Input parameters of SPheno

General

There are two different ways to define the input parameters which shall be used with SPheno to define a parameter point

Scalar valued parameters or parameter which are not part of the model are usually given via the MINPAR or EXTPAR blocks in the Les Houches input file
Parameters which are vectors, matrices or higher rank tensors are given via separated blocks in the Les Houches input file.

Using MINPAR and EXTPAR

Conventions

The MINPAR and EXTPAR blocks are part of the Susy Les Houches Accord (SLHA), see Refs. . The conventions for these blocks in the Les Houches input file are as follows:

Block MINPAR     #
 Integer1 Real1 # Comment1
 Integer2 Real2 # Comment2
...

Thus, each parameter is identified via an Integer (IntegerX) and receives a value Real. The conventions for EXTPAR are exactly the same. While specific conventions for the MSSM and NMSSM for the entries in MINPAR and EXTPAR exist, SARAH does not make any use of them. It offers the user complete freedom in defining the input according to his/her demands.

Complex parameters

In the case of complex parameters, the imaginary parts are given via

Block IMMINPAR     #
 Integer1 Real1 # Comment1
 Integer2 Real2 # Comment2
...

Definition in SARAH

The entries which SPheno expects in MINPAR or EXTPAR are defined in SPheno.m via

MINPAR={
 {Integer1, ParameterName1},
 {Integer2, ParameterName2},
 ...
};

Again, EXTPAR is used in exactly the same way.

Remarks

There is exactly no strict reason to use EXTPAR at all for SARAH generated SPheno versions but all parameters can be defined via MINIPAR. This option exists only if one wants to mimic the existing SLHA conventions for some models.
The variables ParameterNameX must not exist in the model. Otherwise, there will be an error message when compiling SPheno that parameters are defined twice. Note, SARAH also auto-generates for each parameter X the derived parameters XIN, XMZ, and XGUT which can also not be used in MINPAR or EXTPAT
If several, different boundary conditions shall be defined and the boundary conditions needs different input parameters, one can use

MINPAR=Table[{},{N}];
MINPAR[[/1|1]]={
 {Integer1a, ParameterName1a},
 {Integer2a, ParameterName2a},
 ...
};
MINPAR[[/1|1]]={
 {Integer1b, ParameterName1b},
 {Integer2b, ParameterName2b},
 ...
}:

In that case the input parameters MINPAR[ [X]] can only be used in the boundary conditions BoundarySUSYScale[ [X]], BoundaryHighScale[ [X]], BoundaryEWSBScale[ [X]].

Example

CMSSM: the standard input parameters for the constrained MSSM are defined via MINPAR = {{1,m0}, {2,m12}, {3,TanBeta}, {4,SignMu}, {5,Azero}};

in SPheno.m. Thus, the parameter point for the numerical evaluation is given to SPheno via the Les Houches input via
```
 Block MINPAR #
    1  7.000000E+01 #  m_0
    2  2.500000E+02 #  M_1/2
    3  1.000000E+01 #  Tan(beta)
    4. 1.000000E+00 #  Sign(mu)
    5. 0.000000E+00 #  A_0
```
CMSSM and GMSB boundary conditions. In order to define the CMSSM and GMSB boundary conditions in a single SPheno.m, one can use MINPAR=Table[{},{2}];
```
(* CMSSM input*)
MINPAR[[/1|1]]={{1,m0},
             {2,m12},
             {3,TanBeta},
             {4,SignumMu},
             {5,Azero}};

(* GMSB input parameters *)
MINPAR[[/2|2]]={{1,LambdaInput},
             {2,MessengerScale},
             {3,TanBeta},
             {4,SignumMu},
             {6,cGrav},
             {7,n5plets},
             {8,n10plets}};
```
In order to switch between both sets of input parameters and the corresponding boundary conditions, the flag 1 in MODSEL is used:
- CMSSM input Block MODSEL # 1 1 # 1/0: High/low scale input 2 1 # Boundary Condition ... Block MINPAR # Input parameters 1 1.5000000E+03 # m0 2 1.5000000E+03 # m12 3 1.0000000E+01 # TanBeta 4 1.0000000E+00 # SignumMu 5 -2.0000000E+03 # Azero
- GMSB input Block MODSEL # 1 1 # 1/0: High/low scale input 2 2 # Boundary Condition ... Block MINPAR # Input parameters 1 1.0000000E+05 # LambdaInput 2 2.0000000E+05 # MessengerScale 3 1.0000000E+01 # TanBeta 4 1.0000000E+00 # SignumMu 6 1.0000000E+00 # cGrav 7 1.0000000E+00 # n5plets 8 0.0000000E+00 # n10plets
NMSSM boundary conditions: for the constrained NMSSM, the input parameters beyond those of the CMSSM are defined in EXTPAR: MINPAR={ {1, m0}, {2, m12}, {3, TanBeta}, {5, Azero}}; EXTPAR = { {61, LambdaInput}, {62, KappaInput}, {63, ALambdaInput}, {64, AKappaInput}, {65, MuEffinput} };

Note, that the entry 4 of MINPAR is removed because the phase of μ is not a free parameter in this model. The blocks in the Les Houches input file are
```
Block MINPAR      # Input parameters
1   1.0000000E+03    # m0
2   1.0000000E+03    # m12
3   1.0000000E+01    # TanBeta
5   -2.5000000E+03    # Azero
Block EXTPAR      # Input parameters
61 1.0000000E-01    # LambdaInput
62 1.1000000E-01    # KappaInput
63 -1.5000000E+03    # ALambdaInput
64 -3.6000000E+01    # AKappaInput
65 9.6500000E+02    # MuEffinput
```
Complex input parameters: in order to set complex input parameters via MINPAR or EXTPAR no changes in SPheno.m are necessary. The imaginary parts can directly be defined via Block IMMINPAR # Input parameters 2 1.0000000E+02 # Im(m12) Block IMEXTPAR # Input parameters 61 1.0000000E-02 # Im(LambdaInput)

for instance. In that example, the CNMSSM parameters M_1/2 and λ get an imaginary part of 100 GeV, respectively 0.01.

Using parameter specific blocks for the input

Input Conventions

With MINPAR and EXTPAR it is hardly possible to define the input value for an entire vector or matrix. For this purpose, in SPheno generated SARAH versions always the option exists to give entire blocks in the Les Houches input file as input. The name of the blocks to define parameters are the same as used in the output (see parameters.m) together with a suffix IN. Thus the input values for a matrix M could be given as input via

Block MIN      # Input for M
1 1 Real11     #
1 2 Real12     #
1 3 Real13     #
2 1 Real21     #
...

If the matrix is diagonal, one can skip all values which a zero:

Block MIN      # Input for M
1 1 Real11     #
2 2 Real22     #
3 3 Real33     #

Imaginary parts

The imaginary parts can be defined if the additional prefix IM is used, e.g.

Block IMMIN    # Input for Im(M)
1 1 Real11     #
2 2 Real22     #
3 3 Real33     #

Applied boundary conditions

By default, if parameters receive numerical values in that way, these values are applied at the highest considered scale:

In High-scale SPheno versions this is the GUT scale
In Low-scale SPheno versions this is the renormalisation scale

See also Low or High scale SPheno version. One can change this behaviour by using the keyword LHInput in the defined boundary conditions. With

BoundaryCondition={
...,
{X, LHInput[X]}
};

X the input values are applied at the scale corresponding to the used boundary conditions (BoundaryCondition=BoundaryEWSBScale or BoundaryRenScale for instance), but not at the High scale (BoundaryCondition=BoundaryHighScale corresponds to the default choice). One can also make use of this option to overwrite default boundary conditions, see Boundary conditions in SPheno.

Example

Neutrino Yukawa coupling in Seesaw 1: input values for Y_\nu, whose SLHA block is called YV, are given via YVIN Block YVIN # 1 1 1.000000E-03 # Yv(1,1) 1 2 2.000000E-04 # Yv(1,2) 1 3 3.000000E-05 # Yv(1,3) 2 1 0.000000E+00 # Yv(2,1) 2 2 1.000000E-03 # Yv(2,2) 2 3 0.000000E+00 # Yv(2,3) 3 1 0.000000E+00 # Yv(3,1) 3 2 0.000000E+00 # Yv(3,2) 3 3 1.000000E-03 # Yv(3,3)

(Note, these are just random values as example and won't explain any neutrino data).
Flavour violating squark soft masses can be defined via Block MSQ2IN # 1 1 1.00000E6 # msq2(1,1) 1 2 2.00000E4 # msq2(1,2) 1 3 2.00000E4 # msq2(1,3) 2 1 2.00000E4 # msq2(2,1) 2 2 1.00000E6 # msq2(2,2) 3 1 2.00000E4 # msq2(3,1) 3 3 1.00000E6 # msq2(3,3)

Two remarks:
1. All entries which are not defined ((2,3) and (3,2)) are set automatically to zero
2. SPheno doesn't make use of the symmetry of the parameters, i.e. it is necessary to define (consistently!) the entire matrix
Input at SUSY scale: if one want to set in a non-minimal SUSY model a new coupling Y_x at the SUSY instead of the GUT scale, this can be done via LHInput.
1. Define in SPheno.m BoundarySUSYScale = { ... {Yx, LHInput[Yx]} };
2. The input parameters are given as usual Block YXIN # 1 1 1.000000E-01 # Yx(1,1) 2 2 1.000000E-01 # Yx(2,2) 3 3 1.000000E-01 # Yx(3,3)

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