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SUSY Les Houches Accord 2
B. C. Allanach, C. Balazs, G. Belanger, M. Bernhardt, F. Boudjema, D. Choudhury, K. Desch, U. Ellwanger, P. Gambino, R. Godbole, T. Goto, J. Guasch, M. Guchait, T. Hahn, S. Heinemeyer, C. Hugonie, T. Hurth, S. Kraml S. Kreiss, J. Lykken, F. Moortgat, S. Moretti, S. Penaranda, T. Plehn, W. Porod, A. Pukhov, P. Richardson, M. Schumacher, L. Silvestrini, P. Skands, P. Slavich, M. Spira, G. Weiglein, P. Wienemann
TL;DR
Different supersymmetry conventions make results difficult to compare and require tedious, error-prone translations. This paper extends SLHA1 with conventions and interface switches for selected CP-, R-parity-, flavour-violating MSSM scenarios and the NMSSM, while preserving backward compatibility. The resulting accord is presented as a practical solution for future SUSY phenomenology, although comprehensive simultaneous testing was not yet available.
Problem
Different conventions make results from authors or codes difficult to compare and require tedious, error-prone consistency checks and translations.
Method
The paper extends SLHA1 conventions and interfaces to selected CPV, RPV, FLV, and NMSSM models using defined bases, blocks, and global model-selection switches.
Results
SLHA1 had substantially removed the need for separately coded interfaces and supplied a common, comparable, transferable format; SLHA2 preserves backward compatibility where feasible.
Takeaways & Limitations
The proposed conventions constitute a practical solution intended to support SUSY particle phenomenology and future use across codes.
Takeaways & Limitations
Few programs currently use the covered NMSSM, CPV, RPV, or non-trivial FLV scenarios, so comprehensive simultaneous testing was unavailable.
Abstract
from arXiv · showhide
The Supersymmetry Les Houches Accord (SLHA) provides a universal set of conventions for conveying spectral and decay information for supersymmetry analysis problems in high energy physics. Here, we propose extensions of the conventions of the first SLHA to include various generalisations: the minimal supersymmetric standard model with violation of CP, R-parity, and flavour, as well as the simplest next-to-minimal model.
1 Introduction
SLHA1 addressed incompatible supersymmetry conventions by defining a consistent, unambiguous common interface, but its scope was limited to the real, R-parity-conserving MSSM. SLHA2 extends this framework toward RPV, FLV, CPV, and NMSSM scenarios while balancing generality, implementability, and usability.
- Motivation and role of SLHA1: SLHA1 reduced convention-translation problems by uniquely defining consistent conventions and a common interface between supersymmetry codes.This changed translation dependence from factorial to linear in the number of codes.
- Impact: SLHA1 reduced the need for separately coded interfaces and provided input and output in a common, comparable, transferable format.Its convention choices were also being adapted for other tasks such as the SPA project.
- Motivation and role of SLHA1: SLHA1 had been designed exclusively for the MSSM with real parameters and R-parity conservation.SLHA2 targets extensions involving RPV, FLV, CPV phases, and the NMSSM.
- Scope choices: SLHA2 restricts the MSSM treatment to either CPV or RPV, uses the Super-CKM/PMNS basis for RPV and FLV, and assumes CP, R-parity, and flavour conservation in its NMSSM model.These restrictions address the tension between model generality, implementation ease, and practicality for users.
- Interface design: The accord retains programming-language and platform independence through ASCII-based model-input, spectrum-output, and decay-output files.The authors judge implementation independence more advantageous than requiring codes to parse the input.
2 Extensions of SLHA1
SLHA2 collects backward-compatible extensions to SLHA1 for parameter inputs and scale choices. The additions include alternative Higgs-mass inputs and QEXTPAR controls for parameter-specific input scales, while warning that arbitrary multiple scales are not broadly supported by codes.
- Input extensions: SLHA2 introduces optional EXTPAR entries allowing either the A0 or H+ pole mass as input instead of m2_A(Minput).These alternatives represent different ways of specifying the relevant Higgs parameters.
- Input extensions: QEXTPAR allows specific parameters to be defined at alternative scales, overriding default MINPAR and EXTPAR scale choices.For example, µ may be defined at MEWSB while remaining parameters use Minput.
- Input contents: EXTPAR contains entries for gaugino masses, trilinear couplings, Higgs parameters, sfermion masses, and messenger indices.The listed quantities include M1, M2, M3, At, Ab, and model-specific GMSB indices.
- Scale choices: Most codes cannot be expected to support multiple arbitrary scale choices, so manuals and outputs must be checked for the intended behavior.QEXTPAR is normally absent; otherwise it overrides the default input scale or Minput for selected parameters.
- Scale choices: QEXTPAR defines parameter-specific scales for gaugino masses, trilinear couplings, Higgs-sector quantities, and sfermion mass terms.Examples include QM1, QM2, QM3, QAu, QAd, QAℓ, and scales for slepton and squark masses.
3 Model Selection
SLHA2 adds global MODSEL switches to identify particle content and whether R-parity, CP, and flavour are violated. These switches extend SLHA1 while assigning explicit options for MSSM, NMSSM, and generalized phase or flavour choices.
- Model-selection switches: SLHA2 introduces global switches in the SLHA1 MODSEL block to define general model properties.The switches are additional to those already defined in SLHA1.
- Particle content: The particle-content switch selects MSSM or NMSSM, with NMSSM requiring the blocks defined for that model.Option 0 is MSSM and option 1 is NMSSM.
- Discrete symmetries: The R-parity switch selects conservation or violation, with RPV requiring the blocks defined for section 4.2.Option 0 reproduces the SLHA1 R-parity-conserving case.
- Discrete symmetries: The CP switch distinguishes CP conservation, the standard CKM phase only, and completely general CP phases.Imaginary parts of relevant parameters can be supplied through IM-prefixed blocks in the general CP-violating case.
- Flavour violation: The flavour-violation switch separately enables quark, lepton, or simultaneous lepton-and-quark flavour violation.Each violating option requires the blocks defined in section 4.1.
4 General MSSM
This section specifies the MSSM field, interaction, flavour, lepton-mixing, and input-parameter conventions used in the general SLHA framework. It defines super-CKM/PMNS bases, diagonalization conventions, and implementation requirements for spectrum data.
- General MSSM: The MSSM field content and superpotential are given in explicit SLHA notation, including Yukawa couplings and soft SUSY-breaking terms.
- Quark sector and super-CKM basis: The super-CKM basis diagonalizes quark Yukawa matrices while allowing flavour mixing through squark mass matrices and their 6×6 unitary diagonalization.
- Quark sector and super-CKM basis: The CKM matrix characterizes tree-level quark flavour mixing, while simultaneous flavour diagonalization of up- and down-type squark masses requires flavour-universal left-handed soft masses.
- Lepton sector and super-PMNS basis: The super-PMNS basis applies analogous rotations to leptons, charged sleptons, and sneutrinos, with charged-lepton Yukawa matrices and sneutrino masses treated in the corresponding bases.
- Explicit proposal for SLHA2: The proposal uses DR-scheme running parameters in the super-CKM/PMNS basis and requires explicit spectrum-calculator input, with standard input scales by default.
4.2 R-Parity Violation
SLHA2 specifies conventions for R-parity-violating MSSM inputs and outputs, including couplings, sneutrino VEVs, basis choices, dependent parameters, and enlarged fermion mixing matrices.
- R-parity-violating interactions: The R-parity-violating superpotential and soft-breaking sector are expressed in terms of baryon- and lepton-number-violating couplings, with proton stability usually requiring one type of violation to vanish.The trilinear soft terms use the couplings directly rather than factoring them out, allowing Tijk or (T′)ijk to remain nonzero when the corresponding λ coupling is zero.
- VEVs and electroweak breaking: Sneutrino VEVs extend the electroweak-breaking conventions, while tan β remains defined as v2/v1 despite alternative possible definitions.The RPV VEVs contribute to the electroweak scale, but the accord retains the SLHA1 tan β convention.
- Basis conventions: SLHA2 uses the super-CKM/PMNS basis for R-parity-violating input and output, with diagonal Yukawa couplings defining the quark basis and diagonal charged-lepton plus loop-induced neutrino masses defining the PMNS basis.Without right-handed neutrinos, neutrino masses arise solely from lepton-number-violating couplings, so the PMNS matrix is an output rather than an independent input.
- Input/output blocks: The RPV data blocks specify couplings, soft terms, and VEV-related quantities in the super-CKM/PMNS basis, with default RPV couplings set to zero.Input couplings are supplied at Minput, while the corresponding output blocks include the scale Q.
- Input/output blocks: Only 3 of the last 4 RPV input blocks are independent because one bilinear parameter or VEV is fixed by minimizing the Higgs-sneutrino potential.Spectrum calculators may accept different combinations of RVKAPPAIN, RVDIN, RVSNVEVIN, and RVM2LH1IN.
- Particle mixing: RPV neutralino mixing becomes a 7 × 7 neutrino/neutralino problem, and charged leptons mix through unitary 5 × 5 charged-fermion matrices.The neutralino basis is expanded to include three neutrinos, while the five charged states are strictly mass ordered.
4.3 CP Violation
For CP-violating MSSM parameters, SLHA2 separates real and imaginary parts into paired blocks and adds a phase-based representation for μ when its magnitude is fixed by electroweak symmetry breaking.
- Parameter conventions: SLHA1 blocks contain the real parts of CP-violating parameters, while imaginary parts use identically formatted blocks prefixed by IM and default to zero.Examples include IMAU, IMAD, IMAE, and IMEXTPAR.
- The μ parameter: If the real part of μ is supplied in EXTPAR 23, its imaginary part is supplied in IMEXTPAR 23 instead.The phase-based MINPAR representation applies when the magnitude of μ is determined by electroweak symmetry breaking.
- The μ parameter: When |μ| is determined by electroweak symmetry breaking, SLHA2 replaces sign(μ) with cos ϕμ in MINPAR 4 and supplies sin ϕμ in IMMINPAR entry 4.This phase representation generalizes the CP-conserving sign convention.
BLOCK MINPAR
The CP-conserving MINPAR convention represents μ through its sign.
- CP-conserving convention: MINPAR 4 uses sign(μ) when CP is conserved.In the CP-conserving limit, cos ϕμ coincides with sign(μ).
BLOCK IMMINPAR
SLHA2 represents the μ phase with sine and cosine inputs and defines CP-mixed neutral Higgs states through a unified mixing matrix that projects out the Goldstone boson.
- Neutral Higgs mixing: When CP symmetry is broken, CP-even and CP-odd Higgs states mix, so the three physical neutral scalars are represented using a 3 × 4 matrix S.The interaction basis contains the real and imaginary neutral Higgs components.
- Mass-state labeling: The Higgs mass eigenstates are numbered by PDG codes 25, 35, and 36 regardless of flavour composition, requiring caution in the CP-conserving limit.The accord does not preserve the conventional CP-odd labeling for code 36.
- Neutral Higgs mixing: Matrix S directly decomposes the three physical mass eigenstates into four interaction eigenstates while explicitly projecting out the Goldstone boson.Its three rows form orthonormal vectors.
- Convention translation: Unlike conventions that first rotate by β or also rotate CP-even states by α, SLHA2 permits straightforward translation between the matrix conventions using the relevant angles.A simple β rotation relates one alternative convention, while α is additionally needed for the FeynHiggs-style decomposition.
BLOCK ALPHA
For CP violation, SLHA2 retains real parts in the existing SLHA1 blocks and supplies imaginary parts in corresponding IM-prefixed blocks. Neutralino and chargino masses are taken real, removing the need for the CP-conserving negative-mass convention.
- CP-conserving parameters use α, while CP-violating cases use αtree together with the matrix S in CVHMIX and IMCVHMIX.
- In CP violation, neutralino and chargino masses are real because preserving strictly real mixing matrices is no longer required.This removes the original motivation for allowing apparent negative mass eigenvalues.
5 The Next-to-Minimal Supersymmetric SM
The NMSSM extension defines a model with the MSSM field content plus one gauge-singlet chiral superfield, while retaining an SLHA1-like CP-, R-parity-, and flavour-conserving scope. It specifies input, output, and mixing-matrix conventions that extend SLHA1 to the singlet sector.
- 5 The Next-to-Minimal Supersymmetric SM: The NMSSM is defined by adding exactly one gauge-singlet chiral superfield to the MSSM field content.The acronym refers to field content, not to whether particular couplings are present.
- 5 The Next-to-Minimal Supersymmetric SM: The CP-conserving NMSSM superpotential contains the MSSM superpotential, singlet-Higgs coupling λ, singlet cubic coupling κ, and additional singlet terms.A singlet vacuum expectation value contributes λ⟨S⟩ to the effective µ term.
- 5 The Next-to-Minimal Supersymmetric SM: At tree level, 15 Higgs-sector parameters are relevant in addition to mZ, but three minimisation conditions leave 12 independent parameters.The accord permits either a general 12-parameter input or a reduced six-parameter specification for minimal models.
- 5 The Next-to-Minimal Supersymmetric SM: NMSSM-specific parameters are entered through EXTPAR and represented in running output by NMSSMRUN at a common input scale.The listed entries include λ, κ, Aλ, Aκ, λ⟨S⟩, ξF, ξS, and µ′, with corresponding singlet soft parameters also defined.
- 5 The Next-to-Minimal Supersymmetric SM: The NMSSM scalar mixing conventions recover the MSSM angle α in the relevant 2 × 2 submatrix.The approximate relations are S11 ∼ −sin α, S21 ∼ cos α, S12 ∼ cos α, and S22 ∼ sin α.
6 Conclusion and Outlook
SLHA2 was developed with fewer existing implementations and less comprehensive testing than SLHA1, though concrete tests with several nearly finished codes were possible. The authors preserve backward compatibility where feasible and expect the resulting conventions to be practically useful.
- SLHA1 benefited from many existing codes, strong implementation motivation, and testing across diverse situations during its development.
- SLHA2 lacked comprehensive simultaneous testing because few programs used NMSSM, CP-violating, R-parity-violating, or non-trivial flavour-violating scenarios.Several nearly finished codes nevertheless enabled concrete tests during the writeup.
- The authors adhered to backward compatibility wherever feasible.
- The authors expect the agreed conventions to provide a practical solution useful for future SUSY particle phenomenology.
A PDG Codes and Extensions
SLHA2 reuses PDG codes while changing labels when CP, R-parity, or flavour symmetries are broken. Tables 2–6 organise the resulting codes and labels across major particle classes, with an optional sneutrino scalar/pseudoscalar separation.
- A PDG Codes and Extensions: When conserved quantum numbers are broken, states with identical conserved quantum numbers receive common labels and existing PDG codes are reused in increasing mass order.
- A PDG Codes and Extensions: The PDG codes remain unchanged while their labels depend on the considered scenario.The conventions are detailed separately for flavour violation, R-parity violation, CP violation, and the NMSSM.
- A PDG Codes and Extensions: Table 2 lists particle codes and corresponding labels for squarks using current PDG nomenclature.
- A PDG Codes and Extensions: Tables 3–5 cover charged colour-singlet fermions, neutral colour-singlet fermions, and charged colour-singlet scalars, respectively.
- A PDG Codes and Extensions: Table 6 covers neutral colour-singlet scalars and marks the optional separation of sneutrinos into scalar and pseudoscalar components.