[Paper Review] Sarah

Florian Staub|arXiv (Cornell University)|Jun 3, 2008

Dark Matter and Cosmic Phenomena4 citations

TL;DR

SARAH is a Mathematica-based tool for automated model building in supersymmetric particle physics, enabling users to define, compute, and export Lagrangians, renormalization group equations, loop corrections, and model files for various high-energy physics software. Its key contribution is streamlining the construction of complex supersymmetric models—including extensions like the MSSM, NMSSM, and seesaw models—by automating algebraic calculations and generating output for tools like SPheno, FeynArts, CalcHep, and the UFO format.

ABSTRACT

SARAH is a Mathematica package for building and analyzing supersymmetric models. SARAH just needs the gauge structure, particle content and superpotential to produce all information about the gauge eigenstates of a model. Breaking of gauge symmetries and mixings of particles can easily be in a second step and entire Lagrangian is derived automatically. Also the gauge fixing terms are derived by SARAH in R_Xi gauge, and the corresponding ghost interactions are calculated. Using this information, SARAH can calculate the all mass matrices, tadpole equations and vertices at tree-level for the given model. In addition, the expressions for the 1- and 2-loop renormalization group equations of all parameters can be calculated and an automatic calculation for the 1-loop corrections to self energies and the tadpoles are possible. SARAH can write all information about the model to LaTeX files, or create a model files for FeynArts/FormCalc, WHIZARD/OMEGA and CalcHep/CompHep, which can also be used for dark matter studies using MicrOmegas, and in the UFO format which is supported by MadGraph 5. Beginning with version 3, SARAH is also the first available spectrum-generator-generator: based on the derived, analytical expression it creates source code for SPheno to calculate the mass spectrum as well the SUSY decays with high precision. In that way, it is possible to implement new models in SPheno without the need to write any Fortran code by hand. Already many models beyond the MSSM are included in the public version of SARAH and the implementation of new models is easy and straightforward.

Motivation & Objective

• To provide a comprehensive, automated tool for constructing and analyzing supersymmetric models beyond the minimal supersymmetric standard model (MSSM).
• To reduce the manual effort required to compute complex field-theoretic quantities such as vertices, self-energies, and renormalization group equations (RGEs).
• To enable seamless integration with major simulation and calculation tools like SPheno, MadGraph, FeynArts, CalcHep, and WHIZARD.
• To support a wide range of model extensions, including flavor-violating, CP-violating, R-parity violating, and seesaw-type models.
• To facilitate the study of models with multiple U(1) symmetries, Dirac gauginos, and high-scale physics via automated output generation.

Proposed method

• Users define models via a structured model file specifying particle content, superpotential, gauge groups, and interactions.
• SARAH automatically computes mass matrices, tadpole equations, and vacuum expectation values (VEVs) using algebraic field-theory techniques.
• It derives all vertices from the Lagrangian using superfield formalism and implements both Hermitian and non-Hermitian mixing matrices.
• The tool calculates one-loop corrections to self-energies and masses, including fermion, scalar, and vector boson corrections.
• SARAH generates model files in multiple formats: SPheno, UFO, FeynArts/FormCalc, CalcHep/CompHep, WHIZARD, and LaTeX output.
• It supports advanced features such as integrating out heavy particles, defining Dirac spinors, and handling gauge-fixing terms and ghost interactions.

Experimental results

Research questions

• RQ1 How can the construction of complex supersymmetric models be automated to reduce manual error and effort?
• RQ2 What is the most effective way to generate consistent model files for diverse high-energy physics tools like SPheno, MadGraph, and FeynArts?
• RQ3 How can one systematically compute and output renormalization group equations and loop corrections for arbitrary supersymmetric models?
• RQ4 What are the minimal requirements for defining a model with flavor mixing, CP violation, or extended gauge symmetries in a consistent and extensible framework?
• RQ5 How does the performance of automated model generation scale across different model types, such as MSSM, NMSSM, or seesaw models?

Key findings

• SARAH successfully automates the derivation of the full Lagrangian, mass matrices, and tadpole equations for models including the MSSM, NMSSM, and B-L-SSM.
• The tool generates accurate and consistent output for SPheno, including RGEs, branching ratios, loop corrections, and mass spectra, with evaluation times ranging from ~10 seconds (MSSM) to over 4,000 seconds (complex seesaw models) in Mathematica 5.2.
• SARAH supports the automatic computation of one-loop corrections to fermion, scalar, and vector boson self-energies, with validation against known results in the literature.
• The UFO output format is correctly generated, enabling direct use in MadGraph and other Monte Carlo generators.
• The tool handles complex model features such as Dirac gauginos, multiple U(1) symmetries, and R-parity violation, with dedicated support for models like the MRSSM and muνSSM.
• Validation checks confirm consistency with established results for RGEs, self-energies, and vertex structures, as documented in references [65–69].