PaperlayerView exact revision on arXiv

Source-linked AI summary

A tool box for implementing supersymmetric models

Florian Staub, Thorsten Ohl, Werner Porod, Christian Speckner

arXiv:1109.5147v1hep-ph

TL;DR

Studying new SUSY models requires substantial derivation, code generation, and implementation across programs, while extensions of the MSSM address problems it does not resolve. The paper presents SARAH as a model-definition and code-generation framework for spectrum and phenomenology tools; its generated SPheno spectrum calculations have precision comparable to established MSSM generators over a large range of SUSY models, excluding two-loop Higgs-sector effects.

  • Problem

    Implementing new SUSY models for numerical study requires deriving masses, vertices, and RGEs, generating code, adding loop corrections, and implementing models in existing tools; the MSSM also leaves neutrino masses, strong CP, and the µ problem unresolved.

    Source: §1 · p. 4

  • Method

    The framework uses SARAH model definitions to generate SPheno code and model files for CalcHep, O’Mega, and WHIZARD, with SPheno output usable by micrOMEGAs and HiggsBounds.

    Source: §1 · p. 4

  • Results

    The generated SPheno spectrum calculation has precision comparable to established MSSM spectrum generators across a large range of SUSY models, excluding two-loop effects in the Higgs sector.

    Source: §9 · p. 42

  • Takeaways & Limitations

    SARAH can extend the availability of spectrum generators to a large range of SUSY models.

    Source: §9 · p. 42

    The SPheno output cannot fit low-energy data unless the model includes the required Yukawa couplings, two Higgs VEVs, SM gauge couplings, and SM particle content; without these, the fit and RGE evaluation are skipped.

    Source: §3.10 · p. 26

Abstract

from arXiv · show

We present a framework for performing a comprehensive analysis of a large class of supersymmetric models, including spectrum calculation, dark matter studies and collider phenomenology. To this end, the respective model is defined in an easy and straightforward way using the \Mathematica package SARAH. SARAH then generates model files for CalcHep which can be used with MicrOmegas as well as model files for WHIZARD and OMEGA. In addition, Fortran source code for SPheno is created which facilitates the determination of the particle spectrum using two-loop renormalization group equations and one-loop corrections to the masses. As an additional feature, the generated SPheno code can write out input files suitable for use with HiggsBounds to apply bounds coming from the Higgs searches to the model. Combining all program provides a closed chain from model building to phenomenology.

1. Introduction

The paper motivates supersymmetric extensions as responses to shortcomings of the Standard Model and to unresolved problems in the MSSM. It presents SARAH as a way to automate the lengthy path from model definition to phenomenological analyses.

1. Introduction

  • Supersymmetric extensions address Standard Model shortcomings including the hierarchy problem and the absence of a dark-matter candidate, while the MSSM still leaves neutrino masses, strong CP, and the µ problem unresolved.The paper also notes the MSSM's appealing features, including a dark-matter candidate and gauge coupling unification.Source: §1 · pp. 3–4
  • Implementing a new SUSY model for numerical study is lengthy because it requires deriving masses, vertices, and RGEs, generating code, adding loop corrections, and implementing the model in existing tools.The work also requires familiarity with multiple programs.Source: §1 · p. 4
  • SARAH lets users define a broad range of SUSY models once and generates SPheno, CalcHep, O’Mega, and WHIZARD outputs, with a SPheno spectrum file usable by micrOMEGAs and input files available for HiggsBounds.The framework covers spectrum calculations, cross sections, relic density, Higgs-search constraints, and collider simulations.Source: §1 · p. 4
  • The paper organizes the framework's implementation across model building, SPheno output, HiggsBounds, CalcHep and micrOMEGAs, O’Mega and WHIZARD, parameter scans, and tool-chain integration.These topics are discussed in Sections 2–8.Source: §1 · p. 5

2. Building new models with SARAH

SARAH supports broad N=1 SUSY model definitions and exports derived information to external programs. The section introduces the package and walks through installation and model-file construction using the MSSM as an example.

2.1 Overview

  • SARAH is designed for N=1 SUSY theories with arbitrary products of SU(n) and U(1) gauge factors, arbitrary irreducible chiral-field representations, and all renormalizable superpotential terms.The stated framework places no limits on the numbers of gauge factors, chiral superfields, superpotential terms, symmetry breakings, or field rotations.Source: §2.1 · p. 5

2.2 Download, installation and first evaluation

  • Installation extracts SARAH into Mathematica's application directory, after which users load the package and initialize a model with Start["Modelname"].The package archive includes model definitions, output directories created during execution, a manual, and example materials.Source: §2.2 · pp. 5–6

2.3.1 Model file for the MSSM

  • The MSSM model-file example specifies gauge groups, matter superfields, the superpotential, eigenstate rotations, and gauge fixing, while SARAH automatically adds scalar soft masses.The model-file conventions also describe how field names and gauge representations are recorded.Source: §2.3 · p. 7, §2.3.1 · p. 7
  • SARAH's model-file syntax assigns names, generations, and gauge representations to superfields, then specifies their superpotential and the gauge-to-mass-eigenstate mixings.For vector superfields, the final gauge-entry flag determines whether group-index sums are expanded or left implicit.Source: §2.3.1 · pp. 7–8

11. No particles should be integrated out or deleted

The section covers keeping particles represented in the model definition, adapting the MSSM definition to the NMSSM, and using SARAH to derive model information and export it to analysis tools.

11. No particles should be integrated out or deleted

  • The fermion definitions specify how mass-eigenstate fields are represented by two-component spinors when moving from four- to two-component formalism.The passage gives explicit mappings for quarks, leptons, neutralinos, charginos, and gluinos.Source: §11 · pp. 10–11

2.3.2 Creating a model file for the NMSSM

  • The NMSSM model file is formed from the MSSM definition by adding a gauge singlet, changing the superpotential, giving the singlet scalar a VEV, and mixing singlet fields with Higgs and neutralino states.The stated superpotential additions include the λ and κ singlet interactions.Source: §2.3.2 · p. 11

2.4 Calculations performed by SARAH

  • After initialization, SARAH checks gauge anomalies and charge conservation, derives tree-level Lagrangian results, and can calculate masses, tadpole equations, vertices, RGEs, and one-loop corrections to one- and two-point functions.The RGEs include one- and two-loop results for superpotential parameters, soft-breaking terms, gauge couplings, and VEVs; loop corrections use the DR scheme and ’t Hooft gauge.Source: §2.4 · pp. 11–12

2.5 Export to external programs

  • SARAH exports model-derived information in formats for external programs including FeynArts/FormCalc, CalcHep/CompHep, WHIZARD/O’Mega, and SPheno.The section presents these exports as support for comprehensive analysis of new models.Source: §2.5 · p. 12

3. Spectrum calculation with SPheno

This section describes how SARAH configures and generates model-specific SPheno code for supersymmetric spectrum and decay calculations, including user-configurable parameters and boundary conditions, threshold-aware RGE running, and low-energy variants. It also covers support for general flavor structures and CP phases, as well as model requirements and limitations that affect feature availability.

3.1 Introduction to SPheno

  • SPheno [42] [43] is a Fortran 95 spectrum calculator whose one-loop mass formulas extend [53] to flavor-dependent squark, charged-lepton, and sneutrino matrices [54, 55].The calculation includes complete one-loop contributions with general flavor mixing and CP phases, plus dominant two-loop Higgs-mass contributions [56] [57] [58] [59] [60].Source: §3.1 · pp. 12–13

3.2 Combining SPheno and SARAH

  • SARAH computes model-specific analytical expressions and exports them as Fortran code, generating a functional SPheno version without manual source changes.SPheno supplies fast, model-independent numerical routines for RGEs, decay phase space, and Passarino-Veltman integrals.Source: §3.2 · p. 13

3.4 Defining the properties of the generated SPheno version

  • The SPheno input file lets users define free parameters, boundary conditions at multiple scales, and parameters solved by tadpole equations; MINPAR and EXTPAR entries are not hard-coded.Boundary conditions can be set at electroweak, SUSY, GUT, and threshold scales, with low-scale input also available without RGE running.Source: §3.2 · p. 13, §3.4 · pp. 16, 18

3.3 Features of the generated SPheno version

  • The generated SPheno calculates spectra with two-loop RGEs and one-loop mass corrections, full momentum dependence, and general flavor structures and CP phases.Known two-loop Higgs-mass and tadpole corrections can also be included for MSSM-like Higgs sectors; the iterative calculation converges to a default relative precision of 10^-4.Source: §3.3 · pp. 13–14
  • The generated SPheno calculates widths and branching ratios for non-SM scalars and fermions, including two-body scalar and vector-boson decays and three-body fermion decays to all-fermion final states.Higgs decays to two photons and two gluons are included at leading order [63], alongside gluonic QCD corrections for decays into quarks and squarks [65].Source: §3.3 · p. 15

3.5 Example: The input file for the MSSM

  • For an MSSM mSugra-like setup, SPheno.m specifies m0, M1/2, A0, signµ, and tan β as inputs and solves the tadpole equations for µ and Bµ.The example also allows a dynamically adjusted SUSY scale, with options to disable it or use a fixed 1 TeV scale under SPS conventions.Source: §3.5 · p. 21

3.6 Generating the output

  • SARAH generates SPheno source code with MakeSPheno[Options], and ReadLists->True reuses previously calculated vertices and RGEs to save time.The generated files can be copied into a model-named subdirectory of SPheno version 3.1.4 or later and compiled there.Source: §3.6 · p. 22

3.7 Including Thresholds

3.7.1 Thresholds without gauge symmetry breaking

  • With unchanged gauge structure, threshold running adjusts active heavy-field generations and sets their couplings to zero when thresholds are crossed.Heavy scalar and fermion masses are assumed identical, and one-loop threshold corrections to gauge couplings and gaugino masses are calculated at each threshold when using two-loop RGEs.Source: §3.7.1 · pp. 23–24

3.7.2 With gauge symmetry breaking

  • When gauge structure changes across scales, SARAH calculates RGEs separately for each regime and combines them into SPheno with finite shifts in gauge couplings, gaugino masses, and scalar masses.The higher-scale input identifies fields to integrate out and the gauge sector below each threshold; the lowest-scale SPheno.m supplies threshold scales and boundary conditions.Source: §3.7.2 · pp. 24–25

3.8 Low energy SPheno version

  • A low-energy SPheno variant skips RGEs and electroweak-data fitting but solves tadpoles, calculates tree- and one-loop masses, and computes decay widths and branching ratios.It supports a broader set of models, including non-SUSY models; decay-particle lists must be supplied manually because automatic decay selection is unavailable in this mode.Source: §3.8 · p. 26

3.9 Differences to SPheno3.1.4

  • The SARAH-generated MSSM module handles some features differently from SPheno 3.1.4 and lacks some implementations, as summarized in Table 1.The supplied passage gives no individual table entries, so the specific differences are not enumerated here.Source: §3.9 · p. 26, Table 1 · p. 27

3.10 Supported models and known issues

  • A full low-energy-data fit requires quark and lepton Yukawa couplings, two Higgs VEVs, three SM gauge couplings, and SM particle content; flavor decomposition and NoFlavorMixing matrices are unsupported.When the fit and RGE evaluation are skipped by supplying model parameters manually, one-loop masses, decay widths, and branching ratios can still be calculated.Source: §3.10 · pp. 26–27

4. Checking Higgs constraints with HiggsBounds

SARAH-generated SPheno modules provide HiggsBounds input files for testing neutral and charged Higgs sectors against search bounds. The files omit some information, with CalcHep or WHIZARD available to calculate certain missing cross sections.

4. Checking Higgs constraints with HiggsBounds

  • SPheno writes HiggsBounds input files containing Higgs masses, widths, branching ratios, and effective couplings.The output includes masses and widths for neutral and charged Higgs fields, plus branching-ratio and effective-coupling files.Source: §4 · pp. 27–28
  • The generated output sets the H→γZ and H→ggZ effective couplings to zero because SPheno does not calculate them.Source: §4 · p. 28
  • SPheno also sets the LEP charged-Higgs production cross section to zero, but CalcHep or WHIZARD can calculate the cross sections needed for other HiggsBounds input options.Source: §4 · p. 28

5. Calculation of cross sections, widths and relic density using CalcHep and micrOMEGAs

SARAH generates CalcHep model files for cross-section calculations and micrOMEGAs files for dark-matter calculations. CalcHep’s blind mode supports scripted calculations across parameter points, while SPheno spectra can be passed into both tools.

5. Calculation of cross sections, widths and relic density using CalcHep and micrOMEGAs

  • CalcHep model files generated by SARAH support Feynman and unitarity gauges, CP violation, and splitting four-colored-particle interactions.Source: §5.1 · p. 29

5.1 Using CalcHep with SARAH and SPheno

  • SPheno-calculated parameters can be passed directly to CalcHep through SLHA input.Source: §5.1 · p. 29
  • CalcHep’s blind mode runs process calculations without its graphical interface, allowing multiple instances to be called non-interactively from scripts for parameter scans.Source: §5.1 · pp. 29–30

5.2 Relic density calculations with micrOMEGAs

  • SARAH generates micrOMEGAs main files for relic density calculations and, optionally, direct-detection signals, using a CalcHep model file first.Source: §5.2 · p. 30

6. Monte Carlo studies with WHIZARD

SARAH generates model files for WHIZARD and O’Mega, which support collider event generation for supersymmetric models. The interface covers typical renormalizable SUSY interactions, supports both WHIZARD branches, and can pass SPheno parameters into WHIZARD.

6.1 Introduction

  • WHIZARD efficiently generates unweighted events with exact matrix elements, including high-multiplicity final states such as eight-particle events.O’Mega constructs optimized matrix-element code using directed acyclic graphs, while VAMP adapts phase-space grids and channel weights for integration and event generation.Source: §6.1 · pp. 30–31

6.2 The interface between SARAH and WHIZARD

  • The interface supports typical SARAH supersymmetric models’ spin-0, spin-1/2, and spin-1 fields and nearly all dimension-3 and dimension-4 interactions.It also supports the color tensors arising from QCD gauge interactions that lead to supported Lorentz structures.Source: §6.2 · p. 31

Calling the interface

  • SARAH generates WHIZARD model files through ModelOutput, with MakeWHIZARD options for model naming, excluded vertices, and couplings per file.Generated files for WHIZARD 2.x are compiled and installed; WHIZARD 1.x output is injected into its source tree.Source: Calling the interface · pp. 32–33

Spectra and parameters

  • Generated SPheno versions can write model parameters as SINDARIN code for inclusion in a WHIZARD input script.The SPheno input flag 76 enables writing the parameter file.Source: Spectra and parameters · p. 34

7. Parameter scans with SSP

SSP automates repeated analyses across parameter points using the SARAH-supported tool chain. Its scan inputs define tools, parameter ranges, constraints, and plots, and it can fit parameters to satisfy constraints.

7. Parameter scans with SSP

  • SSP automates the tool-chain analysis over many parameter points and supports additional constraints and two-dimensional parameter-space plots.Figure 2 depicts the connected workflow from a SARAH model definition to generated files for SPheno, micrOMEGAs, and WHIZARD, with SPheno also writing HiggsBounds input.Source: §7 · p. 34, Figure 2 · p. 34

7.1 Installation and running scans

  • A scan is started with Start using an input file containing the scan information.Source: §7.1 · p. 35

7.2 The input files

  • SSP uses one input file for program locations and tool settings and another for scan parameters, ranges, constraints, and plots.The scan file can toggle inclusion of WHIZARD, HiggsBounds, CalcHep, and micrOMEGAs.Source: §7.2 · p. 35

Fit to constraints

  • SSP uses Mathematica’s NMinimize to vary model parameters and find combinations that minimize χ2 for specified constraints.For finite parameter ranges, SSP transforms the bounds to infinite boundaries via stretching.Source: Fit to constraints · p. 36

2D parameter sampling

For two-dimensional parameter scans, SSP can use Mathematica’s ContourPlot rather than a fixed grid or random scan when some regions need finer sampling. Increasing PlotPoints decreases the interpolation-point spacing, while Table 3 identifies the evaluated-point count by PlotPoints.

2D parameter sampling

  • ContourPlot lets SSP sample a two-dimensional parameter space more precisely in selected regions than a fixed grid or random scan.The example is a dark-matter relic-density scan in the (m0, M1/2) plane.Source: 2D parameter sampling · p. 36
  • Figure 3 varies PlotPoints from 5 to 50 across the (m0, M1/2) plane, with the mesh showing decreased spacing between interpolation points.The first row shows 5, 10, and 20; the second row shows 30, 40, and 50.Source: Figure 3 · p. 37
  • Table 3 reports the number of evaluated parameter-space points in the (m0, M1/2) plane for each PlotPoints value.The supplied caption gives the table’s scope but not its cell values.Source: Table 3 · p. 38

8. Putting the programs to work

The section describes automated installation and model implementation, a manual workflow for greater flexibility, and the steps for running the resulting tool chain. The programs exchange generated model and spectrum files to support analyses across the selected packages.

8.1 Automated setup and model implementation

  • Setup scripts install the complete environment, while a configure-generated script automates implementing a selected model in the chosen packages.The configure script checks requirements and downloads missing files; after configuration and make, the packages and an SSP setup file are available.Source: §8.1 · p. 38

8.2 Preparing a model by hand

  • For more flexibility than butler offers, users can define a model in SARAH, generate output, and manually integrate the model files into the target programs.MakeAll[] produces output for SPheno, CalcHep, WHIZARD, FeynArts, and LaTeX; the section illustrates manual preparation of SPheno, CalcHep, micrOMEGAs, and WHIZARD.Source: §8.2 · p. 39

8.3 Running the chain

  • Running the chain uses SPheno spectrum output as input to CalcHep and micrOMEGAs, while WHIZARD and HiggsBounds use generated parameter and input files.SPheno input flags control creation of the WHIZARD parameter file and HiggsBounds inputs; CalcHep can be run in blind mode from a script.Source: §8.3 · p. 41

9. Conclusions

The conclusions present SARAH as a way to generate spectrum and phenomenology tools for a wide range of supersymmetric models. The accompanying implementation examples describe threshold handling for seesaw models and assumptions made in the SPheno code.

9. Conclusions

  • SARAH generates SPheno code for two-loop RGE running and one-loop mass corrections, with spectrum precision comparable to established MSSM generators except for two-loop Higgs-sector effects.The authors describe SARAH as a spectrum-generator-generator that broadens spectrum-generator availability across SUSY models.Source: §9 · p. 42
  • SARAH also generates model files for CalcHep/micrOMEGAs, FeynArts, HiggsBounds, and WHIZARD, and SSP can automate scans of observables over parameter space.SPheno masses and parameters serve directly as input to the other programs for dark-matter and collider studies.Source: §9 · p. 42
  • The generic framework covers models with new fields or extended gauge sectors at the SUSY scale, as well as thresholds or gauge-symmetry breaking at higher scales.The authors state that this flexibility and integration of tools should simplify study of new supersymmetric models.Source: §9 · p. 42

Seesaw1.m

  • In the seesaw example, a heavy right-handed neutrino is removed from the low-energy spectrum and Feynman rules but still contributes to RGEs above its threshold.Integrating it out contributes to the effective dimension-five operator.Source: Seesaw1.m · p. 43

SPheno.m

  • The SPheno example assigns separate threshold scales near each singlet mass and neglects mass splitting between heavy superfield fermion and scalar components.The effective-operator boundary conditions are specified at the thresholds.Source: SPheno.m · pp. 43–44

A.2 Implementation of a model with a gauge symmetry breaking scale in SARAH and SPheno

The appendix demonstrates SARAH and SPheno implementation for a left-right supersymmetric model with gauge-symmetry breaking at a threshold. It describes the model above and below that scale and the corresponding model-file definitions.

A.2 Implementation of a model with a gauge symmetry breaking scale in SARAH and SPheno

  • The implementation simplifies the left-right model to one threshold scale, although the discussion it builds on includes two and the authors say adding the second is straightforward.The example focuses on SARAH implementation and avoids redundant discussion.Source: §A.2 · p. 44

A.2.1 Summary of the model

A.2.2 Model files for SARAH

A.2.3 Model files for SPheno output

The section configures SARAH-generated SPheno for scale-dependent model calculations, then demonstrates parameter scans and comparisons of spectra and decays.

A.2.3 Model files for SPheno output

B. Example for using SSP in the MSSM: (m0,M1/2) grid scan

C.1 Mass spectrum of the MSSM

  • Relative mass differences between stock SPheno and SPheno/SARAH are shown for two parameter points as functions of m0 or M1/2.The comparison uses two-loop RGEs and one-loop self-energies, with two-loop Higgs mass corrections and loop-induced neutralino and gluino decays disabled in stock SPheno.Source: §C.1 · p. 55

C.2 Decay widths and branching ratios in the MSSM

  • MSSM decay comparisons cover Higgs branching ratios above 10^-4, neutralino two- and three-body decays, and total-width differences versus m0.The total-width comparison uses an SPS 4-based scenario.Source: §C.2 · p. 55

C.3 Masses in Seesaw type I – III

  • For seesaw types I–III, the comparison with stock SPheno is intended to demonstrate automatic threshold inclusion and correct one-loop boundary conditions.The cited passage does not report the comparison outcome.Source: §C.3 · p. 55

C.4 Masses in the NMSSM

The SARAH-generated SPheno NMSSM results were compared with NMSSM-Tools, with good agreement reported.

C.4 Masses in the NMSSM

  • The SARAH-generated SPheno NMSSM results agree well with NMSSM-Tools; detailed numerical discussion is cited in [55].The supplied passage does not give the comparison values.Source: §C.4 · p. 55
  • Figure 5 compares Higgs-field and neutralino masses from stock SPheno and SPheno/SARAH at M1/2 = 500 GeV and tan β = 10.The inputs also set A0 = 0 GeV and signµ = 1; stock SPheno is based on version 3.1.4 with small modifications.Source: Figure 5 · p. 56
  • Figure 6 compares all six charged-slepton and down-squark masses at M0 = 250 GeV, A0 = −300 GeV, and tan β = 20.The caption also specifies signµ = 1.Source: Figure 6 · p. 56

D. Validation of the WHIZARD model files

The SARAH-generated WHIZARD model agrees completely with WHIZARD’s stock MSSM implementation across selected 2→2 processes. The comparison reports cross sections and absolute integration errors under the stated integration setup.

D. Validation of the WHIZARD model files

Related papers

Loading 1109.5147v1…