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HiggsBounds: Confronting Arbitrary Higgs Sectors with Exclusion Bounds from LEP and the Tevatron

Philip Bechtle, Oliver Brein, Sven Heinemeyer, Georg Weiglein, Karina E. Williams

arXiv:0811.4169v4hep-phhep-ex

TL;DR

HiggsBounds addresses the problem of testing arbitrary Higgs sectors against topology-specific LEP and Tevatron exclusions. It selects the most sensitive channel using expected limits, then tests the model against the observed 95% C.L. bound. The paper presents implementations and examples spanning the Standard Model, a fourth-generation model, and the MSSM.

  • Problem

    Models with arbitrary Higgs sectors cannot generally be tested using exclusion limits derived for a specific model because their signal topologies contribute differently.

  • Method

    HiggsBounds uses model predictions and experimental observed and expected limits on topological cross sections to select one highest-sensitivity channel and test exclusion.

  • Results

    The program provides examples for the Standard Model, a fourth-generation model, and the MSSM with and without CP violation.

  • Takeaways & Limitations

    HiggsBounds enables wide classes of Higgs-sector models to be checked against implemented LEP and Tevatron search results.

  • Takeaways & Limitations

    The implementation is limited to narrow-width exclusion limits and is not intended for models with drastically different signal backgrounds or strongly altered kinematic distributions.

Abstract

from arXiv · show

HiggsBounds is a computer code that tests theoretical predictions of models with arbitrary Higgs sectors against the exclusion bounds obtained from the Higgs searches at LEP and the Tevatron. The included experimental information comprises exclusion bounds at 95% C.L. on topological cross sections. In order to determine which search topology has the highest exclusion power, the program also includes, for each topology, information from the experiments on the expected exclusion bound, which would have been observed in case of a pure background distribution. Using the predictions of the desired model provided by the user as input, HiggsBounds determines the most sensitive channel and tests whether the considered parameter point is excluded at the 95% C.L. HiggsBounds is available as a Fortran 77 and Fortran 90 code. The code can be invoked as a command line version, a subroutine version and an online version. Examples of exclusion bounds obtained with HiggsBounds are discussed for the Standard Model, for a model with a fourth generation of quarks and leptons and for the Minimal Supersymmetric Standard Model with and without CP-violation. The experimental information on the exclusion bounds currently implemented in HiggsBounds will be updated as new results from the Higgs searches become available.

PROGRAM SUMMARY

HiggsBounds is provided as a Fortran-based program with documented compiler requirements.

  • HiggsBounds can be built with compatible Fortran 77 or Fortran 90 compilers.It was tested with Portland Group and GNU Fortran compilers on x86 Linux.

1 Introduction

The paper motivates HiggsBounds as a way to confront diverse Higgs sectors with LEP and Tevatron search constraints. It accepts model predictions, identifies the most sensitive search analysis, and tests exclusion at 95% C.L.

  • Electroweak symmetry breaking requires underlying dynamics that remains unknown, motivating searches for one or more Higgs bosons.
  • Higgs sectors differ substantially across the Standard Model, MSSM, and other beyond-Standard-Model theories.The MSSM contains three neutral and two charged Higgs bosons.
  • LEP and the Tevatron converted the non-observation of Higgs signals into cross-section limits for individual signal topologies.
  • Generic models cannot generally be tested with limits derived for a specific model because their signal topologies contribute in different proportions.
  • HiggsBounds selects the analysis with the highest expected exclusion power, then compares the model prediction with the observed limit in that single channel.This restriction preserves the intended 95% C.L. statistical interpretation.
  • The code accepts Higgs-sector predictions and is available in Fortran 77, Fortran 90, command-line, subroutine, and online forms.

2.1 General approach

HiggsBounds computes model predictions for Higgs signal topologies, selects the topology with the greatest expected sensitivity, and tests that channel against the observed 95% C.L. limit.

  • The cross-section limits assume that new physics does not substantially alter background signatures or signal kinematic distributions.Strongly different distributions require a dedicated experimental analysis, so the returned exclusion may be only an estimate.
  • The implementation is restricted to narrow-width exclusion limits, which can produce tighter bounds than treatments including finite widths.Users should be cautious for parameter regions with very large Higgs widths.
  • Users provide Higgs masses, widths, branching ratios, and normalized production cross sections for the neutral Higgs bosons.
  • The program derives model quantities for each signal topology and reads observed and expected exclusion limits from implemented LEP and Tevatron data tables.Expected limits correspond to background-like observations and are interpolated between mass points.
  • HiggsBounds chooses the topology with the largest ratio of model prediction to expected limit, identifying the highest-sensitivity channel.
  • A parameter point is excluded when its prediction exceeds the observed limit in the selected channel.Testing every available channel would generally invalidate the intended 95% C.L. interpretation.

2.2 LEP limits

HiggsBounds implements LEP limits on Higgs topologies using model masses, branching ratios, effective couplings, and normalized cross sections. Its LEP coverage is broad but excludes several decay and topology classes, and applicability depends on reference-process kinematics.

  • The LEP implementation uses Higgsstrahlung and double-Higgs production processes, treated as s-channel Z-boson exchange at leading order.
  • LEP limits cover b¯b and τ+τ− final states, Standard Model topologies, and many cascades involving an on-shell Higgs decaying into two lighter Higgs bosons.
  • Table 1 records the implemented LEP search topologies and uses finer-grained observed and expected results than the published tables and graphs.
  • LEP constraints are weak for Higgs bosons that decay predominantly invisibly because the implemented analysis is limited mainly to b¯b and τ+τ− final states.
  • For each topology, limits are expressed through S95(X), relating the largest 95% C.L.-compatible cross section to a reference cross section.
  • Users provide Higgs masses, relevant branching ratios, and production-cross-section ratios so HiggsBounds can calculate Qmodel(X) for the implemented topologies.
  • If model kinematic distributions differ significantly from the reference processes, the HiggsBounds exclusion result is only an estimate.
  • Effective couplings can supply the LEP production and decay information needed for the Input Option part.Within the effective-coupling class, reference-process kinematic distributions are preserved and topological limits can be applied exactly.

2.3 Tevatron limits

HiggsBounds implements Tevatron limits on individual and combined Higgs search topologies, comparing model predictions with experimental 95% C.L. bounds. It supports several input strategies for production and decay predictions, with approximations and validity conditions documented for partonic and effective-coupling inputs.

  • Tevatron analyses: The Tevatron analyses implemented in HiggsBounds provide separate limits for individual search topologies and combinations weighted according to Standard Model proportions.The included analyses use Tevatron Run II data from CDF and DØ.
  • Exclusion test: A model point is excluded when its predicted topology cross section exceeds the experimental 95% C.L. upper limit.For normalized limits, the prediction is compared with the corresponding Standard Model-normalized bound.
  • Model inputs: HiggsBounds requires model predictions for Higgs masses, branching ratios, and either absolute or normalized production cross sections, depending on the input option.The program combines these inputs with internally available Standard Model predictions to calculate the quantities compared with experimental limits.
  • Input options: The hadronic input is broadly applicable but requires cross sections convoluted with parton distribution functions, whereas the partonic input uses only partonic cross-section ratios and applies to fewer models.The partonic option is generally more convenient for users because the program supplies the relevant Standard Model cross-section ratios.
  • Validity conditions: The partonic approximation should be checked for the model under study because steeply falling parton luminosities favor threshold regions; users can instead use hadronic inputs when necessary.Branching ratios for decays hk → hihi were not used in Tevatron comparisons because no relevant Tevatron analyses existed at the time.
  • Validity conditions: The effective-coupling treatment estimates VBF production using a mean relation whose mass dependence changes the resulting proportions by less than 1%.The mean relation varies by ±3.6% in the relevant mass range, while interference effects affect the result below 1%.
  • Validity conditions: Effective-coupling parametrizations are expected to reproduce the implemented limits accurately when model kinematics remain sufficiently close to the Standard Model reference processes.For models with significantly different kinematical distributions, the returned exclusion is only an estimate.

3 HiggsBounds Operating Instructions

HiggsBounds can be used through an online interface, command-line program, or subroutine library, with common inputs and outputs across formats. Users provide model predictions and receive exclusion status, the most sensitive process, contributing Higgs-boson count, and the observed-limit ratio.

  • 3 HiggsBounds Operating Instructions: HiggsBounds is available as a library of subroutines, a command-line version, and an online version.The command-line version reads model data from text files, the library can be embedded in other programs, and the online version supports quick checks without installation.
  • 3 HiggsBounds Operating Instructions: The Fortran 77 and Fortran 90 versions provide identical functionality and operating instructions and can interoperate across these Fortran versions.Both versions were tested with multiple compilers, including GNU compilers accompanying many Linux distributions.
  • 3.1 Common features: Input: The input includes the number of neutral Higgs bosons and theoretical predictions supplied in effective-coupling, branching-ratio, or cross-section-ratio formats.Tables 4, 6, 7, and 8 describe the neutral-Higgs count, prediction format, effective normalized squared couplings, branching ratios, and recognized cross-section ratios.
  • 3.1 Common features: Input: The whichexpt setting selects the subset of experimental analyses considered by HiggsBounds.The command-line version likewise expects a subset of input arrays determined by whichinput.
  • 3.2 Common features: Output: HiggsBounds reports exclusion at 95% C.L., the most statistically sensitive process, the number of contributing Higgs bosons, and the theoretical-to-observed-limit ratio.The process-number key is written to Key.dat for library and command-line use and displayed online.
  • 3.3 Library of subroutines: The library provides separate routines for effective-coupling, partonic-ratio, and hadronic-ratio inputs, each returning the principal HiggsBounds output variables.The routines require their corresponding model-prediction arguments, including masses, cross-section information, branching ratios, HBresult, chan, obsratio, and ncombined.
  • 3.3 Library of subroutines: The initialize_HiggsBounds subroutine must be called once before other HiggsBounds routines, while the final HiggsBounds call occurs after the other HiggsBounds subroutines.The library can be linked with -L<HBpath> -lHB, and example programs demonstrate subroutine use.
  • 3.3 Library of subroutines: Users may set irrelevant branching-ratio, effective-coupling, or cross-section arrays to zero without affecting processes that do not use them.Some arrays can also be ignored depending on whichexpt; for example, cascade-decay branching ratios are irrelevant when whichexpt='onlyT'.

4 Examples of use

The examples show how HiggsBounds identifies the most sensitive search topology and applies LEP and Tevatron limits across the SM, fourth-generation, real-MSSM, and CPX scenarios. The results also expose regions where theoretical predictions, experimental sensitivity, or the single-channel procedure affect exclusions.

  • Standard Model: PDF-dependent SM cross-section predictions change the Tevatron exclusion substantially, and with MSTW 2008 PDFs no SM Higgs mass is excluded at 95% C.L.Using MRST 2006 PDFs instead produces an excluded interval of about 5 GeV.
  • Fourth Generation Model: LEP is most sensitive below about 115 GeV, while Tevatron searches become more sensitive at higher Higgs masses.The transition follows LEP’s kinematic limit and the relative sensitivity of the implemented topological bounds.
  • Fourth Generation Model: In the fourth-generation model, LEP exclusion is weaker than in the SM at low Higgs mass because the altered gluonic decay width changes the relevant branching ratio.The fourth-generation scenario enhances the effective Higgs–gluon coupling while leaving other LEP- and Tevatron-relevant couplings largely unchanged.
  • Limits for the real MSSM: Real-MSSM Tevatron searches exclude regions extending from MA = 110–170 GeV and tan β = 39–60, with the dominant channel varying by scenario and parameter region.The relevant signals involve neutral Higgs bosons decaying to tau pairs, while hW and WW channels dominate in additional regions.
  • LEP limits for the complex MSSM in the CPX scenario: In the CPX scenario, different Higgs couplings select different LEP channels, while h2 → h1h1 dominance creates challenging multi-jet final states and suppresses h2 → b¯b sensitivity.The affected region is approximately Mh1 <∼45 GeV and tan β >∼4.
  • LEP limits for the complex MSSM in the CPX scenario: CPX contains sizable unexcluded regions, including a hole near Mh1 ≈45 GeV and tan β ≈8, and additional unexcluded points arise where the single most-sensitive channel changes.The single-channel procedure can lose statistical information near boundaries; dedicated combinations using multiple cross-section limits may exclude more of these regions.

5 Summary

HiggsBounds tests arbitrary Higgs-sector predictions against LEP and Tevatron exclusion limits by selecting the statistically most sensitive channel. The paper documents its experimental inputs, model interfaces, examples, and software versions.

  • Analysis procedure: The program compares model predictions with expected limits to select the single channel with the highest statistical sensitivity before applying the observed exclusion bound.Restricting the interpretation to this channel preserves the intended 95% C.L. statistical meaning.
  • Experimental inputs: HiggsBounds incorporates experimental limits on individual topological cross sections and selected model-specific combinations from LEP and the Tevatron.Some combinations have enhanced statistical power but apply only to special cases such as an SM-type Higgs boson.
  • Scope and outlook: The current implementation uses the narrow-width approximation, while treatment of non-negligible Higgs widths is planned for a future version.The experimental exclusion information is also intended to be updated as new Higgs-search results become available.
  • Model inputs: User-supplied predictions can range from effective couplings to complete production cross sections and branching ratios.Default links to FeynHiggs and CPsuperH support MSSM Higgs-sector predictions.
  • Examples: Examples cover the Standard Model, a fourth-generation model, and the MSSM both with and without CP violation.
  • Availability: HiggsBounds is available in Fortran 77 and Fortran 90, with command-line, subroutine, and online interfaces.

A.1 The CLs method

The CLs method compares background-only and signal-plus-background hypotheses through confidence levels derived from an ordered test statistic. HiggsBounds uses the resulting conservative ratio to define 95% exclusion.

  • Test statistic: The test statistic orders hypothetical experimental outcomes according to their signal-likeness using observed data, expected signal, and background events.
  • Confidence levels: CLb is the probability of obtaining a test-statistic value no larger than observed under the background-only hypothesis.
  • Confidence levels: CLs+b is the corresponding probability under the signal-plus-background hypothesis.
  • Motivation: The CLs ratio avoids excluding hypotheses solely because a downward background fluctuation creates apparent sensitivity where the expected signal is small.
  • Exclusion criterion: A hypothesis is excluded at 95% confidence when CLs is below 0.05, and the resulting limit is conservative because CLs exceeds CLs+b.

A.2 Expected and observed confidence levels

Expected confidence levels estimate search sensitivity using simulated background-only and signal-plus-background outcomes. Expected and observed S95 values are then obtained by varying the channel production rate until the corresponding CLs threshold is reached.

  • Expected confidence levels: Expected confidence levels replace the observed data configuration with many simulated event configurations under background-only or signal-plus-background hypotheses.
  • Expected confidence levels: The expected CLs is the median outcome across simulated experiments with background-only event configurations.
  • S95 construction: Observed and expected S95 values are calculated after deriving the corresponding CLs values for a Higgs signal with SM-strength branching-ratio and cross-section factors.
  • S95 construction: The production-rate scaling factor s is interpreted as observed or expected S95 according to whether observed or expected CLs is used.
  • Experimental implementation: LEP S95 calculations use tools described in references [71] and [72], whereas Tevatron results use methods specified in their individual references.
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