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SPheno 3.1: extensions including flavour, CP-phases and models beyond the MSSM
W. Porod, F. Staub
TL;DR
SPheno is extended to address flavour, CP phases, R-parity violation, seesaw models, low-energy observables, and SLHA conventions beyond its original MSSM scope. The program calculates flavour- and phase-complete one-loop masses and incorporates multiple model and input extensions, while remaining under active development with several planned capabilities.
Problem
SPheno needed capabilities beyond its original MSSM scope, including flavour, CP phases, R-parity violation, seesaw models, low-energy observables, and extended SLHA support.
Method
The paper describes implementations for flavour-complete CP-phase calculations, seesaw and bilinear R-parity-violating models, low-energy observables, and SPheno-specific SLHA extensions.
Results
SPheno calculates supersymmetric masses with complete flavour structure and CP phases at one loop and supports multiple seesaw and R-parity-violating model implementations.
Takeaways & Limitations
The extensions broaden SPheno into a framework for studying supersymmetric spectra and related observables across flavourful, CP-violating, seesaw, and R-parity-violating models.
Takeaways & Limitations
Several capabilities remain planned, including user-defined hadronic parameters, missing SLHA conventions, A0–H0 mixing with CP phases, and R-parity-violating low-energy observables.
Abstract
from arXiv · showhide
We describe recent extensions of the program SPheno including flavour aspects, CP-phases, R-parity violation and low energy observables. In case of flavour mixing all masses of supersymmetric particles are calculated including the complete flavour structure and all possible CP-phases at the 1-loop level. We give details on implemented seesaw models, low energy observables and the corresponding extension of the SUSY Les Houches Accord. Moreover, we comment on the possiblities to include MSSM extensions in SPheno.
1. Program Summary
SPheno determines supersymmetric-particle masses and couplings across several supersymmetric models while applying low-energy constraints and high-scale renormalization-group evolution.
- SPheno determines masses and couplings in the R-parity-conserving MSSM with generation mixing and CP-violating phases, seesaw extensions, and bilinear R-parity violation.
- Low-energy fermion masses, gauge couplings, and electroweak gauge-boson masses serve as constraints on the calculation.
- The program imposes high-scale soft-breaking constraints and obtains electroweak-scale parameters by evaluating renormalization-group equations.
2. Introduction
SPheno began as an MSSM spectrum and decay program without generation mixing or CP violation, and was extended to flavour, CP violation, R-parity violation, and seesaw models.
- The original SPheno calculated the MSSM spectrum while neglecting generation mixing and CP violation.
- The original program also calculated two- and three-body decays of supersymmetric particles and Higgs bosons, plus e+e− production rates.
- The described extensions add flavour aspects, CP violation, R-parity violation, and several seesaw variants.
3. Extensions with MSSM particle content at the electroweak scale and conserved R-parity
The extended SPheno supports flavour and CP phases, leading-order flavour-sensitive decays, multiple MSSM model classes, and high-scale seesaw and unified-model variants with MSSM electroweak particle content.
- SPheno implements complete flavour structures and CP phases in two-loop RGEs and one-loop flavour-dependent mass matrices.The one-loop matrices include 6×6 squark and charged-lepton matrices and a 3×3 sneutrino matrix.
- Decay routines calculate all two- and three-body supersymmetric-particle and Higgs-boson decays at leading order, including flavour effects.
- Implemented MSSM classes include mSUGRA, GMSB, AMSB, freely specified GUT-scale soft parameters, and electroweak-scale input parameters.
- Required inputs are provided through the SLHA convention.
- The program includes neutrino-mass models with additional high-energy states, including seesaw I, seesaw II, seesaw III, and minimal SU(5).
- These models retain the usual MSSM particle content at the electroweak scale; their differences arise from modified parameter evaluation.
4. R-parity violation
SPheno implements the bilinear R-parity-violating model, offering electroweak- or high-scale parameter input, neutrino-consistent choices, loop-corrected neutrino/neutralino masses, and R-parity-violating decays.
- The implemented bilinear model extends the superpotential and soft supersymmetry-breaking sector with R-parity-violating terms.
- Neutrino physics can arise from neutralino–neutrino mixing and loop contributions, while the same parameters correlate neutrino masses with LSP decays.
- Users can specify model parameters at the electroweak scale through SLHA2 blocks or combine high-scale mSUGRA, GMSB, or AMSB inputs with R-parity parameters.
- A dedicated flag can calculate ε_i and sneutrino vacuum expectation values so that neutrino physics is respected, using specified neutrino data.
- Mass matrices are calculated at tree level except for the neutrino/neutralino matrix, which includes full one-loop contributions; all possible R-parity-violating decays are calculated.
5. Low energy observables
SPheno calculates low-energy observables only for an effective MSSM at the electroweak scale with conserved R-parity, using scale-evolved parameters and running masses or mixing matrices. Its observables cover B physics, lepton magnetic and electric dipole moments, lepton radiative decays, the neutron EDM, and the ρ-parameter.
- Low-energy observables are calculated only when an effective MSSM exists at the electroweak scale and R-parity is conserved.
- B-physics observables: SPheno calculates B-physics observables including BR(b →sγ), BR(b →sµ+µ−), BR(b → s P, and neutral B-meson mass differences.
- B-physics observables: For Wilson coefficients, running couplings and SUSY masses are generally evolved to Q = mZ, except BR(b →sγ), whose coefficients use Q = 160 GeV.
- Lepton sector: The lepton-sector implementation covers SUSY contributions to anomalous magnetic moments, lepton EDMs, and the radiative decays µ →eγ, τ →eγ, and τ →µγ.
- Lepton sector: SPheno also calculates the neutron EDM using two neutron models and SUSY contributions to the ρ-parameter.
6. Extensions to SLHA
SPheno extends SLHA with complex Yukawa information, model-specific inputs, control flags, neutrino and seesaw parameters, and flavour-ordered output conventions. These extensions support flavour violation, several seesaw realizations, R-parity violation, and associated neutrino constraints.
- The SLHA extensions add new control and model-parameter blocks, while complex Yukawa couplings can be passed through corresponding blocks beginning with IM.
- Model extensions: MODSEL switches select minimal SU(5), right-handed-neutrino, Higgs-triplet seesaw II, Higgs-24-plet seesaw III, and alternative Higgs-15-plet seesaw II contents.
- Model extensions: The seesaw inputs specify right-handed-neutrino masses, Higgs-triplet masses, 24-plet mass matrices, and neutrino Yukawa couplings at their stated scales.
- Neutrino constraints: NeutrinoBoundsIn defines lower and upper bounds for atmospheric and solar mass differences, atmospheric and solar mixing angles, and the squared reactor mixing element.
- Program controls: SPhenoInput controls cross sections, branching ratios, scales, precision, iteration limits, RGE loop order, R-parity additions, neutrino-data fitting, and reduced mixing-matrix output.
- Output conventions: In flavour-violating cases, an SLHA extension provides flavour-ordered states instead of mass-ordered states.
7. Installation and implementing new models
SPheno is distributed with source, documentation, input, output, library, include, and executable directories and can be compiled with several Fortran compilers. Seesaw RGE modules are optional at compilation, and SARAH-generated models can be added in new directories.
- Installation: The distribution contains directories for the executable, documentation, module files, example inputs, example outputs, library, and source code.
- Installation: The Makefile defaults to Intel ifort but also supports NAG nagfor, Lahey lf95, g95, or a user-specified compiler.
- Optional seesaw modules: The long two-loop RGEs for seesaw type II and type III are not compiled by default because compilation can be time consuming.
- Optional seesaw modules: Adding -DSEESAWIII to PreDef enables the seesaw-III RGEs, while removing -DONLYDOUBLE enables quadrupole precision but can substantially slow the program.
- Implementing new models: SARAH-generated code can be placed in a new SPheno directory and built with its Makefile to create an additional executable in bin.
8. Input and output
Starting with SPheno 3.1, input and output use the SLHA format, with extensions for program-specific and model-specific features. Users can provide input and output filenames, while errors and warnings are written separately.
- SPheno 3.1 accepts only SLHA input and produces SLHA output, disabling the former HighScale.in, StandardModel.in, Control.in, and SPheno.out interfaces.
- The SLHA extensions control program-specific features and model extensions, while detailed errors and warnings are written to Messages.out.
- The command SPheno InName OutName selects input and output files, with LesHouches.in and SPheno.spc as defaults when names are omitted or unavailable.
9. Conclusions and comments
SPheno continues to expand its model, observable, and data-interface coverage, while several planned features and user-configurability improvements remain outstanding.
- SPheno is still being developed to add additional models and low energy observables.
- Planned updates include missing SLHA conventions, CP-phase mixing between A0 and H0, and R-parity-violating low energy observables.
- Hadronic parameters used for low energy observables are hard-coded, although routines for user-defined changes are planned.
- Default inputs include CKM Wolfenstein parameters, gauge-sector quantities, charged-lepton masses, and quark masses.
Appendix B. Unsupported SLHA features
Appendix B catalogs SLHA features and input conditions that SPheno does not yet support, alongside numerical and physical error conditions reported by its error system.
- Unsupported SLHA features include selected MODSEL and EXTPAR entries, such as scale choices, charged-Higgs pole mass, and GMSB messenger indices.These features are planned for implementation in subsequent updates.
- The error system reports integration failures including excessively small step sizes, excessive steps, and unfulfilled boundary conditions.
- It also reports eigenvalue-system dimension mismatches, numerical problems, excessive iterations, and quadrature precision failures.
- Input validation flags unknown MODSEL or MINPAR entries, incomplete model or Higgs specifications, and matrix or vector indices exceeding boundaries.
Appendix C.5. Module SugraRuns
This appendix lists SugraRuns and related diagnostics for invalid electroweak inputs, non-perturbative running, non-convergence, negative masses, and loop-correction failures.
- BoundaryEW diagnostics flag negative scalar mass-squared inputs and extreme ratios among down-type and up-type running masses.
- RunRGE diagnostics identify non-perturbative regimes and failure of the expected g1̸ = g2 unification condition at MGUT.
- Sugra diagnostics report failure to converge and conditions with |µ|2 < 0 at mZ.
- Mass routines report negative mass-squared values or failed p2 iterations for sleptons, sneutrinos, and squarks.
- The appendix also records loop-mass failures involving invalid µ, Z, h0, A0, and H+ squared quantities.
- Implemented improvements include the gluon contribution to the 1-loop gluino mass correction and flavour-violation effects.