A Python program to generate the Lagrangians for dark matter models
Project description
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] 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
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
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