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$\texttt{HEPfit}$: a Code for the Combination of Indirect and Direct Constraints on High Energy Physics Models

Jorge de Blas, Debtosh Chowdhury, Marco Ciuchini, Antonio M. Coutinho, Otto Eberhardt, Marco Fedele, Enrico Franco, Giovanni Grilli di Cortona, Victor Miralles, Satoshi Mishima, Ayan Paul, Ana Penuelas, Maurizio Pierini, Laura Reina, Luca Silvestrini, Mauro Valli, Ryoutaro Watanabe, Norimi Yokozaki

arXiv:1910.14012v2hep-phhep-ex

TL;DR

HEPfit addresses the need to combine experimental and theoretical constraints across Standard Model extensions. It provides an extensible framework for observable calculations, Bayesian MCMC fits, and library-based predictions, with a release covering multiple models and observable classes. Its main scope boundary is that MCMC convergence slows as parameter dimensionality and correlations increase.

  • Problem

    Combining direct and indirect information is needed to constrain viable New Physics parameter regions, while direct searches can be computationally demanding and model-limited.

  • Method

    HEPfit uses extensible model and observable definitions, Bayesian MCMC sampling through BAT, and a library interface usable within any statistical framework.

  • Results

    The release implements EWPO, Higgs signal strengths, flavour, and LFV observables across the SM, THDM, several NP parameterizations, and MSSM.

  • Takeaways & Limitations

    HEPfit provides a multipurpose framework for fitting models to experimental and theoretical constraints and obtaining predictions for implemented models.

  • Takeaways & Limitations

    MCMC convergence is slower with more parameters and stronger parameter correlations, so fits benefit from minimizing the number of parameters.

Abstract

from arXiv · show

$\texttt{HEPfit}$ is a flexible open-source tool which, given the Standard Model or any of its extensions, allows to $\textit{i)}$ fit the model parameters to a given set of experimental observables; $\textit{ii)}$ obtain predictions for observables. $\texttt{HEPfit}$ can be used either in Monte Carlo mode, to perform a Bayesian Markov Chain Monte Carlo analysis of a given model, or as a library, to obtain predictions of observables for a given point in the parameter space of the model, allowing $\texttt{HEPfit}$ to be used in any statistical framework. In the present version, around a thousand observables have been implemented in the Standard Model and in several new physics scenarios. In this paper, we describe the general structure of the code as well as models and observables implemented in the current release.

1 Introduction

HEPfit is an open-source framework designed to combine experimental and theoretical information when constraining New Physics models. It supports model fitting, observable predictions, and extensibility across multiple models and observables.

  • HEPfit combines available information to select allowed regions in the parameter space of New Physics models.This addresses the need to integrate direct and indirect constraints when direct searches are computationally demanding or limited to simplified models.
  • The framework computes observables using state-of-the-art theoretical expressions in extensible sets of models.
  • HEPfit supports Bayesian Markov Chain Monte Carlo sampling through the BAT library and can also provide predictions as a library for any statistical framework.
  • The first public release includes EWPO, Higgs signal strengths, flavour observables, and LFV observables across the SM, THDM, several NP parameterizations, and MSSM.
  • The paper describes HEPfit’s statistical framework, MPI parallelization, implemented models and observables, and validation through previous physics analyses.

2 The HEPfit code

HEPfit is a modular framework for combining constraints on high-energy-physics models through Bayesian MCMC or library-based analyses. It supports custom models and observables, correlated likelihood inputs, MPI parallelization, and scalable fits.

  • Framework and extensibility: HEPfit combines selectable observables and models, while allowing users to define customized models and observables for phenomenological analyses.Its modular structure lets users choose the model and observables to analyze.
  • Statistical framework: HEPfit incorporates parametric and experimental correlations and can read likelihood distributions directly from ROOT histograms.This avoids approximating experimental constraints with parameterized distributions when histogram likelihoods are available.
  • Statistical framework: The tool supports Bayesian MCMC analyses through BAT or library use with any statistical framework.The library can compute observable predictions independently of the built-in statistical framework.
  • Statistical framework: MCMC sampling addresses the inefficiency of naive Monte Carlo methods for posterior distributions in high-dimensional parameter spaces.The implementation uses Metropolis-Hastings sampling of the unnormalized posterior, with burn-in and convergence monitoring.
  • Practical considerations: Fits can include more than 90 parameters and more than 200 observables, although convergence slows with correlated or numerous parameters.For more than 30 parameters, the paper advises comparing factorized and non-factorized priors; computationally expensive observables also increase fit time.
  • Parallelization: HEPfit is parallelized with OpenMPI, enabling chains to run across multiple cores or cluster nodes and scaling to hundreds of processing units.The code is designed to reduce MCMC runtime through parallel chain execution.

3 Models defined in HEPfit

HEPfit organizes models and observables through extensible C++ classes, supporting Standard Model calculations and successive new-physics extensions. The current model set includes THDM variants, custodial Georgi-Machacek, electroweak-precision parameterizations, and SMEFT descriptions.

  • Model architecture: HEPfit builds models by extending Model sequentially, allowing derived classes to reuse or redefine parent methods for additional contributions.The class hierarchy includes QCD, StandardModel, and further extensions such as THDM.
  • Standard Model: The StandardModel class adds electroweak, Higgs, CKM, and lepton parameters to QCD and supplies weak effective-Hamiltonian matching.It is the base class for subsequent new-physics models.
  • Two-Higgs-Doublet models: The THDM implementation assumes softly broken Z2 symmetry, excludes tree-level flavour-changing neutral currents and Higgs-sector CP violation, and provides four Yukawa variants.Types I, II, X, and Y differ in their Higgs-field Yukawa couplings; the model contains five physical Higgs bosons.
  • Additional scalar models: HEPfit also implements the custodial Georgi-Machacek model, with additional scalars organized into custodial-SU(2) quintet, triplet, and singlet representations.Their masses are denoted m5, m3, and m1, respectively.
  • Effective descriptions: Electroweak new physics is represented through epsilon, STU, and effective-field-theory parameterizations based on gauge-boson self-energies or higher-dimensional operators.The SMEFT uses Lorentz- and gauge-invariant local operators built from Standard Model fields and symmetries.

4 Some important observables implemented in HEPfit

HEPfit implements a broad, extensible set of electroweak, Higgs, flavour, collider, and model-specific observables for constraining Standard Model extensions. These include both experimental predictions and theoretical requirements such as unitarity and vacuum-stability conditions.

  • Overview: HEPfit classifies its observables into electroweak, Higgs, and flavour physics, while also supporting theoretical constraints on model parameter spaces.Such constraints include unitarity bounds and other requirements beyond experimentally accessible quantities.
  • Electroweak physics: Its electroweak implementation covers Z-pole and W-boson observables with state-of-the-art Standard Model radiative corrections and several new-physics parameterizations.Implemented scenarios include oblique parameters, modified Z couplings, and SMEFT.
  • Higgs physics: Higgs observables include production cross sections, branching ratios, and normalized signal strengths for testing new-physics hypotheses at current and future colliders.The implementation covers LHC studies and selected lepton-, electron-proton, and 100 TeV proton-proton collider scenarios.
  • Flavour physics: Flavour observables span leptonic and semileptonic weak decays, meson oscillations, and lepton-flavour or universality violations in the Standard Model and beyond.The dedicated flavour program reports several ΔF = 2 and ΔF = 1 observables implemented to state-of-the-art precision, alongside processes under development.
  • Model-specific observables: Model-specific implementations include particle-property observables and theoretical checks such as boundedness of the Higgs potential, perturbative scalar-scattering unitarity, renormalization-group running, and vacuum-minimum structure.These conditions are illustrated for Two-Higgs-Doublet Models with a softly broken Z2 symmetry.
  • Illustrative results: Selected HEPfit results combine constraints through probability distributions and contours for new-physics and Higgs-sector parameters.Examples include ε1–ε3 distributions with ε2 fixed to its Standard Model value and κV–κf contours from Higgs signal strengths and electroweak precision observables.

5 Selected results using HEPfit

HEPfit has supported electroweak, Higgs, flavour, charm-decay, and scalar-sector analyses. These applications illustrate how combined theoretical and experimental constraints restrict possible new-physics explanations.

  • Electroweak and Higgs physics: HEPfit analyses of electroweak precision observables and Higgs data examined modified couplings and effective couplings, including correlations and future-collider projections.The analyses also contributed to a future-collider comparison study summarized in the Physics Briefing Book.
  • Flavour physics: The angular anomalies in B →K∗ℓ+ℓ− observables P′ could be explained by adopting a more conservative estimate of theoretical uncertainties.The result is illustrated in Figure 2.
  • Flavour physics: Flavour-universal deviations in RK(∗) could be explained by enlarged hadronic effects, whereas flavour-non-universal effects required NP contributions in the combined fits.The fits varied NP Wilson coefficients and non-perturbative hadronic contributions simultaneously.
  • Flavour physics: HEPfit was used to study final-state interactions and CP asymmetries in D →PP decays following the LHCb observation of ∆ACP.The supplied passages introduce this analysis but do not state a further quantitative outcome.
  • Extended scalar sectors: In softly broken-Z2 THDMs, theoretical, oblique, Higgs, and flavour constraints restrict scalar couplings, mass splittings, alignment, and Yukawa couplings.Theoretical constraints are described as independent of the THDM type I, II, X, or Y.

6 Installation

HEPfit is installed with CMake after satisfying dependencies such as GSL, ROOT, BOOST, and optionally MPI and BAT. The build can produce either a local or system installation, with libraries, headers, and configuration utilities.

  • Dependencies: HEPfit installation requires CMake and depends on GSL, ROOT, and BOOST, while MPI and BAT support are optional for parallel MCMC use.BAT is not required for library-only operation.
  • Build configuration: A fully MPI-compatible MCMC build can be configured with cmake using -DLOCAL_INSTALL_ALL=ON and -DMPIBAT=ON, then compiled with make and make install.The quick-install example runs an analysis on 5 cores.
  • Build configuration: A separate build directory is recommended because it allows the build to be deleted easily without removing the source tree.The documented commands create HEPfit-x.y/build and invoke cmake .. from there.
  • Build configuration: The -DNOMCMC=ON option builds HEPfit without MCMC, whereas -DBAT INSTALL=ON installs the patched BAT libraries needed for MCMC mode.MPI MCMC requires -DMPIBAT=ON together with BAT installation.
  • Installed outputs: The installation provides the hepfit-config executable, the libHEPfit.a library, and the combined HEPfit.h header.hepfit-config supplies compilation include paths with --cflags and linking flags with --libs.

7 Usage and examples

HEPfit is controlled through configuration files that specify the model, parameters, correlations, and observables. These inputs support MCMC likelihood analyses as well as direct predictions and varied observable constraint formats.

  • Execution modes: HEPfit can compute observables through a library or perform Bayesian MCMC analyses using BAT, with configuration files controlling the model and analysis inputs.The library mode permits use of a statistical framework chosen by the user.
  • Configuration files: Configuration files define the model, model flags, model parameters, correlated parameters, and observables used by HEPfit.Model parameters include central values, Gaussian errors, and flat errors.
  • Correlations: Correlations among parameters or observables are specified by declaring their number, listing the corresponding entries, and supplying the correlation matrix.The required matrix has Npar or Nobs rows and columns, respectively.
  • Observables: Observable definitions can include MCMC inclusion, weights, ROOT-histogram likelihoods, prediction-only mode, and chain output.The noMCMC noweight combination is used to obtain an observable prediction.
  • Specialized observables: BinnedObservable, FunctionObservable, and AsyGausObservable extend the basic observable definition with bin limits, an evaluation point, or asymmetric errors.BinnedObservable retains central-value and error fields even in the noMCMC noweight case.

Step 3: Run

The example workflow builds the MonteCarloMode example and runs the analysis executable with model and Monte Carlo configuration files.

  • Step 3: Run: Build the MonteCarloMode example with make before running an analysis.The documented commands change to examples/MonteCarloMode and invoke make.
  • Step 3: Run: Run the analysis executable with the model configuration and Monte Carlo configuration as its two arguments.The command format is ./analysis <model conf> <Monte Carlo conf>.

Alternative: Run with MPI

HEPfit supports parallel MCMC and observable computations through MPI, running across processors or clusters with MPI support. MPI use requires compatible compilation of HEPfit and BAT, including BAT's MPI-patched version.

  • MPI enables parallel processing of MCMC runs and observable computations in HEPfit.
  • MPI operation requires HEPfit and BAT to be compiled with MPI support and uses BAT's MPI-patched version rather than its --enable-parallel build.
  • The MPI launcher starts an analysis on N threads, cores, or processors according to the hardware's smallest processing unit.
  • HEPfit's MPI implementation supports both multithreaded single processors and clusters with MPI support.

7.2 Event generation mode

The event-generation mode evaluates observables at random or central parameter points and organizes results for interactive inspection or downstream programmatic use. HEPfit also provides library interfaces in minimal and non-minimal forms for obtaining observable predictions without a Monte Carlo run.

  • Event generation mode: The event-generation mode evaluates observables at random parameter-space points or, with zero iterations, at all parameters' central values.Positive iteration counts generate random points; specifying an output folder saves runs only when the iteration count exceeds zero.
  • Event generation mode: Generated output can be printed on screen or saved under ./GeneratedEvents in CGO, Observables, Parameters, and Summary.txt entries.Summary.txt records the model, varied parameters, computed observables, and number of generated events.
  • Library mode: The library mode exposes implemented observables without a Monte Carlo run, allowing users to vary model parameters with their own algorithm.Predictions are obtained through the ComputeObservables interface and returned as an observable map.
  • Library mode: Minimal mode uses default values from InputParameters, whereas non-minimal mode reads default model-parameter values from a Model conf file.The library provides combined HEPfit.a and HEPfit.h files, with hepfit-config options for library and include paths.

7.4 Custom models and observables

HEPfit provides templates and factory-based procedures for extending the framework with custom models, which add parameters, and custom observables, which can use existing or newly defined parameters.

  • Custom models: Custom models add an additional set of parameters over those defined in an existing HEPfit model, typically starting from StandardModel.The examples/myModel directory provides a template for implementation.
  • Custom models: The model header and implementation files define the number of additional parameters, their variables, and getters.
  • Custom models: A custom model requires parameter names, corresponding variables, getters, parameter mappings, and setParameter links.The template illustrates names such as c1, c2, c3, and c4 and maps them to their variables.
  • Custom models: After definition, the custom model is registered by name with the ModelFactory in the main function.Model flags can also control model aspects, although they are described as advanced and less commonly used.

Custom Observables

Custom observables can be added independently of custom models and may depend on parameters from HEPfit models, custom models, or both. They are registered explicitly through the ThObsFactory.

  • Custom Observables: A custom observable is any observable not already defined in HEPfit and does not require a custom model.
  • Custom Observables: Custom observables may combine parameters from an existing HEPfit model and a custom model.
  • Custom Observables: Each custom observable must be explicitly registered with the ThObsFactory, using boost::bind when an argument is required.The example registers BIN1 through BIN6 with arguments, while the last two observables require none.
  • Custom Observables: The observable implementation uses classes derived from THObservable and requires a StandardModel object reference.

7.5 Example run in the Monte Carlo Mode

The example run demonstrates how to configure and execute a Unitarity Triangle fit in Monte Carlo mode, then inspect its generated parameter and observable outputs. The workflow uses configuration files, MCMC settings, parallel execution, and multiple result formats.

  • Configuration: The example Unitarity Triangle fit is configured through StandardModel.conf and UTfit.conf, which define the model, parameters, observables, and run-specific flags.UTfit.conf is included from StandardModel.conf and contains parameters relevant to the fit together with the observables and model flags.
  • Execution: Convergence occurred below 400,000 prerun iterations, while the configured run took approximately 50 minutes using 40 CPU cores.Increasing analysis iterations provides a moderate amount of statistics.
  • Outputs: The run produces logs, ROOT output, parameter summaries, parameter plots, observable histograms, and statistics files.The outputs include log.txt, MCout.root, MonteCarlo results.txt, MonteCarlo plots.pdf, and the Observables directory with related text files.
  • Outputs: The observable statistics include marginalized means, modes, and smallest intervals, illustrated for EpsilonK across approximately 69.2531%, 95.8769%, and 99.7487% probability regions.For EpsilonK, the marginalized mode is 0.0022853, with intervals (0.002168, 0.0023924), (0.0020558, 0.0025046), and (0.0019436, 0.0026066).
  • Outputs: The results also include goodness-of-fit and model-comparison measures such as log probabilities, log likelihoods, IC, and DIC.The example reports IC value 13.437 and DIC value 9.6258.

8 Summary

HEPfit is a flexible framework for fitting models to experimental and theoretical constraints through parallel Bayesian MCMC or user-selected statistical analyses. Its extensibility, scalability, and prior validation support use across models, observables, and computing environments.

  • Key features: HEPfit supports Bayesian analyses with efficiently parallelized MCMC and custom statistical analyses through its observable-computation library.The framework uses BAT for Bayesian analysis while allowing users to integrate other statistical methods.
  • Key features: BAT-based Bayesian analysis is MPI-parallelized and designed to scale from desktop computers to large clusters.The paper states that scaling to many processors does not substantially increase overhead.
  • Key features: Users can define models with new parameters and observables that depend on those parameters or on parameters already defined in HEPfit.This permits analyses using user-selected models and observable sets beyond the built-in implementations.
  • Validation and use: The framework has been tested through published physics results, and its publicly available configuration files can reduce the effort needed to begin using it.The paper also summarizes the code structure, BAT framework, parallelization, implemented models and observables, and prior physics results.
  • Validation and use: The article is intended as a starting point for installing and running HEPfit, with further technical details available in the online documentation.The documentation covers HEPfit usage and code structure.
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