model_file.dox

/**
\page model_file_options FlexibleSUSY model file
\tableofcontents

\section model_info Model information

_____________________________________________________________________

__Symbol__: `FSModelName`

__Default value__: _unset_

__Description__:

Name of the model class within the generated code.  If `FSModelName`
is set to the string "@CLASSNAME@", it will be replaced by the
`createmodel` script to the name of the FlexibleSUSY model given
during the `./createmodel --name=<model_name>` command.

_____________________________________________________________________

__Symbol__: `FSEigenstates`

__Default value__: ``SARAH`EWSB``

__Description__:

The name of the particle eigenstates in SARAH.  Usually,
``SARAH`EWSB`` corresponds to the mass eigenstates after breaking of
the electroweak symmetry.

_____________________________________________________________________

__Symbol__: `FSDefaultSARAHModel`

__Default value__: _unset_

__Description__:

Name of the SARAH model to be used.  A sub-model can be specified
after a `/`.

Example: In the constrained CP-conserving MSSM (`CMSSM`) the SARAH
model `MSSM` is used as:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
FSDefaultSARAHModel = MSSM;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Example: In the constrained CP-violating MSSM (`CMSSMCPV`) the SARAH
model `MSSM` together with the sub-model `CPV` is used:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
FSDefaultSARAHModel = MSSM/CPV;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

\section input_parameters Input parameters

_____________________________________________________________________

__Symbol__: `MINPAR`

__Default value__: `{}`

__Description__:

In the `MINPAR` variable a list of input parameters for the spectrum
generator can be given, which is read of the `MINPAR` block of the
SLHA input file.

`MINPAR` is supposed to contain a list.  The list elements are
two-component lists, where the first in element is an integer number
representing the index inside the `MINPAR` block.  The second element
is the input parameter.  The input parameter must be either a symbol
or a sign of the form `Sign[p]`, where `p` is the name of a model
parameter.

__Example__: In the CMSSM the `MINPAR` block has the form

~~~~~~~~~~~~~~~~~~~~{.m}
MINPAR = {
    {1, m0},
    {2, m12},
    {3, TanBeta},
    {4, Sign[\[Mu]]},
    {5, Azero}
};
~~~~~~~~~~~~~~~~~~~~

In this case the input parameters can be given in the SLHA input file
as

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Block MINPAR                 # Input parameters
    1   125                  # m0
    2   500                  # m12
    3   10                   # TanBeta
    4   1                    # SignMu
    5   0                    # Azero
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_Note_: Unspecified parameters are assumed to be zero.

_____________________________________________________________________

__Symbol__: `EXTPAR`

__Default value__: `{}`

__Description__:

The `EXTPAR` variable is a list of input parameters for the spectrum
generator, which is read of the `EXTPAR` block of the SLHA input file.
The list assigned to the `EXTPAR` variable must have the same form as
`MINPAR` variable.

__Example__: In the NUTNMSSM the `EXTPAR` block has the form

~~~~~~~~~~~~~~~~~~~~{.m}
EXTPAR = {
    {61, LambdaInput},
    {62, KappaInput},
    {63, ALambdaInput},
    {64, AKappaInput},
    {65, MuEff}
};
~~~~~~~~~~~~~~~~~~~~

In this case the input parameters can be given in the SLHA input file
as

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Block EXTPAR                 # Input parameters
   61   0.650                # LambdaInput
   62   0.164                # KappaInput
   63   763.8                # ALambdaInput
   64   1268.2               # AKappaInput
   65   265.2                # MuEff
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_Note_: Unspecified parameters are assumed to be zero.

_____________________________________________________________________

__Symbol__: `FSExtraInputParameters`

__Default value__: `{}`

__Description__:

In the `FSExtraInputParameters` variable vector- or matrix-like input
parameters can be given.  `FSExtraInputParameters` is contains a list,
whose elements are three-component lists.  The first element of this
list is a symbol, which represents the input parameter.  The second
element is the name of the block, from which the input parameter is
read.  The third element is a list specifying the vector- or
matrix-type of the input parameter.  A list of the form `{N,M}` with
`N` and `M` being integer numbers defines a NxM matrix.  A list of the
form `{N}`, with `N` > 1 defines a vector with `N` rows.  A list of
the form `{1}` or `{}` defines a scalar.

__Example__: In the MSSM the `FSExtraInputParameters` block has the
form

~~~~~~~~~~~~~~~~~~~~{.m}
FSExtraInputParameters = {
    {Aeij, AeijIN, {3,3}}, (* 3x3 matrix *)
    {Adij, AdijIN, {3,3}}, (* 3x3 matrix *)
    {Auij, AuijIN, {3,3}}  (* 3x3 matrix *)
};
~~~~~~~~~~~~~~~~~~~~

Here, three 3x3 matrix-valued input parameters are specified: `Aeij`,
`Adij` and `Auij`.  These matrices are read from the blocks `AeijIN`,
`AdijIN` and `AuijIN`, respectively.

These input parameters can be given in the SLHA input file as

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Block AeijIN
    1   1   100
    1   2   100
    1   3   100
    2   1   100
    2   2   100
    2   3   100
    3   1   100
    3   2   100
    3   3   100
Block AdijIN
    1   1   200
    1   2   200
    1   3   200
    2   1   200
    2   2   200
    2   3   200
    3   1   200
    3   2   200
    3   3   200
Block AuijIN
    1   1   300
    1   2   300
    1   3   300
    2   1   300
    2   2   300
    2   3   300
    3   1   300
    3   2   300
    3   3   300
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_Note_: Unspecified parameters are assumed to be zero.

_____________________________________________________________________

__Symbol__: `RealParameters`

__Default value__: `{ All }`

__Description__:

`RealParameters` is a list, which contains the names of all model
parameters, which should be treated as real parameters.  By default,
`RealParameters` is set to `{ All }`, meaning that by default all
paramerters are treated to be real.  If `RealParameters` is set to the
empty list `{}`, FlexibleSUSY takes the information which paramerters
are real and which are complex from the SARAH model file.

Example: In the complex Standard Model (`cSM`), the parameters `mu2`
and `\[Lambda]` should be defined to be real:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
RealParameters = { mu2, \[Lambda] };
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Note: The gauge couplings and VEVs are always assumed to be real in
SARAH.

Example: In the CP-violating MSSM (`CMSSMCPV`), the `B[\[Mu]]`
parameter should be defined to be real:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
RealParameters = { B[\[Mu]] };
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

\section boundary_conditions Boundary conditions

In FlexibleSUSY, spectrum generators with two or three boundary
conditions can be generated.  (Future versions will support more than
three boundary conditions.)  By default, a spectrum generator with
three boundary conditions is generated.  These boundary conditions are
named "high-scale", "susy-scale" and "low-scale" boundary condition
and are described in the following.  In order to generate a spectrum
generator with only two boundary conditions, set

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
OnlyLowEnergyFlexibleSUSY = True;  (* only 2 BCs, default: False *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `LowScale`

__Default value__: _unset_

__Description__:

The scale of the low-scale boundary condition, at which the model is
matched to the Standard Model.

Example: In the CMSSM the low-energy scale should be set to the Z or
top pole mass.  This choice is achieved by the following expression:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
LowScale = LowEnergyConstant[MZ];
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `LowScaleFirstGuess`

__Default value__: _unset_

__Description__:

First guess of the low-energy scale.

Example: In the CMSSM the first guess for the low-energy scale should
be set to the Z or top pole mass:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
LowScaleFirstGuess = LowEnergyConstant[MZ];
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `LowScaleInput`

__Default value__: `{}`

__Description__:

With the `LowScaleInput` variable boundary conditions at the
low-energy scale can be specified.  `LowScaleInput` is a list.  Please
refer to \ref input_format for details about the list format.

At the low-energy scale, FlexibleSUSY automatically determines the
three gauge couplings from the SLHA input parameters
\f$\alpha_{em}\f$, \f$M_Z\f$ and \f$G_F\f$ or \f$M_W\f$.

_TODO_: Add note about how the the user can chose between \f$G_F\f$ or
\f$M_W\f$ as input.

Example: In the CMSSM `LowScaleInput` is given as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
LowScaleInput = {
   {Yu, Automatic},
   {Yd, Automatic},
   {Ye, Automatic},
   {vd, 2 MZDRbar / Sqrt[GUTNormalization[g1]^2 g1^2 + g2^2] Cos[ArcTan[TanBeta]]},
   {vu, 2 MZDRbar / Sqrt[GUTNormalization[g1]^2 g1^2 + g2^2] Sin[ArcTan[TanBeta]]}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `SUSYScale`

__Default value__: _unset_

__Description__:

The scale of the susy-scale boundary condition, which is defined to be
between the low-scale and the high-scale.  This is the scale at which
the electroweak symmetry breaking conditions are imposed by default,
see \ref input_format.

Example: In the CMSSM the SUSY scale should be set to the geometric
average of the two stop masses.  This choice is achieved by the
following expression:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SUSYScale = Sqrt[Product[M[Su[i]]^(Abs[ZU[i,3]]^2 + Abs[ZU[i,6]]^2), {i,6}]];
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `SUSYScaleFirstGuess`

__Default value__: _unset_

__Description__:

First guess of the SUSY scale.

Example: In the CMSSM a reasonable first guess for the SUSY scale can
be given by the following combination of the mSUGRA parameters:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SUSYScaleFirstGuess = Sqrt[m0^2 + 4 m12^2];
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `SUSYScaleInput`

__Default value__: `{}`

__Description__:

With the `SUSYScaleInput` variable boundary conditions at the SUSY
scale can be specified.  `SUSYScaleInput` is a list.  Please refer to
\ref input_format for details about the list format.

Example: In the NUTNMSSM `SUSYScaleInput` is given as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SUSYScaleInput = {
   {\[Lambda], LambdaInput},
   {\[Kappa], KappaInput},
   {vS, Sqrt[2] MuEff / LambdaInput}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `HighScale`

__Default value__: _unset_

__Description__:

This is the scale of the high-scale boundary condition.

Example: In the CMSSM the high-energy scale, \f$M_X\f$, is given by
the equality of the gauge couplings \f$g_1(M_X)\f$ and \f$g_2(M_X)\f$:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HighScale = g1 == g2;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `HighScaleFirstGuess`

__Default value__: _unset_

__Description__:

First guess of the high-energy scale.

Example: In the CMSSM a reasonable initial guess for the high-energy
scale is:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HighScaleFirstGuess = 2.0 10^16;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `HighScaleMinimum`

__Default value__: _unset_

__Description__:

Minimum value of the high-energy scale during the iteration.

Example: In the E6SSM the high-energy scale can vary a lot between the
iteration steps.  For this reason, it makes sense to use a minimum
high-energy scale in intermediate steps as:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HighScaleMinimum = 1.0 10^4;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `HighScaleMaximum`

__Default value__: _unset_

__Description__:

Maximum value of the high-energy scale during the iteration.

Example: In the E6SSM the high-energy scale can vary a lot between the
iteration steps.  For this reason, it makes sense to use a maximum
high-energy scale in intermediate steps as:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HighScaleMaximum = 5.0 10^17;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `HighScaleInput`

__Default value__: `{}`

__Description__:

With the `HighScaleInput` variable boundary conditions at the
high-energy scale can be specified.  `HighScaleInput` is a list.
Please refer to \ref input_format for details about the list format.

Example: In the CMSSM `HighScaleInput` is set to the mSUGRA boundary
conditions:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HighScaleInput = {
   {T[Ye], Azero Ye},
   {T[Yd], Azero Yd},
   {T[Yu], Azero Yu},
   {mHd2, m0^2},
   {mHu2, m0^2},
   {mq2, UNITMATRIX[3] m0^2},
   {ml2, UNITMATRIX[3] m0^2},
   {md2, UNITMATRIX[3] m0^2},
   {mu2, UNITMATRIX[3] m0^2},
   {me2, UNITMATRIX[3] m0^2},
   {MassB, m12},
   {MassWB,m12},
   {MassG, m12}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `InitialGuessAtLowScale`

__Default value__: `{}`

__Description__:

With the `InitialGuessAtLowScale` variable initial values for the
model MS-bar parameters can be given at the low-energy scale
`LowScale`.

Example: In the CMSSM `InitialGuessAtLowScale` is given as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
InitialGuessAtLowScale = {
   {vd, LowEnergyConstant[vev] Cos[ArcTan[TanBeta]]},
   {vu, LowEnergyConstant[vev] Sin[ArcTan[TanBeta]]},
   {Yu, Automatic},
   {Yd, Automatic},
   {Ye, Automatic}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `InitialGuessAtHighScale`

__Default value__: `{}`

__Description__:

With the `InitialGuessAtHighScale` variable initial values for the
model MS-bar parameters can be given at the high-energy scale
`HighScale`.

Example: In the CMSSM `InitialGuessAtHighScale` is given as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
InitialGuessAtHighScale = {
   {\[Mu]   , 1.0},
   {B[\[Mu]], 0.0}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `EWSBOutputParameters`

__Default value__: `{}`

__Description__:

In the `EWSBOutputParameters` variable the model parameters must be
specified, which are fixed by the electroweak symmetry breaking (EWSB)
conditions, \f$\partial V_\text{Higgs}/\partial v_i = 0\f$.  The
length of the `EWSBOutputParameters` list must be equal to the number
of EWSB conditions.

Example: In the CMSSM `EWSBOutputParameters` is given as follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
EWSBOutputParameters = { B[\[Mu]], \[Mu] };
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The elements of the `EWSBOutputParameters` must be _real_ parameters.
In a model with complex parameters, as in the CMSSMCPV for example,
`EWSBOutputParameters` is set to be:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
EWSBOutputParameters = { Re[B[\[Mu]]], Im[B[\[Mu]]], \[Mu] };
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_____________________________________________________________________

__Symbol__: `FSSolveEWSBTreeLevelFor`

__Default value__: `{}`

__Description__:

In the `FSSolveEWSBTreeLevelFor` variable the model parameters can be
specified, which are fixed by the tree-level electroweak symmetry
breaking (EWSB) conditions when the running (tree-level) masses are
calculated.  The length of the `FSSolveEWSBTreeLevelFor` list must be
either zero (default) or equal to the number of EWSB conditions.  If
`FSSolveEWSBTreeLevelFor` is the empty list, then the temporary EWSB
output parameters are chosen automatically as follows:

- In SUSY models, by default the soft-breaking squared Higgs mass
  parameters are fixed by the tree-level EWSB equation temporarily
  when the running (tree-level) masses are calculated.

- In non-SUSY models, by default the parameters given in
  `EWSBOutputParameters` are fixed by the tree-level EWSB equation
  temporarily when the running (tree-level) masses are calculated.


\subsection input_format Boundary condition format

The variables `LowScaleInput`, `SUSYScaleInput` and `HighScaleInput`
are lists which specify the boundary conditions for the running model
parameters at the corresponding scale.  The boundary conditions can be
expressed as follows.

### Setting a running model parameter to a value or expression ###

A running model parameter can be assigned at the corresponding scale
to a fixed numerical value or a value which is the result of the
evaluation of an expression.  Such an assignment is made by a
two-component list, `{p, v}`, where the first list element must be the
model parameter (`p` in this case) and the second list element is a
numerical value or an expression.

Example: An example is the mSUGRA boundary condition in the CMSSM at
the GUT scale:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
HighScaleInput = {
   {T[Ye], Azero*Ye},
   {T[Yd], Azero*Yd},
   {T[Yu], Azero*Yu},
   {mHd2, m0^2},
   {mHu2, m0^2},
   {mq2, UNITMATRIX[3] m0^2},
   {ml2, UNITMATRIX[3] m0^2},
   {md2, UNITMATRIX[3] m0^2},
   {mu2, UNITMATRIX[3] m0^2},
   {me2, UNITMATRIX[3] m0^2},
   {MassB, m12},
   {MassWB,m12},
   {MassG, m12}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The model parameters in the expression in the second list element are
running parameters at the corresponding scale.  I.e. the setting
`{T[Ye], Azero*Ye}` means \f$T_{y_e}(Q) := A_0 y_e(Q)\f$, where
\f$Q\f$ is the scale.

For matrix- or vector-valued assignments, the following convenient
symbols can be used in the second list element:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
UNITMATRIX[rows]              (* quadratic unit matrix with `rows' rows *)
UNITMATRIXCOMPLEX[rows]       (* complex quadratic unit matrix with `rows' rows *)
ZEROMATRIX[rows,cols]         (* zero matrix with `rows' rows and `cols' columns *)
ZEROMATRIXCOMPLEX[rows,cols]  (* complex zero matrix with `rows' rows and `cols' columns *)
ZEROVECTOR[rows]              (* zero vector with `rows' rows *)
ZEROVECTORCOMPLEX[rows]       (* complex zero vector with `rows' rows *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

On the r.h.s. of the assignment it is possible to refer to a model
parameter, which is read from an SLHA input block.  These model
parameter input blocks are named after the model parameter output
blocks concatenated with an additionan "IN" (see the SLHA-2 standard,
arXiv:0801.0045, Section 4.1.3).  To refer to such an input model
parameter on the r.h.s. of an assignment one can either add an entry
in `FSExtraInputParameters` or use the `LHInput[p]` symbol, where `p`
is the name of the model parameter.

Example:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
SUSYScaleFirstGuess = Sqrt[Sqrt[LHInput[mq2[3,3]] * LHInput[mu2[3,3]]]];

SUSYScaleInput = {
   {mq2, 2 g2^2 LHInput[mq2]}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

It is also possible to access the \f$\beta\f$ functions on the
r.h.s. of an assignment using the `BETA` head: `BETA[p]` represents
the \f$\beta\f$ function of the parameter `p` using the loop level
given in the SLHA input.  `BETA[l,p]` represents the `l`-loop
\f$\beta\f$ function of the parameter `p`.

Example:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
HighScaleInput = {
    {\[Lambda], BETA[g1] + BETA[g2] + BETA[1,Yu][3,3]}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

### Temporary parameter re-definitions ###

Since FlexibleSUSY 1.4.0, the user can perform a temporary parameter
definition to be used in the boundary conditions using the Temporary[]
head.

If a parameter `p` set in a boundary conditions in the form
`Temporary[p,<expr>]`, the following happens: Immediately after the RG
running the value of the parameter is saved locally.  Afterwards, the
parameter is assigned to `<expr>`.  Now, all further boundary
conditions are imposed and calculations are performed (calculation of
running masses, solution of the EWSB conditions, etc.).  Finally, the
parameter `p` is restored to the locally saved value.

Example in `U1xMSSM3G`: Temporarily rotate the gauge couplings to the
triangular basis:

~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
g1T  = (g1*gX - g1X*gX1)/Sqrt[gX^2 + gX1^2];
gXT  = Sqrt[gX^2 + gX1^2];
g1XT = (g1X*gX + g1*gX1)/Sqrt[gX^2 + gX1^2];

SUSYScaleInput = {
    {Temporary[g1], g1T},
    {Temporary[gX], gXT},
    {Temporary[g1X], g1XT},
    {Temporary[gX1], 0},
    {xS, vSInput},
    {x2, Sqrt[4*MZpInput^2 - gX^2*(vu^2 + vd^2)]/(2*gX*Sqrt[1 + TanBetaX^2])},
    {x1, (TanBetaX*Sqrt[4*MZpInput^2 - gX^2*(vu^2 + vd^2)])/(2*gX*Sqrt[1 + TanBetaX^2])},
    {L[lw], 0},
    FSSolveEWSBFor[{mHd2, mHu2, mC12, lw, mS2}]
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~

In this example the gauge couplings, defined in the triangular basis,
are used in every calculation performed at the SUSY scale.  This
includes the calculation of `x1` and `x2` as well as solving the EWSB
conditions.

### Imposing the electroweak symmetry breaking conditions ###

The scale, at which the electroweak symmetry breaking (EWSB)
conditions are imposed can be specified by adding
`FSSolveEWSBFor[parameters]` to the corresponding boundary condition.
The argument `parameters` must be the list of model parameters which
are fixed by the electroweak symmetry breaking conditions.

Example: Impose the EWSB conditions at the low-energy scale:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~
LowScaleInput = {
   FSSolveEWSBFor[EWSBOutputParameters]
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If `FSSolveEWSBFor[EWSBOutputParameters]` is not given in any boundary
condition, then it is added to `SUSYScaleInput`.  This implies, that
by default, the EWSB conditions are imposed at the scale `SUSYScale`.

### Automatic input of unspecified model parameters ###

In low-energy models (models where `OnlyLowEnergyFlexibleSUSY ===
True`) parameters, which are _not_ set in any boundary condition are
automatically input at the `SUSYScale`.  The values of these
parameters are automatically read from the corresponding SLHA input
blocks.

To disable the automatic input of unspecified parameters, set

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
AutomaticInputAtMSUSY = False;   (* default: True *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

### Sub-iterations ###

It is possible to fix model parameters at a scale by performing an
iteration.  Two kinds of iterations are supported:

#### Minimization ####

Model parameters can be fixed by requiring that a function is minimal.
The parameters to be fixed and the function to be minimized must be
specified by the symbol `FSMinimize[parameters, f]`, where
`parameters` is the list of parameters to be fixed and `f` is the
scalar function to be minimized.

Example:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
SUSYScaleInput = {
   FSMinimize[{vd,vu}, (LowEnergyConstant[MZ] - Pole[M[VZ]])^2 / STANDARDDEVIATION[MZ]^2
                     + (LowEnergyConstant[MH] - Pole[M[hh[1]]])^2 / STANDARDDEVIATION[MH]^2]
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#### Root finding ####

Model parameters can be fixed by requiring that a function is zero.
The parameters to be fixed and the function whose zero should be found
must be specified by the symbol `FSFindRoot[parameters, f]`, where
`parameters` is the list of parameters to be fixed and `f` is the
vector-valued function to be zero.

Example:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
SUSYScaleInput = {
   FSFindRoot[{vd,vu}, {LowEnergyConstant[MZ] - Pole[M[VZ]], LowEnergyConstant[MH] - Pole[M[hh[1]]]}]
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

\section convergence_tester Convergence tester

FlexibleSUSY solves the given boundary value problem (BVP) by running
to each scale and imposing the corresponding boundary conditions until
a convergent solution has been found.

The convergence criterion can be customized using the
`FSConvergenceCheck` variable.  The default is

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
FSConvergenceCheck = Automatic; (* default *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If `FSConvergenceCheck` is set to `Automatic`, then the following
convergence criteria are used:

- In SUSY models the BVP solver stops if the maximum number of
  iterations has been reached (`FlexibleSUSY[1]`, see @ref
  slha_input_fields) or the maximum relative difference of the DR-bar
  masses of the SUSY particles at the SUSY scale between two
  successive iterations is less than the precision goal
  (`FlexibleSUSY[0]`, see @ref slha_input_fields).

- In non-SUSY models the BVP solver stops if the maximum number of
  iterations has been reached (`FlexibleSUSY[1]`, see @ref
  slha_input_fields) or the maximum relative difference of all MS-bar
  masses of the model at the SUSY scale between two successive
  iterations is less than the precision goal (`FlexibleSUSY[0]`, see
  @ref slha_input_fields).

To create a custom convergence tester, the `FSConvergenceCheck`
variable must be set to a list containing the running masses and/or
running parameters to be compared between two successive iterations.
The BVP solver stops if the maximum number of iterations has been
reached (`FlexibleSUSY[1]`) or the maximum relative difference of all
running masses and/or parameters given in the `FSConvergenceCheck`
list at the SUSY scale between two successive iterations is less than
the precision goal (`FlexibleSUSY[0]`).

Example: In the following MSSM example the running masses of all
massive particles as well as the running parameters `g1, g2, g3, Yu,
Yd[3,3], Ye, B[\[Mu]], \[Mu]` are tested for convergence.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
FSConvergenceCheck = {
    M[hh], M[Ah], M[Hpm],
    M[Su], M[Sd], M[Se],
    M[Chi], M[Cha], M[Glu],
    M[Fu], M[Fd], M[Fe],
    M[VZ], M[VWm],
    g1, g2, g3, Yu, Yd[3,3], Ye, B[\[Mu]], \[Mu]
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

_Note_: For matrix- or vector-valued parameters every component is
used in the convergence test, if the matrix/vector indices are
omitted.


\section rges Renormalization group equations (RGEs)

The loop order of the RGEs to be used can be selected in the model
file using the `FSRGELoopOrder` variable: By setting `FSRGELoopOrder =
0;` no RGEs will be generated by SARAH.  By setting `FSRGELoopOrder =
1;` only one-loop RGEs will be generated by SARAH.  By setting
`FSRGELoopOrder = 2;` the two-loop RGEs will be generated by SARAH
(this is the default).

Example:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
FSRGELoopOrder = 2; (* generate two-loop RGEs using SARAH *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

### Three-loop RGEs for specific models ###

#### Standard Model ####

In the Standard Model the known three-loop RGEs from [arxiv:1303.4364,
arXiv:1307.3536] can be used by setting in the model file

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
UseSM3LoopRGEs = True; (* use three-loop SM RGEs *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#### MSSM ####

In the MSSM the known three-loop RGEs from [arxiv:hep-ph/0308231,
http://www.liv.ac.uk/~dij/betas/allgennb.log] can be used by setting
in the model file

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
UseMSSM3LoopRGEs = True; (* use three-loop MSSM RGEs *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

\section pole_masses Pole masses

In order to tune the spectrum generator for speed, the precision of
the pole mass calculation can be selected for each particle.  There
are three different pole mass calculation algorithms available:
`LowPrecision`, `MediumPrecision` and `HighPrecision`.  Please refer
to Section 6.5 of Ref. [<a href="http://arxiv.org/abs/1406.2319">CPC
190 (2015) 139-172</a>] for details.

By default, the pole masses of all particles are calculated with
`MediumPrecision`, except for the CP-even, CP-odd and charged Higgs
bosons, which are calculated with `HighPrecision` in order to include
some momentum-dependent 2-loop corrections.

Example:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
DefaultPoleMassPrecision = MediumPrecision;
HighPoleMassPrecision    = {hh, Ah, Hpm};
MediumPoleMassPrecision  = {};
LowPoleMassPrecision     = {};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

\section lsps Lightest supersymmetric particle (LSP)

FlexibleSUSY can generate the helper function `get_lsp()`, which
returns the mass of the lightest supersymmetric particle (LSP) as well
as the particle type.  The particles which are candidates for being an
LSP must be specified in the `PotentialLSPParticles` variable.

Example: In the MSSM the lightest supersymmetric particles might be

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
PotentialLSPParticles = { Chi, Sv, Su, Sd, Se, Cha, Glu };
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

\section output_blocks Output blocks

The user can define additional SLHA output blocks.  These additional
blocks must be defined in the FlexibleSUSY model file using the
`ExtraSLHAOutputBlocks` variable.  The `ExtraSLHAOutputBlocks`
variable is a nested list of the following form:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
ExtraSLHAOutputBlocks = {
   {<blockname>, [<scale>,]
      {{<index>, <expression>},
       {<index>, <expression>},
       {<index>, <expression>}}
   },
   ...
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`<blockname>` is the name of the output block.

Optionally, the renormalization scale can be added to the block head.
`NoScale` (default) specifies that the block head should have no
scale.  `CurrentScale` specifies that the scale written in the block
head should be the current scale of the model.  Otherwise, `<scale>`
can be numeric value.

The fields inside the block are specified in form of a list of
2-component lists, where the first entry is an integer number
representing the field index.  The second entry is an expression to be
evaluated and whose numeric result is written to the field value.

Example: In the MSSM mode file the following additional output blocks
are defined

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
ExtraSLHAOutputBlocks = {
   {FlexibleSUSYOutput, NoScale,
           {{0, Hold[HighScale]},
            {1, Hold[SUSYScale]},
            {2, Hold[LowScale]} } },
   {EFFHIGGSCOUPLINGS, NoScale,
           {{1, FlexibleSUSYObservable`CpHiggsPhotonPhoton},
            {2, FlexibleSUSYObservable`CpHiggsGluonGluon},
            {3, FlexibleSUSYObservable`CpPseudoScalarPhotonPhoton},
            {4, FlexibleSUSYObservable`CpPseudoScalarGluonGluon} } },
   {ALPHA, NoScale,
           {{ArcSin[Pole[ZH[2,2]]]}}},
   {HMIX , {{1, \[Mu]},
            {2, vu / vd},
            {3, Sqrt[vu^2 + vd^2]},
            {4, M[Ah[2]]^2},
            {101, B[\[Mu]]},
            {102, vd},
            {103, vu} } },
   {Au,    {{1, 1, T[Yu][1,1] / Yu[1,1]},
            {2, 2, T[Yu][2,2] / Yu[2,2]},
            {3, 3, T[Yu][3,3] / Yu[3,3]} } },
   {Ad,    {{1, 1, T[Yd][1,1] / Yd[1,1]},
            {2, 2, T[Yd][2,2] / Yd[2,2]},
            {3, 3, T[Yd][3,3] / Yd[3,3]} } },
   {Ae,    {{1, 1, T[Ye][1,1] / Ye[1,1]},
            {2, 2, T[Ye][2,2] / Ye[2,2]},
            {3, 3, T[Ye][3,3] / Ye[3,3]} } },
   {MSOFT, {{1, MassB},
            {2, MassWB},
            {3, MassG},
            {21, mHd2},
            {22, mHu2},
            {31, SignedAbsSqrt[ml2[1,1]]},
            {32, SignedAbsSqrt[ml2[2,2]]},
            {33, SignedAbsSqrt[ml2[3,3]]},
            {34, SignedAbsSqrt[me2[1,1]]},
            {35, SignedAbsSqrt[me2[2,2]]},
            {36, SignedAbsSqrt[me2[3,3]]},
            {41, SignedAbsSqrt[mq2[1,1]]},
            {42, SignedAbsSqrt[mq2[2,2]]},
            {43, SignedAbsSqrt[mq2[3,3]]},
            {44, SignedAbsSqrt[mu2[1,1]]},
            {45, SignedAbsSqrt[mu2[2,2]]},
            {46, SignedAbsSqrt[mu2[3,3]]},
            {47, SignedAbsSqrt[md2[1,1]]},
            {48, SignedAbsSqrt[md2[2,2]]},
            {49, SignedAbsSqrt[md2[3,3]]} } }
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

\section model_specific_switches Model-specific switches

### 2- and 3-loop corrections to pole masses ###

#### MSSM ####

In the MSSM the dominant two-loop Higgs pole mass corrections
[arxiv:hep-ph/0105096, arxiv:hep-ph/0112177, arxiv:hep-ph/0212132,
arxiv:hep-ph/0206101, arxiv:hep-ph/0305127] can be used by setting in
the model file

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
UseHiggs2LoopMSSM = True; (* use 2-loop Higgs corrections *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In addition, the effective \f$\mu\f$ parameter must be specified using
the `EffectiveMu` variable:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
EffectiveMu = \[Mu];
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#### NMSSM ####

In the NMSSM the dominant two-loop Higgs pole mass corrections from
Ref.  [arXiv:0907.4682] plus the MSSM-like contributions from Refs.
[hep-ph/0105096, hep-ph/0112177, hep-ph/0212132, hep-ph/0206101,
hep-ph/0305127] can be used by setting in the model file

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
UseHiggs2LoopNMSSM = True; (* use 2-loop Higgs corrections *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In addition, the effective \f$\mu\f$ parameter must be specified using
the `EffectiveMu` variable, Furthermore, the tree-level value of the
effective CP-odd MSSM-like Higgs must be specified in the
`EffectiveMASqr` variable.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
EffectiveMu = \[Lambda] vS / Sqrt[2];
EffectiveMASqr = (T[\[Lambda]] vS / Sqrt[2] + 0.5 \[Lambda] \[Kappa] vS^2) (vu^2 + vd^2) / (vu vd);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#### Standard Model (SM) ####

In the Standard Model the two-loop Higgs pole mass corrections
[arxiv:1205.6497, Eq.(20)] of the order \f$O(\alpha_t\alpha_s +
\alpha_t^2)\f$ can be used by setting in the model file

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
UseHiggs2LoopSM = True;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#### Split-MSSM (SplitMSSM) ####

In the split-MSSM the two-loop Higgs pole mass corrections from
[arxiv:1312.5220, Eq. (4.8)] of the order \f$O(\alpha_t \alpha_s^2)\f$
can be used by setting in the model file

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
UseHiggs3LoopSplit = True;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

### 3-loop QCD corrections to the top Yukawa coupling ###

In non-SUSY models the known 3-loop (Standard Model) QCD corrections
\f$O(\alpha_s^3)\f$ [arxiv:hep-ph/9911434, arxiv:hep-ph/9912391] can
be used in the determination of the running \f$\overline{MS}\f$ top
Yukawa coupling \f$y_t\f$ at the low-energy scale by setting

~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
UseYukawa3LoopQCD = Automatic;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
or
~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
UseYukawa3LoopQCD = True;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Note, that these 3-loop corrections are only applied at run-time if
the threshold correction loop order (block `FlexibleSUSY[7]`) is set
to a value > 2.

*/