{array} \right)= U^{+,\dagger}{ij} \lambda^+_j$
Rotation without flavour violation
With the above definitions, SARAH assumes always the most case that the new eigenstates can be a general mixture of all old eigenstates. However, when adding the keyword NoFlavorMixing
only a mixing between the same generations is considered. Thus, in the definition
{{O1,O2},{N, M},NoFlavorMixing}
it is assumed that the ith generation of O1
can only mix with the ith generation of O2
. As consequence, the mass eigenstates carry an additional index 'flavour'.
Example
If one uses the flag in the MSSM for the upsquark mixing
{{SuL, SuR}, {Su, ZU},NoFlavorMixing}
the mixing is taken to be
\left(\begin{array}{c} \tilde{d}_L^1 \\ \tilde{d}_R^1 \end{array}\right)_k = Z^{D_1,\dagger}_{kj} \tilde{d}_{1j} \\ \left(\begin{array}{c} \tilde{d}_L^2 \\ \tilde{d}_R^2 \end{array}\right)_k = Z^{D_2,\dagger}_{kj} \tilde{d}_{2j} \\ \left(\begin{array}{c} \tilde{d}_L^3 \\ \tilde{d}_R^3 \end{array}\right)_k = Z^{D_3,\dagger}_{kj} \tilde{d}_{3j}
or more compact
\left(\begin{array}{c} \tilde{d}_L^f \\ \tilde{d}_R^f \end{array}\right)_k = Z^{D_f,\dagger}_{kj} \tilde{d}_{fj} \\
The consequences are
 There are three 2 × 2 rotation matrices which get labelled by a flavour index
 There are three flavours of fields d̃ which come with two genetations each.
The parameter and particle definitions read therefore
{ZU, {generation, flavor, flavor}, {3, 2, 2}}
{Su, 1, 3, S, {{generation, 3}, {flavor, 2}, {color, 3}}, 2}
While the usage of flavour indices is supported in the FeynArts, CalcHep/CompHep, UFO and WHIZARD output, it is not possible to generate a SPheno version for such a model.