minimal-lagrangians 1.1.2

A Python program to generate the Lagrangians for dark matter models

minimal-lagrangians

This 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 fields
• SU(3) singlets
• SU(2) singlets, doublets or triplets
• arbitrary hypercharge
• charged under a global ℤ₂ symmetry
• charged under an arbitrary number of global U(1) symmetries

Requirements

The program requires Python 3 (tested with Python ≥ 3.4). No external libraries are necessary.

Installation

minimal-lagrangians is available on pip, so it can simply be installed by running

pip install minimal-lagrangians

Usage

minimal-lagrangians only 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 file data.py. Models can be added in a user-defined file (to be used with the --model-file option, 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 parameter u1:

        # 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 with minimal-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 exit

Test cases can be run using

./test.py

Among 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]).

Examples

For example, running

minimal-lagrangians --omit-equivalent-scalars T1-1-A 0

prints 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.)

Running

minimal-lagrangians STS

prints 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 S⁴

Source files

• minimal-lagrangians.py: The main executable file, responsible for parsing command line arguments and starting execution of the selected model
• minimal-lagrangians: A symbolic link to minimal-lagrangians.py
• test.py: The program’s test suite
• setup.py: The setuptools script used to create the program’s distribution package
• Directory min_lag/: The main program package
  • min_lag/__init__.py: Python package file for the min_lag package
  • min_lag/data.py: Contains the predefined models
  • min_lag/fields.py: Contains the class definitions Field objects, such as ScalarField or FermionField
  • min_lag/models.py: Contains the class definitions Model and BSMModel objects, 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 data
  • min_lag/version.py: Contains the program’s version number; generated by setup.py
  • Directory min_lag/output/: Contains the different output modules
    • min_lag/output/__init__.py: Contains the base (abstract) class definition for the formatter classes and other common output definitions
    • min_lag/output/LaTeX.py: Contains the output module for the LaTeX output format
    • min_lag/output/plain.py: Contains the output module for the (Unicode) plain text output format
    • Directory min_lag/output/SARAH/: Contains the code and data for the SARAH output format
      • min_lag/output/SARAH/__init__.py: Contains the code for the SARAH output format
      • Directory min_lag/output/SARAH/data/: Contains data files for the SARAH output format
        • min_lag/output/SARAH/data/model.m: Template for the main SARAH model file
        • min_lag/output/SARAH/data/parameters.m: Template for the SARAH model file parameters.m
        • min_lag/output/SARAH/data/particles.m: Template for the SARAH model file particles.m
        • min_lag/output/SARAH/data/SPheno.m: Template for the SARAH model file SPheno.m