DefaultParamCard
DefaultParamCard[lag]
creates a template for the parameter card for the given Lagrangian lag, which is saved as a JSON file in the current working directory or, if specified, in the directory dir given as option OutputDirectory dir.
Details and Options
- In order to create a UFO file from a model lag defined in Matchete, it is required to provide a parameter card as a JSON file. To help getting started, the routine DefaultParamCard creates a template for this parameter JSON file by collecting every bit of information obtainable through the model itself. The remaining pieces (i.e. the parameter values) need to be added manually by the user.
- The following options can be given:
-
OutputDirectory Automatic Allows to specify the path to the output directory where the parameter card should be saved. When set to Automatic it is saved in the current working directory (Directory[]) DefaultValues False If set to True, default values for the SM input parameters will be included and automatically assigned to the model parameters. This feature only serves as help for simple models and might not work in more complicated scenarios, where the electroweak symmetry breaking patterns of the SM are modified. FlavorInvariants Can be used to provide an association of flavor invariant structures that are used to parametrized all present couplings. The provided option value should match the output format of ImposeFlavorSymmetry. Gauge Automatic By default the Rξ/Feynman gauge is used for exporting the Feynman rules to the UFO format. The restriction from general Rξ gauge to Feynman gauge (ξ=1) is achieved through the option Rξ. The allowed values are Automatic, Manual, Rξ, and Unitary. Rξ 1 Sets all gauge parameters to unity (ξ=1) , thus restricting to Feynman gauge for the vector fields that have not been fixed to unitary gauge before. Note that MadGraph can still use the resulting UFO files for unitary gauge simulations, by internally switching the propagators and neglecting Goldstone bosons. The allowed values are 1 and General.
Examples
open allclose allBasic Examples (1)
Consider loading the Standard Model as a basic example:
The SM Lagrangian in the vacuum of the broken phase in unitary gauge can be obtained using:
The default parameter card for this Lagrangian can be generated using:
Here, the option "Internal"True is used only to output the parameter card data as association directly in the notebook. By default ("Internal"False) this data is written into a JSON file instead.
Options (1)
DefaultValues (1)
Default numerical values for the SM parameters can be included using:
where the relations between SM inputs and model parameters are also included.
Note that an automatic inclusion of the CKM matrix is currently not supported.
The value"ZERO" denotes that this parameter should be removed from the UFO files entirely.
Here, the option "Internal"True is used again only to output the parameter card data as association directly in the notebook. By default ("Internal"False) this data is written into a JSON file instead.
Applications (1)
One can also generate the parameter card using flavor symmetry assumptions. For example, consider a U(2)5 flavor symmetry for the SM, which only allows Yukawa couplings for the third generation fermions.
First, the global symmetry groups have to be defined:
Note that one has to identify U(2)~SU(2)U(1) since Matchet only allows to define simple groups. The flavor symmetry can then be assigned to the chiral fields in terms of an association, where for every flavor its representations are specified:
Note that since no representation was specified for the third generation it is automatically assumed to be a Singlet (equivalently, one can also explicitly include {3}->Singlet for all fermions. At most one non-Abelian representation is allowed per flavor, while an arbitrary number of U(1) charges can be given.
This flavor symmetry can then be assigned to the SM Lagrangian using
which determines for all flavored couplings present in the Lagrangian ℒSM that are invariants under the flavor groups and associates these to the couplings in form of SparseArrays, which are returned in the form of an association.
Note that ImposeFlavorSymmetry requires the Lagrangian ℒSM in the unbroken electroweak phase as input, since the flavor symmetry is defined on the level of the chiral fields. In addition, it requires the coupling indices to be directly contracted with the fields and not with other couplings.
The flavor invariants are then used to parametrize the couplings of the theory when calling DefaultParamCard afterwards with the option FlavorInvariants: