Source-linked AI summary
From Superpotential to Model Files for FeynArts and CalcHep/CompHep
Florian Staub
TL;DR
Supersymmetric model extensions require substantial manual work to derive consistent Lagrangians, spectra, interactions, and phenomenology-ready model files. SARAH automates these calculations and generates outputs for FeynArts and CalcHep/CompHep, while supporting broad model extensions and configurable CP and flavor violation. Its main practical scope includes automated model analysis and output generation, with CalcHep/CompHep imposing a limitation on four-point interactions involving four colored particles.
Problem
Studying supersymmetric models beyond the MSSM requires time-consuming manual checks, derivations, diagonalizations, and model-file construction before phenomenological analysis.
Method
SARAH takes a superpotential and gauge sector, automates model consistency and Lagrangian-related calculations, and generates phenomenology and documentation files.
Results
SARAH calculates interactions for different eigenstates, tadpole equations, gauge-fixing and ghost interactions, spectra-related quantities, and model files for FeynArts and CalcHep/CompHep.
Takeaways & Limitations
SARAH supports extensible N = 1 supersymmetric theories, effective-theory limits, and independently switchable CP and flavor violation for model exploration.
Takeaways & Limitations
CalcHep/CompHep cannot directly handle four-point interactions of four colored particles because their color structure is implicit.
Abstract
from arXiv · showhide
SARAH is a Mathematica package for building and studying supersymmetric models. It calculates for a given superpotential and gauge sector the full Lagrangian of a model. With the new version of SARAH it is possible to calculate automatically all interactions for the different eigenstates and write model files for FeynArts and CompHep/CalcHep. In addition, the tadpole equations are calculated, gauge fixing terms can be given and ghost interactions are added, particles can be integrated out and non supersymmetric limits of the theory can be chosen. CP and flavor violation can easily be switched on or off.
1. Introduction
SARAH addresses the extensive preparatory work required to study supersymmetric models beyond the MSSM, from consistency checks and Lagrangian extraction to phenomenological model-file generation.
- Extending the MSSM requires checking gauge anomalies, deriving interactions from the superpotential, calculating and diagonalizing mass matrices, and deriving tadpole equations.
- Writing model files for existing phenomenology programs is another time-consuming task before new models can be studied.
- SARAH automates this preparatory work for supersymmetric model building and phenomenology.
2. Overview
SARAH automates model checks, Lagrangian and spectrum calculations, and output generation, enabling inspection and phenomenological use of models after only a few minutes on modern computers.
- SARAH automatically checks gauge anomalies and calculates Lagrangians for gauge and mass eigenstates.
- Ghost terms are calculated from gauge-fixing terms, and particles can be integrated out when selected.
- The automated calculations derive mass matrices and tadpole equations, calculate tree-level masses, and compute mixing matrices from an input spectrum file.
- On modern computers, the automated calculations take only a few minutes and support vertex checks, mass-matrix inspection, numerical parameter assignments, and spectrum calculations.
- SARAH can generate model files for FeynArts and CompHep/CalcHep and write LaTeX output containing model information and corresponding Feynman diagrams.
3. What Models are possible
SARAH supports broad classes of N = 1 supersymmetric theories with extensible gauge and matter sectors, configurable symmetry breaking, effective-theory limits, and independently controlled parameter properties.
- SARAH can handle N = 1 supersymmetric theories whose chiral superfields are arranged in SU(2) doublets and singlets.
- The gauge sector can include additional abelian or nonabelian groups, while the matter content can include extra particles or generations.
- Users can define gauge-symmetry breakings, integrate out or delete particles, add noncanonical terms, and redefine existing interactions.
- Flavor and CP violation can be switched independently for all parameters, which can also be related, numerically assigned, or specified in a Les Houches input file.
- The package archive includes models such as the MSSM, NMSSM, µνSSM, SM, and MSSM variants with integrated-out or additional gauge sectors.
4. The Model Files
SARAH stores model information across three editable files, with Model.m containing the essential gauge, particle, superpotential, and mixing definitions.
- Model.m, parameters.m, and particles.m store the model information in three files.
- Model.m is the only required file and contains the gauge sector, particle content, superpotential, and mixings.
- parameters.m assigns parameter properties, numerical values, and LaTeX names.
- particles.m supplies particle information such as R-parity, mass, width, PDG, LaTeX name, and output name.
- All three files are written in an intuitive form and can be changed quickly.
5. The Output
SARAH generates model files for FeynArts and CalcHep/CompHep, together with comprehensive LaTeX documentation for specified eigenstates. CalcHep/CompHep output requires special handling of colored four-point interactions and ghost types.
- 5. The Output: SARAH can generate FeynArts, CalcHep/CompHep, and LaTeX model outputs for a chosen set of eigenstates.The output includes model information for further phenomenological studies.
- 5. The Output: Generated LaTeX files include particle content, mixing matrices, tadpole equations, all interactions, and corresponding Feynman diagrams.SARAH also writes batch files for producing PDFs on Linux and Windows.
- 5.2 CalcHep/CompHep: CalcHep/CompHep cannot directly handle four-point interactions containing four colored particles because their color structure is implicit.SARAH addresses this using auxiliary-field-style splitting based on F- and D-term results.
- 5.2 CalcHep/CompHep: Splitting four-point interactions avoids separately writing every possible combination of four scalars and increases model-file generation speed.The method follows CalcHep/CompHep's auxiliary-field treatment.
- 5.2 CalcHep/CompHep: SARAH supports Faddeev–Popov and Goldstone ghosts in CalcHep/CompHep, with vertices calculated dynamically.Tensor ghosts are not identified as supported in the passage.
- 5.1 FeynArts: For FeynArts, SARAH additionally writes information on parameter and mass dependences, numerical values when available, and FormCalc abbreviations.These additions are intended to speed calculations with FormCalc.
6. Checks
The SARAH-generated MSSM model files were checked against existing FeynArts and CalcHep files at both vertex and process levels, with additional relic-density tests.
- 6. Checks: The generated MSSM model files were compared with existing FeynArts and CalcHep files at the vertex and process levels.Vertex comparisons covered more than 15000 combinations of generations for given parameter sets.
- 6. Checks: The checks compared the value of each vertex for given parameters and calculated several processes using both old and new model files.Relic density was also calculated with micrOmegas for two parameter sets.
A.1.1 The Model File
The MSSM model file defines the gauge and matter superfields, superpotential terms, gauge fixing, rotations to mass eigenstates, and spinor conventions. These entries encode the model before SARAH derives interactions and related outputs.
- Gauge and superfield definitions: The MSSM gauge sector is U(1) × SU(2) × SU(3), represented by the corresponding vector superfields and gauge couplings.The gauge entries specify each superfield, group dimension, group name, and coupling name.
- Matter superfields: Doublet and singlet entries define component fields, generations, superfields, and their gauge charges.The doublets are q, l, Hd, and Hu; the singlets are d, u, and e.
- Superpotential: The trilinear superpotential terms encode the Yukawa interactions through Yu, Yd, and Ye.SARAH represents these terms in the TriW list with the corresponding superfields and signs.
- Superpotential: The model file includes a bilinear superpotential term that produces the Higgsino mass.The supplied passage identifies the role of the term but does not show its explicit expression.
- Gauge fixing: Gauge-fixing entries are specified for the unbroken gauge groups and later updated for the mass eigenstates.The mass-eigenstate expressions include vector-boson masses, Goldstone fields, and gauge parameters.
- Rotations and mass eigenstates: After electroweak symmetry breaking, vector bosons, gauginos, Higgs fields, sfermions, neutralinos, and charginos rotate into mass eigenstates.The neutral gauge bosons obey Z = −sin ΘW B + cos ΘW W3 and A = sin ΘW W3 + cos ΘW B.
- Rotations and mass eigenstates: The chargino rotations mix charged winos and Higgsinos into negative and positive charged eigenstates through U− and U+.The negative states combine fWm with FHdm, while the positive states combine fWp with FHup.
- Spinors and particle content: The model file specifies Dirac-spinor assignments and retains all particles without integrating out or deleting any.The listed assignments include up-type fermions, neutrinos, neutralinos, and charginos.
A.1.2 Parameter and Particle - File
The parameter and particle files store numerical, naming, convention, and physical-property information needed to describe the model's parameters and particles.
- Parameter file: Parameter entries can specify numerical values, Les Houches positions, parameter dependences, reality, diagonality, and LaTeX names.The Yu example marks the parameter real and diagonal and gives its Les Houches entries.
- Particle file: Particle entries define properties such as R-parity, PDG codes, widths, masses, FeynArts numbers, LaTeX names, and output names.The particle file therefore records conventions and physical metadata for model particles.
A.2 From MSSM to NMSSM
SARAH extends an MSSM model file to the NMSSM by adding a singlet, its interactions, vacuum structure, mixings, and related eigenstate definitions. The example also demonstrates CP and flavor rotations, vertex and tadpole calculations, ghost interactions, R-parity violation, and additional gauge structure.
- Changing the model file: The NMSSM implementation adds a gauge-singlet superfield with one generation and no couplings to the three gauge groups.The singlet couples through Hu Hd S and has a cubic self-interaction.
- Changing the model file: The singlet scalar receives a vacuum expectation value and splits into scalar and pseudoscalar components, producing CP-even and CP-odd Higgs eigenstates.In the CP-conserving case, scalar and pseudoscalar sectors decouple, with mixing matrices ZH and ZA.
- Changing the model file: The singlet fermion mixes with neutral fermions to form five neutralinos, while SARAH defines the corresponding spinors and can calculate Higgs–quark and ghost vertices.Generated vertices include left- and right-polarization entries with generation and color indices.
- Changing the model file: SARAH automatically computes electroweak-symmetry-breaking tadpole equations and outputs explicit vacuum minimum conditions.The example gives the full down-Higgs tadpole expression in terms of masses, gauge couplings, vacuum expectation values, and superpotential parameters.
- Adding CP violation and flavor: Dropping CP conservation makes the Higgs matrix irreducible, while flavor rotations move quarks and squarks to the CKM basis and retain the CKM product in the Lagrangian.The same framework supports bilinear R-parity violation, neutrino–neutralino mixing, charged-lepton–chargino mixing, and additional U(1) gauge structure.