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model_file.dox
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model_file.dox
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/**
\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;
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
_____________________________________________________________________
__Symbol__: `FSBVPSolvers`
__Default value__: `{ TwoScaleSolver }`
__Description__:
A list of algorithms to use for solving the boundary value problem.
One or both of `TwoScaleSolver` or `SemiAnalyticSolver` may be
specified in the list.
\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
the `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__: `IMMINPAR`
__Default value__: `{}`
__Description__:
The `IMMINPAR` variable is a list of input parameters for the spectrum
generator, which is read of the `IMMINPAR` block of the SLHA input
file. The list assigned to the `IMMINPAR` variable must have the same
form as the `MINPAR` variable.
__Example__: In the CP-violating MSSM (`CMSSMCPV`) the `IMMINPAR` block
has the form
~~~~~~~~~~~~~~~~~~~~{.m}
IMMINPAR = {
{2, Imm12},
{5, ImAzero}
};
~~~~~~~~~~~~~~~~~~~~
In this case the input parameters can be given in the SLHA input file
as
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Block IMMINPAR
2 10 # Imm12
5 10 # ImAzero
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
_Note_: Unspecified parameters are assumed to be zero.
_____________________________________________________________________
__Symbol__: `IMEXTPAR`
__Default value__: `{}`
__Description__:
The `IMEXTPAR` variable is a list of input parameters for the spectrum
generator, which is read of the `IMEXTPAR` block of the SLHA input
file. The list assigned to the `IMEXTPAR` variable must have the same
form as the `MINPAR` variable.
__Example__: In the CP-violating MSSM (`MSSMCPV`) the `IMEXTPAR` block
has the form
~~~~~~~~~~~~~~~~~~~~{.m}
IMEXTPAR = {
{1, ImM1Input},
{2, ImM2Input},
{3, ImM3Input},
{23, ImMuInput}
};
~~~~~~~~~~~~~~~~~~~~
In this case the input parameters can be given in the SLHA input file
as
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Block IMEXTPAR
1 100 # Im(M1(MSUSY))
2 100 # Im(M2(MSUSY))
3 100 # Im(M3(MSUSY))
23 100 # Im(Mu(MSUSY))
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
_Note_: Unspecified parameters are assumed to be zero.
_____________________________________________________________________
__Symbol__: `FSAuxiliaryParameterInfo`
__Default value__: `{}`
__Description__:
In the `FSAuxiliaryParameterInfo` variable additional input or extra
parameters can be defined, and extra information provided can be
provided about existing input parameters. `FSAuxiliaryParameterInfo`
is expected to be a list, whose element are two-component lists. The
first element of this list is a symbol representing the parameter.
The second element is a list of properties for that parameter,
specified as replacement rules. The supported properties are
- `InputParameter`: A value of `True` or `False` indicating if the
parameter is an input parameter.
- `LesHouches`: The name of the SLHA block from which the
parameter should be read, if it is an input parameter.
- `MassDimension`: A number specifying the mass dimension of the
parameter.
- `ParameterDimensions`: 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 `FSAuxiliaryParameterInfo` variable has
the form
~~~~~~~~~~~~~~~~~~~~{.m}
FSAuxiliaryParameterInfo = {
{Aeij, { LesHouches -> AeijIN,
ParameterDimensions -> {3,3},
InputParameter -> True
} },
{Adij, { LesHouches -> AdijIN,
ParameterDimensions -> {3,3},
InputParameter -> True
} },
{Auij, { LesHouches -> AuijIN,
ParameterDimensions -> {3,3},
InputParameter -> True
} }
};
~~~~~~~~~~~~~~~~~~~~
Here, three 3x3 matrix-valued parameters are specified: `Aeij`,
`Adij` and `Auij`. They are defined as input parameters. 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 maximum 3 boundary
conditions can be generated. These boundary conditions are named
"high-scale", "susy-scale" and "low-scale" boundary condition and are
described in the following.
However, it is possible to disable the high-scale boundary condition.
In order to do so, set
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
OnlyLowEnergyFlexibleSUSY = True; (* disable high-scale BC, 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.
\note `LowScale` is ignored if `FlexibleEFTHiggs == True`
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.
\note `LowScaleFirstGuess` is ignored if `FlexibleEFTHiggs == True`
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$M_W\f$.
\note `LowScaleInput` is ignored if `FlexibleEFTHiggs == True`
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]]}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The method to determine the weak mixing angle can be chosen by setting
the variable `FSWeakMixingAngleInput` to either `Automatic`,
`FSFermiConstant` or `FSMassW`. `FSWeakMixingAngleInput` is set to
`Automatic` by default.
| Value of `FSWeakMixingAngleInput` | Parameters from which weak mixing angle is determined |
|------------------------------------|-------------------------------------------------------|
| `FSFermiConstant` | \f$G_F\f$ and \f$M_Z\f$ |
| `FSMassW` | \f$M_W\f$ and \f$M_Z\f$ |
| `Automatic` (default) (recommended)| chose most precise method automatically |
Example: Automatically chose most precise method to determine the weak
mixing angle
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
FSWeakMixingAngleInput = Automatic; (* recommended *)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
\note If `FSWeakMixingAngleInput = FSMassW;` is chosen, FlexibleSUSY
looks for the definition of the weak mixing angle in the symbol \c
SARAH\`Weinberg. If \c SARAH\`Weinberg is not defined, FlexibleSUSY
uses the expression assigned to `FSWeakMixingAngleExpr`, which is by
default set to \c ArcSin[Sqrt[1-Mass[SARAH`VectorW]^2/Mass[SARAH`VectorZ]^2]].
_____________________________________________________________________
__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/DR-bar parameters can be given at the low-energy scale
`LowScale`.
\note `InitialGuessAtLowScale` is ignored if `FlexibleEFTHiggs == True`
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__: `InitialGuessAtSUSYScale`
__Default value__: `{}`
__Description__:
\note `InitialGuessAtSUSYScale` is only used if `FlexibleEFTHiggs == True`
With the `InitialGuessAtSUSYScale` variable initial values for the
model MS-bar/DR-bar parameters can be given at the SUSY scale
`SUSYScale`.
Example: In the MSSMEFTHiggs `InitialGuessAtSUSYScale` is given as follows:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
InitialGuessAtSUSYScale = {
{Yu, Automatic},
{Yd, Automatic},
{Ye, Automatic}
{MassB, Ms},
{MassWB, Ms},
{MassG, Ms},
{mq2, UNITMATRIX[3] Ms^2},
{mu2, UNITMATRIX[3] Ms^2},
{md2, UNITMATRIX[3] Ms^2},
{ml2, UNITMATRIX[3] Ms^2},
{me2, UNITMATRIX[3] Ms^2},
{\[Mu], Ms},
{B[\[Mu]], Sqr[Ms]/(TanBeta + 1/TanBeta)},
{T[Yu], Ms/TanBeta Yu},
{T[Yd], Ms TanBeta Yd},
{T[Ye], Ms TanBeta Ye},
{T[Yu][3,3], (Ms/TanBeta + Xtt Ms) Yu[3,3]}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
_____________________________________________________________________
__Symbol__: `InitialGuessAtHighScale`
__Default value__: `{}`
__Description__:
With the `InitialGuessAtHighScale` variable initial values for the
model MS-bar/DR-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__: `EWSBInitialGuess`
__Default value__: `{}`
__Description__:
In the `EWSBInitialGuess` variable initial guesses for some or all
of the EWSB output parameters can be specified.
Example: In the VCMSSM `EWSBInitialGuess` is defined as
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
EWSBInitialGuess = {
{TanBeta, vu / vd},
{MuSq, \[Mu]^2}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
_____________________________________________________________________
__Symbol__: `EWSBSubstitutions`
__Default value__: `{}`
__Description__:
In the `EWSBSubstitutions` variable, substitutions for model
parameters in terms of other parameters can be given.
`EWSBSubstitutions` should be a list of two-component lists, in which
the first element is the parameter to be substituted for, and the
second element is the expression to be substituted in its place.
Example: In the VCMSSM `EWSBSubstitutions` is defined as
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
EWSBSubstitutions = {
{vd, vMSSM Cos[ArcTan[TanBeta]]},
{vu, vMSSM Sin[ArcTan[TanBeta]]},
{\[Mu], Sign[\[Mu]] Sqrt[MuSq]}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
_____________________________________________________________________
__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.
_____________________________________________________________________
__Symbol__: `MatchingScaleInput`
__Default value__: `{}`
__Description__:
\note `MatchingScaleInput` is only used if `FlexibleEFTHiggs == True`
In the `MatchingScaleInput` variable, relations between the parameters
of the full model and the Standard Model (the EFT) at the `SUSYScale`
can be specified.
An important application is the relation between the vacuum
expectation values (VEVs) in a SUSY model and \f$v\f$ in the Standard
Model: In `FlexibleEFTHiggs` the running Yukawa couplings of the full
model are determined from a pole mass matching of the Standard Model
fermions (which need to be present in both models). For this
determination the running VEVs of the full model must be known and
non-zero. `MatchingScaleInput` allows the user for example to fix the
running VEVs of the full model as a function of the running SM-like
VEV \f$v\f$ in the full model.
_Example:_ In the MSSM the vacuum expectation values \f$v_u\f$ and
\f$v_d\f$ are related to the MSSM SM-like VEV \f$v = \sqrt{v_u^2 +
v_d^2}\f$ as
\f{align*}{
v_u &= v \sin\beta , \\
v_d &= v \cos\beta .
\f}
To fix \f$v_u\f$ and \f$v_d\f$ in the MSSM in this way,
`MatchingScaleInput` can be used:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{.m}
MatchingScaleInput = {
{vu, VEV Sin[ArcTan[TanBeta]]},
{vd, VEV Cos[ArcTan[TanBeta]]}
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
where `TanBeta` is an input parameter. The symbol `VEV` is a
FlexibleSUSY constant which is assigned the value
\f{align*}{
\text{VEV} = \frac{2 m_Z}{\sqrt{g_Y^2 + g_2^2}} ,
\f}
where \f$m_Z\f$ is the running Z boson mass in the full model,
detetermined by requiring the equality of the Z boson pole masses of
the full model and the Standard Model. \f$g_Y\f$ and \f$g_2\f$ are
the running gauge couplings of \f$U(1)_Y\f$ and \f$SU(2)_L\f$ in the
full model, respectively. These two gauge couplings are calculated
using the 1-loop threshold correction for \f$\alpha_{\text{em}}\f$ and
the running weak mixing angle, \f$\cos\theta_W = m_W / m_Z\f$.
\f$m_W\f$ is the running W boson mass in the full model, detetermined
by requiring the equality of the W boson pole masses of the full model
and the Standard Model.
\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 `FSAuxiliaryParameterInfo` 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]
};
~~~~~~~~~~~~~~~~~~~~~~~~~~~~