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SARAH 3.2: Dirac Gauginos, UFO output, and more

Florian Staub

arXiv:1207.0906v3hep-ph

TL;DR

Supersymmetric model studies require compact model implementations and precise numerical tools beyond the MSSM. SARAH derives the relevant model information and exports it to analysis and spectrum-generation tools; its newer version adds UFO output, Dirac-gaugino support, and consistency checks. Higher-dimensional operators remain only partially supported in downstream outputs.

  • Problem

    Studying supersymmetric models beyond the MSSM requires connecting compact model definitions to tools that produce precise numerical results.

  • Method

    SARAH derives Lagrangians, vertices, mass matrices, RGEs, and corrections, then exports them to UFO, SPheno, and other tool formats.

  • Results

    SARAH 3.2 adds UFO output, full Dirac-gaugino model support, and physical and formal consistency checks for implementations.

  • Takeaways & Limitations

    The new interfaces expand the SARAH-supported model studies to MadGraph and extend automated spectrum and model-file generation across multiple tools.

  • Takeaways & Limitations

    Higher-dimensional operators are only partially supported, and they are not included in Monte Carlo-tool or FeynArts model-file output.

Abstract

from arXiv · show

SARAH is a Mathematica package optimized for the fast, efficient and precise study of supersymmetric models beyond the MSSM: a new model can be defined in a short form and all vertices are derived. This allows SARAH to create model files for FeynArts/FormCalc, CalcHep/CompHep and WHIZARD/OMEGA. The newest version of SARAH now provides the possibility to create model files in the UFO format which is supported by MadGraph 5, MadAnalysis, GoSam, and soon by Herwig++. Furthermore, SARAH also calculates the mass matrices, RGEs and one-loop corrections to the mass spectrum. This information is used to write source code for SPheno in order to create a precision spectrum generator for the given model. This spectrum-generator-generator functionality as well as the output of WHIZARD and CalcHep model files have seen further improvement in this version. Also models including Dirac Gauginos are supported with the new version of SARAH, and additional checks for the consistency of model implementations have been created.

Program Summary

SARAH 3.2 extends the package with UFO model-file generation and support for Dirac gaugino models, while retaining automated derivation and multi-tool output.

  • SARAH 3.2 generates UFO model files supported by MadGraph, MadAnalysis, GoSam, and other tools.The UFO format is presented as a standardizing interface for model files.
  • Models with Dirac gauginos are supported, including their Lagrangian terms and renormalization-group equations.
  • SARAH derives vertices from compact model information and exports them to UFO, CalcHep, WHIZARD, FeynArts, and SPheno.Users provide the gauge structure, particle content, superpotential, and symmetry-breaking rotations rather than a complete Lagrangian.

1. Introduction

SARAH addresses the difficulty of obtaining precise numerical results for supersymmetric models beyond the MSSM by deriving model information and connecting it to several analysis tools.

  • SARAH derives mass matrices, tadpole equations, renormalization-group equations, and vertices from a compact supersymmetric model definition.
  • The SPheno interface exports information for 2-loop RGEs and 1-loop corrected masses as Fortran code that becomes a model-specific spectrum generator.
  • UFO output allows models implemented in SARAH to be studied with MadGraph 5, GoSam, MadAnalysis, and Aloha.
  • SARAH 3.2 adds full Dirac-gaugino support and consistency checks covering physical and formal aspects of model implementations.

2. Implementation and checks of models in SARAH

SARAH constructs supersymmetric Lagrangians and model outputs from compact inputs, supports configurable interaction structures including Dirac gauginos, and checks implementations for consistency.

  • Lagrangian derivation: SARAH derives the full Lagrangian from gauge structure, particle content, superpotential, symmetry breaking, and field rotations.This reduces the required model input and enables automated vertex derivation.
  • Configurable structures: Users can independently enable or disable soft-breaking, F-term, D-term, and Dirac-gaugino structures through model flags.The default for AddDiracGauginos is False, while the other listed structures generally default to True.
  • Dirac gauginos: Dirac-gaugino support includes both the gaugino–adjoint-fermion mass term and new D-term contributions, with kinetic mixing and 2-loop RGEs taken into account.
  • Supported structures: SARAH fully supports the listed renormalizable Lorentz structures and internally handles color structures through representation and tensor-product methods.
  • Scope boundary: Higher-dimensional operators receive partial support: dimension-5 fermion interactions and 2-loop RGEs are included, but six-scalar operators and Monte Carlo or FeynArts output are excluded.
  • Model checks: Consistency checks test particle and parameter definitions, anomalies, superpotential terms, mixings, Dirac spinors, bilinear terms, and mass-matrix irreducibility.The checks include gauge and Witten anomalies and compatibility with unbroken gauge groups.
  • Scope boundary: Anomaly checks currently work only for supersymmetric models.

3. Calculations performed by SARAH

SARAH derives model information including mass matrices, tadpole equations, vertices, RGEs, and one-loop corrections, with outputs configurable for different eigenstates and interaction classes.

  • Mass matrices and tadpoles: MassMatrix and TadpoleEquation automatically provide tree-level mass matrices and tadpole equations for model eigenstates.For example, SARAH returns a 6×6 d-squark matrix and a neutral Higgs vacuum condition.
  • Vertices: Vertex calculates selected external-particle interactions, while MakeVertexList can generate all interactions for specified eigenstates or generic classes.Results are organized by Lorentz structure and may use unitarity, group-generator properties, and parameter assumptions for simplification.
  • Vertices: Vertex calculations have been cross-checked against references for several models and tested for self-consistency in others through the SPheno interface.One non-trivial check examines one-loop relations between Goldstone and vector-boson masses.
  • Renormalization group equations: SARAH calculates SUSY RGEs at one- and two-loop level, including gauge kinetic mixing and two-loop effects from Dirac gaugino masses.The results are stored in parameter-specific arrays containing one-loop and two-loop β-functions.
  • Renormalization group equations: RGE calculations support configurable loop order, cached results, variable superfield generations, explicit generation sums, and selected parameters ignored at two loops.The IgnoreAt2Loop option can reduce computation time when only dominant one-loop effects are needed.

4. Output of SARAH

SARAH 3.2 expands model-file generation through a UFO interface, integrates Dirac-gaugino effects across outputs, and improves SPheno, validation, and WHIZARD capabilities.

  • UFO output: SARAH supports UFO models in MadGraph 5 and preserves the model’s full flavor and CP structure for other compatible tools.The format is also supported by GoSam, Aloha, MadAnalysis 5, and soon Herwig++.
  • UFO output: SARAH derives the mass-eigenstate Lagrangian, mass matrices, and tadpole equations before generating UFO model files for the final defined eigenstates.For public models, these are the mass eigenstates after electroweak symmetry breaking.
  • UFO output: The UFO output includes particles, parameters, Lorentz structures, vertices, couplings, and coupling-order hierarchies for use by external tools.The generated files are written under $SARAH/Output/$MODEL/$EIGENSTATES/UFO/.
  • Validation: UFO validation found exact numerical agreement for all tested 1 →2 decays, while 2 →2 differences remained below MadGraph’s estimated numerical error.Additional permutation, gauge-invariance, and Lorentz-invariance checks covered MSSM, NMSSM, B-L-SSM, and MRSSM processes.
  • SPheno and model support: SARAH-generated SPheno modules provide 2-loop RGEs, 1-loop mass corrections, decay widths, branching ratios, and electroweak precision observables.The calculations use general CP and flavor structure and can target models beyond the MSSM and NMSSM.

5. Other new features since version 3.0

SARAH 3.2 adds automatic gauge fixing, optional PDG.IX numbering, and an LHPC spectrum-plotting workflow for SPheno-generated spectra.

  • Gauge fixing: Gauge-fixing terms are derived automatically from the kinetic terms by imposing vanishing scalar–vector mixing, after which ghost interactions are calculated.The procedure supports models where gauge fixing and ghost vertices would otherwise require manual specification.
  • Generalized PDG numbering scheme: PDG.IX encodes particle properties and identifiers in a nine-digit number, including spin, CP character, B−L charge, electric charge, and SU(3)C representation.The scheme is intended to help organize models containing many new particles.
  • Generalized PDG numbering scheme: PDG.IX is optional and, when enabled, is used in SPheno, WHIZARD, CalcHep, and UFO output instead of the default PDG entries.The switch is made with UsePDGIX = True;.
  • LHPC Spectrum Plotter: The LHPC Spectrum Plotter creates SUSY mass-spectrum plots from SLHA output using a separate control file for tool paths, labels, colors, and columns.SARAH can generate the control file to work with spectra produced by SARAH-created SPheno modules.

6. Conclusion

SARAH 3.2 broadens automated supersymmetric-model support through UFO output, Dirac gauginos, consistency checks, and faster or more capable downstream interfaces.

  • Conclusion: SARAH 3.2 adds UFO model files readable by MadGraph 5, extends supported models to Dirac gauginos, and adds physical and formal consistency checks.It also simplifies gauge fixing, optionally supports PDG.IX, improves WHIZARD speed, and expands CalcHep functionality.

Appendix A. Model file for the MSSM/NMSSM with Dirac gauginos

The appendix specifies how to construct a SARAH model file for the MSSM/NMSSM with Dirac gauginos, including fields, interactions, mixings, and mass eigenstates.

  • Model-file structure: SARAH stores model information in Model.m, parameters.m, and particles.m, with Model.m containing the essential model definition.These files encode the gauge sector, particle content, superpotential, mixings, parameter properties, and particle-output information.
  • Gauge and matter sectors: The model uses the U(1) × SU(2) × SU(3) gauge sector and defines matter fields through their generations, superfields, and gauge representations.The Fields array specifies component-field names and transformation properties, while gauge declarations specify group and coupling information.
  • Dirac gauginos: Dirac gaugino masses require adjoint superfields in the singlet, triplet, and color-octet representations.The corresponding parameters are named MDBS, MDWBT, and MDGoc for the bino-singlet, wino-triplet, and gluino-octet mass terms.
  • Superpotential: The superpotential includes Yukawa, Higgs, singlet, triplet, and adjoint-sector terms and is entered through SARAH’s SuperPotential array.The displayed entries encode couplings and mass terms involving S, T, and the color-octet field.
  • EWSB and mixings: After electroweak symmetry breaking, SARAH defines rotations from gauge eigenstates to vector, scalar, fermion, and particle mass eigenstates.The construction includes Higgs VEVs, scalar and pseudoscalar decompositions, matter-sector mixings, and chargino-sector rotations.
  • Spectrum: Relative to the MSSM, the model contains four CP-even Higgs states, four CP-odd states, four charged Higgs particles, six neutralinos, three charginos, and two fermionic color octets.The color-octet states arise from gluino–octino mixing induced by the Dirac mass term.

Appendix B. Models

SARAH 3.2 includes models spanning the MSSM and its extensions, seesaw constructions, Dirac-gaugino theories, and several non-supersymmetric cases.

  • MSSM and extensions: SARAH 3.2 includes multiple minimal supersymmetric standard model variants with different flavor and CP structures.Listed variants include general flavor and CP structure, no flavor violation, explicit Higgs-sector CP violation, and the SCKM basis.
  • MSSM and extensions: The model collection includes NMSSM variants, near-MSSM, singlet-extended, triplet-extended, R-parity-violating, and U(1)- or B−L-extended theories.The listed examples cover NMSSM, TMSSM, TNMSSM, several RpV realizations, UMSSM, secluded MSSM, and B−L models.
  • Seesaw and other models: SARAH 3.2 provides SUSY-scale seesaw models, including inverse, linear, singlet-extended, B−L, and minimal R-symmetric constructions.It also includes SU(5) seesaw models, the left/right model, Standard Model variants, and the inert Higgs doublet model.

Appendix C. Validation of UFO output

The UFO validation compares MadGraph 5 cross sections and numerical uncertainties obtained from native MSSM files and SARAH-generated UFO files.

  • Comparison setup: The validation compares cross sections and numerical errors from MadGraph 5’s included MSSM model files with SARAH-generated UFO model files.The quantities are denoted by σM, δM for the included files and σS, δS for the SARAH output.
  • Error definition: Relative uncertainty is defined as δS,M = ΔσS,M / σS,M, where ΔσS,M is MadGraph’s absolute error estimate.This provides the uncertainty measure used for both model-file calculations.
  • Difference measure: The cross-section difference is calculated as D = (σS − σM) / σS using the run and parameter cards from Appendix C.1.The comparison therefore normalizes the difference to the SARAH-generated result.

Appendix C.1. Parameter and run card

The validation uses MadGraph 5.1.4.8.4 run and parameter cards, with selected run-card settings changed to reduce numerical uncertainty.

  • Cards and reproducibility: The calculations use the run and parameter cards delivered with MadGraph 5.1.4.8.4.The full cards used for reproducing the comparison are identified as being available from the author.
  • Run-card settings: The run card sets both beam types to no PDF and fixes the renormalization and factorization scales.The displayed settings are lpp1 = 0, lpp2 = 0, fixed_ren_scale = T, and fixed_fac_scale = T.
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