Minimal-lagrangians: Generating and studying dark matter model Lagrangians with just the particle content

Abstract

minimal-lagrangians is a Python program which allows one to specify the field content of an extension of the Standard Model of particle physics and, using this information, to generate the most general renormalizable Lagrangian that describes such a model. As the program was originally created for the study of minimal dark matter models with radiative neutrino masses, it can handle additional scalar or Weyl fermion fields which are SU(3)C singlets, SU(2)L singlets, doublets or triplets, and can have arbitrary U(1)Y hypercharge. It is also possible to enforce an arbitrary number of global U(1) symmetries (with Z2 as a special case) so that the new fields can additionally carry such global charges. In addition to human-readable and LaTeX output, the program can generate SARAH model files containing the computed Lagrangian, as well as information about the fields after electroweak symmetry breaking (EWSB), such as vacuum expectation values (VEVs) and mixing matrices. This capability allows further detailed investigation of the model in question, with minimal-lagrangians as the first component in a tool chain for rapid phenomenological studies of “minimal” dark matter models requiring little effort and no unnecessary input from the user. Program summaryProgram title:minimal-lagrangiansCPC Library link to program files:https://doi.org/10.17632/4mm2zk5r84.1Licensing provisions: GPLv3Programming language:PythonNature of problem: Given a quantum field theory’s gauge group, it is sufficient to specify the particle (field) content in order to identify the full renormalizable theory, up to the parameters in its Lagrangian. However, the process of determining the Lagrangian manually is not only tedious and error-prone, but also involves additional complications such as redundant terms or the question of whether the theory is anomaly-free.Solution method:minimal-lagrangians generates the complete renormalizable Lagrangian for a given model with the Standard Model gauge group SU(3)C×SU(2)L×U(1)Y, including interaction terms. Redundant terms in the Lagrangian are eliminated in order to avoid duplicated parameters. The particle content is also checked for gauge anomalies, including the Witten SU(2) anomaly [1]. The model will automatically be modified to make fermions vector-like if necessary. The generated Lagrangian can be output in SARAH [2,3] model file format so that the model is immediately available for detailed phenomenological study using the capabilities of SARAH.Additional comments including restrictions and unusual features: Instead of manually determining the details of a model, the only input to the program minimal-lagrangians is the particle content. Using the output to SARAH, minimal-lagrangians thus forms the first step in a tool chain which enables the complete implementation and study of a new model with minimal effort and no “boilerplate” user input. The focus is on “minimal” dark matter models, i.e. those with the Standard Model gauge group (no additional gauge fields), where the new fields are color singlets and at most triplets under SU(2)L.