Package: minimal-lagrangians
minimal-lagrangiansThis is a Python program which allows one to specify the field content of an extension
of the Standard Model of particle physics (SM) and, using this information, generates the
most general renormalizable Lagrangian that describes such a model. As the program was
written for the study of minimal dark matter models with radiative neutrino masses,
it can handle additional fields with the following properties:scalar or Weyl fermion fieldsSU(3) singletsSU(2) singlets, doublets or tripletsarbitrary hyperchargecharged under a global ℤ₂ symmetrycharged under an arbitrary number of global U(1) symmetriesRequirementsThe program requires Python 3 (tested with Python ≥ 3.4).
No external libraries are necessary.Installationminimal-lagrangiansisavailable on pip, so it can simply be installed by runningpip install minimal-lagrangiansUsageminimal-lagrangiansonly prints the potential involving at least one new (i. e. non-SM) field,
i. e. the kinetic terms and the Standard Model Lagrangian are omitted. The models are
not checked for anomalies (tools like SARAH can be used for this purpose).The new models are currently defined in the filedata.py. Models can be
added in a user-defined file (to be used with the--model-fileoption, see below) in
the following form:[BSMModel('<model_name>',(# list of fields# type       name   SU(2) rep.  hypercharge# for a scalar field, e.g. a scalar doublet with hypercharge 1:ScalarField('S',2,Y=1),# for a fermion field, e.g. a fermion singlet with hypercharge 0:FermionField('F',1,Y=0),# ℤ₂-even scalar field:ScalarField('S',1,Y=0,z2=1),# …),# optional: parameter values for different hypercharge assignments (offsets), e.g.(0,2,…)),# …]To add fields with global U(1) charges, use the optional parameteru1:# type       name   SU(2) rep.  hypercharge  U(1) charges# for a scalar field, e.g. a scalar doublet with hypercharge 1:ScalarField('S',2,Y=1,u1=[1,3,…]),# for a fermion field, e.g. a fermion singlet with hypercharge 0:FermionField('F',1,Y=0,u1=[-1,2,…]),The Standard Model fields are assumed to be neutral (z2=1, U(1) charges zero) under the new global symmetries.Information on how to run the program on the command line can be obtained withminimal-lagrangians -h:usage: minimal-lagrangians [-h] [--format {LaTeX,SARAH,plain}]
                           [--model-file [path/to/file.py]]
                           [--omit-equivalent-scalars]
                           [--omit-self-interaction] [--list-discarded-terms]
                           [--sarah-no-scalar-cpv] [--version]
                           model [parameter α]

A Python program to generate the Lagrangians for dark matter models

positional arguments:
  model                 name of the model whose Lagrangian is to be generated
                        (specify “list” in order to list all available models)
  parameter α           value of the model parameter α (determines
                        hypercharges of the fields)

optional arguments:
  -h, --help            show this help message and exit
  --format {LaTeX,SARAH,plain}
                        output format for the generated Lagrangian (default:
                        plain)
  --model-file [path/to/file.py]
                        file containing user-defined models; a file is only
                        read if this option is present (default: ./models.py)
  --omit-equivalent-scalars
                        keep only scalar fields from the model which have
                        unique quantum numbers and absolute hypercharge values
                        (omit duplicates)
  --omit-self-interaction
                        omit pure self-interactions of the new fields in the
                        Lagrangian, that is, output only interaction terms
                        which involve both SM and new fields (default: output
                        all terms)
  --list-discarded-terms
                        list redundant terms which were discarded from the
                        Lagrangian due to identities
  --sarah-no-scalar-cpv
                        assume that there is no CP violation causing mixing
                        between scalar and pseudoscalar fields for SARAH
                        output
  --version             show program’s version number and exitTest cases can be run using./test.pyAmong other checks, this currently tests whether the program produces the correct
Lagrangian for the following models:T1-3-B with α = 0, which is studied in(Fiaschi, Klasen, May; arXiv:1812.11133 [hep-ph]).T1-1-A with α = 0, as given in(Farzan; arXiv:0908.3729 [hep-ph]), which
presents an implementation of this model.The models given in(Cheung, Sanford; arXiv:1311.5896 [hep-ph]):singlet–doublet fermion model (SDF, “model A”)singlet–doublet scalar model (SDS, “model B”)singlet–triplet scalar model (STS, “model C”)The Higgs triplet model (→ seesaw type II), see e. g.(Kanemura, Yagyu; arXiv:1201.6287 [hep-ph]).ExamplesFor example, runningminimal-lagrangians --omit-equivalent-scalars T1-1-A 0prints the Lagrangian for the model T1-1-A with α = 0 from(Restrepo, Zapata, Yaguna; arXiv:1308.3655 [hep-ph]):- M_ϕ'² ϕ'^† ϕ' - ½ M_φ² φ²
 - (λ₁ (H ϕ') φ + H.c.)
 - λ₂ (H^† H) (ϕ'^† ϕ') - λ₃ (H^† ϕ') (ϕ'^† H) - λ₄ (ϕ'^† ϕ')² - λ₅ (H^† H) φ² - λ₆ (ϕ'^† ϕ') φ² - (λ₇ (H ϕ')² + H.c.) - λ₈ φ⁴
 - (½ M_ψ ψ ψ + H.c.)
 - (y₁ (ϕ'^† L) ψ + H.c.)Runningminimal-lagrangians STSprints the Lagrangian for model C (singlet–triplet scalar) from(Cheung, Sanford; arXiv:1311.5896 [hep-ph]):- ½ M_T² Tr(T²) - ½ M_S² S²
 - λ₁ H^† T² H - λ₂ (H^† T H) S - λ₃ (H^† H) S² - λ₄ Tr(T²)² - λ₅ Tr(T²) S² - λ₆ S⁴Source filesminimal-lagrangians.py:
The main executable file, responsible for parsing command line arguments and starting execution of the selected modelminimal-lagrangians:
A symbolic link tominimal-lagrangians.pytest.py:
The program’s test suitesetup.py:
Thesetuptoolsscript used to create the program’s distribution packageDirectorymin_lag/:
The main program packagemin_lag/__init__.py:
Python package file for themin_lagpackagemin_lag/data.py:
Contains the predefined modelsmin_lag/fields.py:
Contains the class definitionsFieldobjects, such asScalarFieldorFermionFieldmin_lag/models.py:
Contains the class definitionsModelandBSMModelobjects, as well as the definition of the Standard Model (STANDARD_MODEL)min_lag/terms.py:
Contains the class definitions for Lagrangians and their terms (Lagrangian,InvariantTerm)min_lag/unicode_util.py:
Contains some small utility functions dealing with to Unicode characters, and related datamin_lag/version.py:
Contains the program’s version number; generated bysetup.pyDirectorymin_lag/output/:
Contains the different output modulesmin_lag/output/__init__.py:
Contains the base (abstract) class definition for the formatter classes and other common output definitionsmin_lag/output/LaTeX.py:
Contains the output module for the LaTeX output formatmin_lag/output/plain.py:
Contains the output module for the (Unicode) plain text output formatDirectorymin_lag/output/SARAH/:
Contains the code and data for the SARAH output formatmin_lag/output/SARAH/__init__.py:
Contains the code for the SARAH output formatDirectorymin_lag/output/SARAH/data/:
Contains data files for the SARAH output formatmin_lag/output/SARAH/data/model.m:
Template for the main SARAH model filemin_lag/output/SARAH/data/parameters.m:
Template for the SARAH model fileparameters.mmin_lag/output/SARAH/data/particles.m:
Template for the SARAH model fileparticles.mmin_lag/output/SARAH/data/SPheno.m:
Template for the SARAH model fileSPheno.m