HEPfit: High-Energy Physics Global Fits

• HEPfit is a flexible open-source computational framework designed for global statistical fits in high-energy physics.
• It employs a modular C++/MPI architecture and Bayesian Markov Chain Monte Carlo methods to integrate diverse experimental and theoretical constraints.
• HEPfit is widely used for Standard Model precision studies, beyond the Standard Model analyses, and global fits in modern phenomenological research.

Searching arXiv for HEPfit and related papers to ground the article in current literature. HEPfit is a flexible open-source computational framework for high-energy physics that, given the Standard Model or one of its extensions, allows one to fit model parameters to a set of experimental observables and obtain predictions for observables. Its defining purpose is the combination of indirect and direct constraints in a single statistical environment, and in the version described in its code paper around a thousand observables are implemented in the Standard Model and in several new-physics scenarios (Blas et al., 2019).

1. Definition, scope, and scientific purpose

HEPfit is used for phenomenological analyses in which many heterogeneous measurements and theory conditions must be combined consistently. In Monte Carlo mode it performs a Bayesian Markov Chain Monte Carlo analysis of a given model using BAT, while in library mode it evaluates observables at a chosen point in parameter space and can therefore be embedded in an external statistical framework (Blas et al., 2019). The same framework is used for Standard-Model precision studies, model-independent parameterizations such as $S,T,U$, $\epsilon_i$, SMEFT and Higgs $\kappa$-framework analyses, and explicit beyond-the-Standard-Model realizations including Two-Higgs-Doublet models, the Georgi–Machacek model, aligned two-Higgs-doublet models, and color-octet scalar sectors (Blas et al., 2019).

The code is intended to exploit the complementarity of direct and indirect information. Indirect constraints include electroweak precision observables, Higgs signal strengths, flavour observables, unitarity and stability conditions, and related quantities probing virtual effects, while direct constraints include experimental searches for new particles and direct limits on masses, couplings, and decay rates (Blas et al., 2019). In this sense, HEPfit functions both as a prediction engine and as a global-fit engine.

2. Software architecture and execution modes

The software is organized as a modular object-oriented architecture in C++. Its basic building blocks are the classes Model and Observable, with models inheriting in a layered way, for example

$$\text{QCD} \leftarrow \text{StandardModel} \leftarrow \text{THDM} \leftarrow \dots$$

so that extended models reuse Standard-Model machinery while adding their own parameters and corrections (Blas et al., 2019). Observables are represented by an Observable class that stores the experimental information and an associated ThObservable object that computes the theoretical prediction in the chosen model (Blas et al., 2019).

The code is explicitly modular and extensible. Users can choose which observables to include and which model to analyze, and can define custom models and custom observables; custom observables can also be defined without introducing a new model if the required parameters already exist in a built-in model (Blas et al., 2019). This design has made HEPfit suitable not only for standard benchmark fits but also for bespoke phenomenological analyses.

A major technical feature is parallelization with MPI. In MCMC mode different chains can run across processors, and likelihood and observable computations are distributed; the implementation uses OpenMPI and a patched BAT version integrated with HEPfit (Blas et al., 2019). Output products include 1D and 2D marginalized distributions and posterior histograms stored in ROOT files (Blas et al., 2019).

3. Statistical formulation and analysis workflow

In Monte Carlo mode HEPfit uses Bayes’ theorem. The posterior distribution is written as

$$P(\vec{x}|D)=\frac{P(D|\vec{x})P_0(\vec{x})}{\int P(D|\vec{x})P_0(\vec{x})d\vec{x}},$$

with $\vec{x}$ the model parameters, $D$ the data, $P_0(\vec{x})$ the prior, and $P(D|\vec{x})$ the likelihood (Blas et al., 2019). Marginalized one-dimensional posteriors are obtained through

$P(x_i|D)=\int P(\vec{x}|D)\prod_{j\ne i}dx_j .$

This is the basis for credibility intervals and posterior contours (Blas et al., 2019).

Sampling is performed with BAT’s Metropolis–Hastings machinery. The run contains a pre-run or burn-in stage followed by the main sampling stage; during burn-in, proposal widths are tuned until convergence diagnostics are satisfactory, and convergence is monitored through an $\epsilon_i$0-measure whose values are required to be close to one (Blas et al., 2019). The framework supports correlated priors and correlated observables, and it can read likelihoods directly from ROOT histograms rather than approximating them by simple analytic forms when that is not appropriate (Blas et al., 2019).

The user-facing workflow is configuration-driven. In Monte Carlo mode one supplies a model configuration file listing model name, flags, model parameters, observables, and optional correlated blocks, together with a separate Monte Carlo configuration file specifying chain settings, pre-run length, main-run iterations, convergence criteria, and output settings (Blas et al., 2019). In library mode the framework is compiled into libHEPfit.a and a combined header HEPfit.h, enabling direct use inside external C++ codes (Blas et al., 2019).

4. Implemented physics content

HEPfit includes high-precision Standard-Model predictions for electroweak precision observables such as $\epsilon_i$1-pole observables and the $\epsilon_i$2-boson mass and width, together with Higgs production cross sections and branching ratios and a broad flavour-physics sector containing leptonic and semileptonic meson decays, meson mixing, flavour universality tests, lepton-flavour violation, and $\epsilon_i$3-type quantities (Blas et al., 2019). For beyond-the-Standard-Model scalar sectors it also implements theory constraints such as boundedness from below, perturbative unitarity, vacuum stability or metastability, and renormalization-group running (Blas et al., 2019).

Model-independently, HEPfit has been used for oblique-parameter fits, $\epsilon_i$4 coupling deformations, generalized $\epsilon_i$5-parameter fits, Higgs-coupling deformations in the $\epsilon_i$6-framework, and Warsaw-basis dimension-6 SMEFT analyses (Blas et al., 2016, Blas et al., 2016). In the SMEFT context, the code has been used both in one-operator-at-a-time mode and in global fits where flat directions are removed by field redefinitions (Blas et al., 2016).

In explicit BSM settings, HEPfit has supported global fits of softly broken $\epsilon_i$7-symmetric 2HDMs, aligned two-Higgs-doublet models in both heavy- and low-mass regimes, the Manohar–Wise color-octet scalar extension, and CP-violating triplet-Higgs sectors (Cacchio et al., 2016, Eberhardt, 2017, Eberhardt, 2018, Eberhardt et al., 2020, Karan et al., 2023, Karan et al., 2023, Karan et al., 2024, Coutinho et al., 2024, Coutinho et al., 2024, Eberhardt et al., 2021, Miralles et al., 2022, Chen et al., 2023). This breadth of implementations is one reason HEPfit appears frequently in global new-physics inference studies.

5. Representative analyses and results

In electroweak precision studies, HEPfit has been used to revisit the global Standard-Model fit to electroweak precision observables and to constrain model-independent new-physics parameterizations. A representative result is the fit to oblique parameters yielding

$\epsilon_i$8

with strong correlations, while the Standard-Model fit remains broadly consistent with data except for the well-known $\epsilon_i$9 tension at about $\kappa$0 (Blas et al., 2016). The same framework has also been used for future-collider projections, where FCCee and CEPC-like facilities can improve sensitivities by roughly an order of magnitude in several scenarios, provided Standard-Model theory uncertainties are reduced accordingly (Blas et al., 2016, Blas et al., 2016).

In softly broken $\kappa$1-symmetric 2HDMs, HEPfit has been used to combine Higgs signal strengths, direct heavy-Higgs searches, theoretical consistency conditions, electroweak precision data, and flavour observables. These studies consistently found that the data drive the model close to the alignment limit $\kappa$2, with type II much more constrained than type I; one analysis reports that, after combining constraints, $\kappa$3 at $\kappa$4 probability, and another finds heavy type-II scalar masses pushed to roughly $\kappa$5 GeV or above after all constraints are included (Cacchio et al., 2016, Eberhardt, 2017, Eberhardt, 2018).

In the aligned two-Higgs-doublet model, HEPfit has been the main engine for both heavy-scalar and low-mass-scalar analyses. For heavy additional scalars, the global fits combine boundedness from below, perturbative unitarity, electroweak precision observables, flavour observables, Higgs signal strengths, and direct LHC searches, yielding posterior regions with heavy masses above several hundred GeV and $\kappa$6 very close to zero (Eberhardt et al., 2020, Karan et al., 2023, Karan et al., 2023). In low-mass analyses, the same framework has been used to test scenarios with light pseudoscalars, charged scalars, or multiple light states; one A2HDM study reports that masses below $\kappa$7 GeV are strongly disfavoured in most scenarios because they open exotic Higgs decays, while another concludes that all seven light-scalar scenarios remain viable, though neutral scalars lighter than $\kappa$8 are excluded at $\kappa$9 probability and charged Higgs masses below about $$\text{QCD} \leftarrow \text{StandardModel} \leftarrow \text{THDM} \leftarrow \dots$$0 GeV are excluded by LEP (Karan et al., 2024, Coutinho et al., 2024, Coutinho et al., 2024).

Beyond extended Higgs-doublet sectors, HEPfit has been used in color-octet scalar models and CP-violating triplet models. In the Manohar–Wise framework, a global Bayesian fit combining theory constraints, Higgs data, electroweak precision observables, flavour observables, and direct searches yields the conclusion that colored octet scalars lighter than about $$\text{QCD} \leftarrow \text{StandardModel} \leftarrow \text{THDM} \leftarrow \dots$$1 TeV are excluded unless they are nearly fermiophobic, with mass splittings constrained to be below about $$\text{QCD} \leftarrow \text{StandardModel} \leftarrow \text{THDM} \leftarrow \dots$$2 GeV in the most conservative setup (Eberhardt et al., 2021). In a CP-violating model with real and complex Higgs triplets, HEPfit is used to combine vacuum uniqueness, vacuum stability, perturbative unitarity, EDM limits, the $$\text{QCD} \leftarrow \text{StandardModel} \leftarrow \text{THDM} \leftarrow \dots$$3 parameter, and collider data, leaving viable regions where $$\text{QCD} \leftarrow \text{StandardModel} \leftarrow \text{THDM} \leftarrow \dots$$4, $$\text{QCD} \leftarrow \text{StandardModel} \leftarrow \text{THDM} \leftarrow \dots$$5, and $$\text{QCD} \leftarrow \text{StandardModel} \leftarrow \text{THDM} \leftarrow \dots$$6 can all be significant (Chen et al., 2023).

HEPfit has also been used in flavour effective-field-theory analyses. In rare $$\text{QCD} \leftarrow \text{StandardModel} \leftarrow \text{THDM} \leftarrow \dots$$7 transitions it supports Bayesian global fits of Wilson-coefficient shifts together with hadronic nuisance parameters, enabling explicit comparisons between optimistic and conservative treatments of hadronic power corrections (Ciuchini et al., 2017). In a different role, HEPfit has provided realistic posterior samples for machine-learning studies: the NFLikelihood work uses posterior samples from HEPfit for electroweak and flavour EFT fits as training and test data for autoregressive normalizing flows (Reyes-Gonzalez et al., 2023).

6. Terminological clarification and related misconceptions

HEPfit should not be confused with unrelated HEP software or infrastructure whose names begin with “HEP.” A particularly common misidentification arises from (Chalotra et al., 2012), which is not about HEPfit at all. That paper describes a HEP Analysis Facility, a cluster designed and implemented in Scientific Linux CERN 5.5 for High Energy Physics analysis, with a shell-script resource-aware job-selection system called HEPINFO, centralized storage under /Jugrid, and worker-node dispatch for root and aliroot workloads (Chalotra et al., 2012). It is therefore a cluster-based HEP computing environment rather than the HEPfit statistical framework.

A second potential misconception is methodological. HEPfit is not itself a machine-learning likelihood emulator. In the NFLikelihood study, it serves as the source of posterior samples for electroweak and flavour fits, while the normalizing-flow architecture is a separate unsupervised density-estimation framework (Reyes-Gonzalez et al., 2023). This distinction is important because HEPfit’s core identity is statistical inference and prediction for physics models, not learned surrogate modeling.

Taken together, the literature presents HEPfit as an extensible, Bayesian, C++/MPI-based framework for global high-energy-physics inference, designed to combine direct searches, indirect precision data, and theory constraints into a unified analysis pipeline (Blas et al., 2019).