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2HDMC - Two-Higgs-Doublet Model Calculator

David Eriksson, Johan Rathsman, Oscar Stål

arXiv:0902.0851v2hep-ph

TL;DR

The general 2HDM contains diverse possible Higgs-sector phenomena, creating a need for tools to study viable models. This paper presents 2HDMC, a modular C++ calculator for the CP-conserving 2HDM with flexible model specification, theoretical and phenomenological constraints, and Higgs-decay calculations. Its documented scope includes general model studies while retaining limitations such as the inability of its MadGraph/MadEvent model to handle flavour-changing neutral currents.

  • Problem

    Theoretical interest in the general 2HDM's possible new phenomena motivates phenomenological tools for studying viable models.

  • Method

    2HDMC provides a modular C++ framework supporting multiple potential parametrizations, flexible Yukawa sectors, theoretical checks, observables, collider constraints, and Higgs decay calculations.

  • Results

    2HDMC enables phenomenological studies of a general CP-conserving 2HDM through model specification, parameter-space constraints, observables, and Higgs decay-width calculations.

  • Takeaways & Limitations

    The code can be used as a library, in stand-alone applications, or for exchanging data with other codes through a LesHouches-inspired format.

  • Takeaways & Limitations

    The MadGraph/MadEvent model cannot handle flavour-changing neutral currents.

Abstract

from arXiv · show

This manual describes the public code 2HDMC which can be used to perform calculations in a general, CP-conserving, two-Higgs-doublet model (2HDM). The program features simple conversion between different parametrizations of the 2HDM potential, a flexible Yukawa sector specification with choices of different Z_2-symmetries or more general couplings, a tree-level decay library including all two-body - and some three-body - decay modes for the Higgs bosons, and the possibility to calculate observables of interest for constraining the 2HDM parameter space, as well as theoretical constraints from positivity and unitarity. The latest version of the 2HDMC code and full documentation is available from: http://www.isv.uu.se/thep/MC/2HDMC

1 Introduction

The general 2HDM offers a theoretically rich extension of the SM Higgs sector, motivating phenomenological tools that help assess viable models. 2HDMC is introduced as such a tool, with the paper covering its physics, constraints, code structure, and compilation.

  • The general 2HDM extends the SM Higgs sector and permits phenomena including CP violation, lepton number violation, charged Higgs bosons, dark matter, and heavy neutral Higgs bosons.
  • 2HDMC is presented as a phenomenological tool for helping theorists provide experimentalists with viable 2HDM models.
  • The code supports different potential parametrizations, flexible Yukawa couplings, theoretical checks, electroweak observables, collider constraints, and Higgs decay-width calculations.
  • The paper covers the 2HDM physics, parameter-space constraints, 2HDMC structure and usage, and obtaining and compiling the code.

2 Physics of the 2HDM

The 2HDM extends the Higgs sector with five physical Higgs states and flexible potential and Yukawa-sector parametrizations. 2HDMC focuses on the CP-conserving model, supporting basis choices, theoretical checks, Yukawa structures, decay calculations, and phenomenological examples.

  • The Higgs potential: The scalar potential is basis-dependent in its parameters, while the Higgs basis is a special CP-conserving basis with only one doublet acquiring a non-zero vev.The convention takes all potential parameters real and ξ = 0 to exclude CP-violating effects.
  • 2HDM spectrum: The general 2HDM contains five physical Higgs bosons: two CP-even neutral states h and H, one CP-odd neutral state A, and charged H± bosons.Three Goldstone modes are absorbed by W± and Z after symmetry breaking.
  • Higgs masses and couplings: The CP-even Higgs states mix through a mass matrix that is diagonalized by a rotation angle α, yielding their mass eigenvalues.Gauge-boson couplings are determined by the basis-invariant quantities sβ−α and cβ−α.
  • The Yukawa sector: The Yukawa sector permits arbitrary symmetric ρF matrices or standard Z2-symmetric choices, but non-diagonal ρF elements generate tree-level flavour-changing neutral currents.The Glashow–Weinberg theorem motivates assigning Z2 quantum numbers so each fermion type couples to no more than one Higgs doublet.
  • Decay widths: 2HDMC calculates Higgs decay widths into fermion, gauge-boson, mixed Higgs, and lighter-Higgs pairs, with γγ and gg decays induced at one loop.The code also includes QCD corrections and running-mass improvements for relevant decays.
  • Examples: The tree-level MSSM example has mh ≤ mZ, while the dark scalar doublet example yields pair production of H-odd particles and a stable lightest H-odd dark-matter candidate.The dark scalar doublet can also accommodate a heavier SM-like Higgs compatible with electroweak precision data.

3 Constraints

2HDMC constrains the CP-conserving 2HDM through theoretical consistency requirements, precision electroweak observables, muon anomalous-moment contributions, and collider limits. The implementation includes positivity and unitarity tests, oblique-parameter calculations, dominant two-loop muon contributions, and interfaces to external search codes.

  • 3.1 Positivity of the potential: Positivity requires the Higgs potential’s quartic part to remain positive in every field-space direction at asymptotically large field values.The quartic terms dominate the potential in this limit and are parametrized using angular variables before minimization.
  • 3.1 Positivity of the potential: When λ6 = λ7 = 0, the derived conditions together with eq. (34) provide necessary and sufficient positivity criteria; nonzero λ6 or λ7 requires modified conditions.For nonzero λ6 or λ7, additional expressions from the boundaries cos θ = ±1 and ρ = 1 are needed and are included in the program.
  • 3.2 Tree-level unitarity: Tree-level unitarity constrains scattering eigenvalues through |Li| ≤ 16π, while the partial-wave requirement |Re(a0)| < 1/2 corresponds to |Li| ≤ 8π.These bounds apply to Higgs-boson and longitudinal electroweak-gauge-boson scattering.
  • 3.3 Oblique parameters: The oblique parameters S, T, and U probe electroweak effects from the extra Higgs doublet, with large Higgs-mass splittings potentially generating sizeable loop contributions.2HDMC also provides the full set of six oblique parameters, including V, W, and X; comparisons require a consistent reference Higgs mass mh,ref.
  • 3.4–3.5 Additional observables and collider constraints: 2HDMC includes dominant positive two-loop Barr–Zee contributions to aµ for all fermions, subdominant one-loop corrections, and interfaces for collider and flavour constraints.Collider consistency can be checked through HiggsBounds or NMSSMTools, while flavour observables require an interface to SuperIso; charged-Higgs limits include τν and cs decay channels.

4 2HDMC code structure

2HDMC organizes general 2HDM calculations around modular THDM, SM, DecayTable, and Constraints classes. It accepts multiple potential and Yukawa parametrizations and returns model properties, decays, couplings, and constraint observables.

  • 4.1 General description: The modular C++ design centers each studied model on a THDM object containing its own SM-parameter instance.This supports flexible specification of the underlying Standard Model parameters.
  • 4.2 Physics input: THDM functions change the basis or potential parametrization, specify Yukawa couplings, return Higgs couplings, and handle file input/output.Yukawa matrices may be non-diagonal, but the program does not check flavour-changing neutral-current limits.
  • 4.2 Physics input: Users can enter Higgs-potential parameters in multiple bases and parametrizations, with corresponding functions for retrieving each representation.Some parametrizations impose assumptions such as tan β ≡ 0 in the Higgs basis or λ6 = λ7 = 0 for soft Z2 breaking.
  • 4.2 Physics input: The code offers standard and special Yukawa-sector choices, including type I, type II, MSSM, and inert-model input functions.Yukawa matrices related to quark masses should be specified using pole masses; using MS masses can produce unwanted consequences such as a broken Z2 symmetry.

5 Downloading and compiling the package

2HDMC is distributed with documentation and requires standard C++ build tools plus the GNU Scientific Library. Compilation includes library and example programs, with optional interfaces for collider-constraint codes.

  • 5 Downloading and compiling the package: The package includes the manual and complete class documentation, including required function inputs and outputs.Both can be downloaded from the same URL as the code.
  • 5 Downloading and compiling the package: Compilation requires a C++ compiler, common build utilities such as make, and the GNU Scientific Library.GCC is given as an example compiler.
  • 5 Downloading and compiling the package: The library has been compiled successfully with GCC 4 under Linux, with no expected difficulty using GCC 3 or another compiler or architecture.Users are encouraged to report compilation and runtime experience on other platforms.
  • 5 Downloading and compiling the package: Running the primary compilation command builds the library and example programs whose filenames begin with Calc.The Demo program can verify the installation by comparison with appendix A.
  • 5 Downloading and compiling the package: Collider constraints can be accessed through HiggsBounds or NMSSMTools independently or together, but neither is required to run 2HDMC.HiggsBounds provides LEP and Tevatron limits, while NMSSMTools includes LEP limits only.

A Sample output

The Demo program prints a representative 2HDM parameter point in several bases, checks theoretical and mass constraints, reports electroweak observables, and gives Higgs total widths.

  • A Sample output: The Demo program reports a physical-basis parameter point with m_h = 80.00000, m_H = 200.00000, m_A = 140.00000, and m_H+ = 160.00000.It also reports sin(beta-alpha) = 0.20000, lambda_6 = lambda_7 = 0, m12^2 = 800.00000, and tan(beta) = 10.00000.
  • A Sample output: The same point is converted into generic-basis and Higgs-basis parameters.The generic basis lists lambda_1 through lambda_7 and m12^2, while the Higgs basis lists Lambda_1 through Lambda_7 and m_Hp.
  • A Sample output: Potential stability, tree-level unitarity, perturbativity, and mass constraints are all reported as OK.These checks demonstrate the status of the sample point under the displayed criteria.
  • A Sample output: The sample point has oblique S = 6.77200e-02, T = -1.62816e-02, and U = 2.95734e-04.The output also reports V, W, X, and Delta_rho.
  • A Sample output: The total widths are 1.707e-01 GeV for h, 5.212e+00 GeV for H, 2.979e-01 GeV for A, and 4.083e-02 GeV for H+.These are the Demo program's displayed widths for the four Higgs states.

B LesHouches output

The Demo program also produces a LesHouches file containing a model-selection block, Standard Model inputs, and general-potential parameters in the generic basis.

  • B LesHouches output: The Demo program writes a LesHouches file named Demo out.lha.The file contains the displayed LesHouches-card output produced by 2HDMC.
  • B LesHouches output: The file begins with a Two-Higgs Doublet Model LesHouches-card header and a MODSEL block selecting the THDM.The model-selection entry identifies THDM with the value 10.
  • B LesHouches output: The SMINPUTS block records Standard Model inputs including alpha_em, the Fermi constant, alpha_s, MZ, bottom and top masses, and the tau mass.The displayed card labels the mass schemes and whether masses are pole values.
  • B LesHouches output: The MINPAR block stores generic-basis potential parameters, tan(beta), sin(beta-alpha), cos(beta-alpha), and the Yukawa type.The shown entries include tan(beta) = 10, lambda_1 = 2.25553058, lambda_2 = 0.615852536, m12^2 = 800, and Yukawa Type = 2.
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