[Paper Review] $ exttt{SpaceMath v.2.0}$ with Machine Learning. A $ exttt{Mathematica}$ package for Beyond the Standard Model parameter space searches

M. A. Arroyo-Ureña, T. A. Valencia-Pérez|arXiv (Cornell University)|Aug 2, 2020

Particle physics theoretical and experimental studies28 references4 citations

TL;DR

SpaceMath v.2.0 is a Mathematica-based package that enables phenomenological constraints on Beyond the Standard Model (BSM) models using LHC Higgs data and lepton flavor-violating processes. It integrates machine learning (Linear Regression, Decision Trees, Gradient Boosting, Neural Networks, Gaussian Processes) to generate benchmark points, offering an intuitive, symbolic interface for exploring parameter spaces in models like the Two-Higgs Doublet Model (2HDM) type III with high accuracy and compatibility to experimental data.

ABSTRACT

exttt{SpaceMath v.2.0} with Machine Learning is an extension of the previous version which we implement observables related with LHC Higgs boson data and their projections for the High Luminosity and High Energy Large Hadron Collider. In this version we implemented processes with Flavor-Changing Neutral Currents at tree and one-loop level, namely, i) Radiative decays $\ell_i o\ell_j γ$, ii) $\ell_i o \ell_j \ell_k \bar{\ell}_k$ decays ($\ell_i=τ,\,μ$, $\ell_{j,\,k}=μ,\,e$, with $\ell_i eq\ell_j eq\ell_k$) and iii) anomalous magnetic dipole moment of the muon $δa_μ$. exttt{SpaceMath v.2.0} is able to find allowed regions for free parameters of models with both real and complex singlets and real and complex doublets using the processes previously mentioned within a friendly interface and an intuitive environment in which the user enters the couplings symbolically, sets parameters and execute exttt{Mathematica} in the traditional way. As result, both tables as plots with values and areas agree with experimental data are generated. We present examples using exttt{SpaceMath v.2.0} to analyze the free extit{Two-Higgs Doublet Model of type III} parameter space, step by step, in order to start new users in a fast and efficient way. Finally, we have implemented in this version of exttt{SpaceMath} algorithms of Machine Learning to generate specific Benchmark Points to be used directly in numerical evaluations of calculations of physical observables.

Motivation & Objective

• To extend the SpaceMath package to include LHC Higgs signal strength modifiers and coupling deviations from the Standard Model.
• To incorporate lepton flavor-violating processes such as ℓᵢ → ℓⱼγ, ℓᵢ → ℓⱼℓₖℓ̄ₖ, and the muon anomalous magnetic moment δaμ.
• To enable automated, user-friendly constraint of free parameters in BSM models (e.g., 2HDM type III) using experimental data.
• To integrate machine learning algorithms for generating predictive benchmark points for physical observables.
• To validate the package’s results against established tools like HDecay and the Gfitter group, ensuring consistency with experimental and theoretical benchmarks.

Proposed method

• The package implements theoretical expressions for Higgs signal strength modifiers 𝒪ᵣ and coupling modifiers κᵢ based on LHC data and projections for HL-LHC and HE-LHC.
• It models lepton flavor-violating processes including radiative decays ℓᵢ → ℓⱼγ, flavor-changing decays ℓᵢ → ℓⱼℓₖℓ̄ₖ, and the anomalous magnetic dipole moment δaμ.
• Users define model couplings symbolically in Wolfram Language, execute commands, and receive plots and tables of allowed parameter regions.
• The package integrates five machine learning algorithms—Linear Regression, Decision Trees, Gradient Boosting, Neural Networks, and Gaussian Processes—to predict benchmark points.
• It uses Feynman rules and decay width expressions derived from the Two-Higgs Doublet Model (2HDM) type III, with parameters like tanβ and α.
• Validation is performed by comparing branching ratios and signal strengths against HDecay and Gfitter group results, showing full agreement.

Experimental results

Research questions

• RQ1 Can SpaceMath v.2.0 accurately reproduce Higgs boson branching ratios and signal strengths for the Two-Higgs Doublet Model (2HDM) type I, as computed by HDecay?
• RQ2 How well do the machine learning-generated benchmark points in SpaceMath v.2.0 match known physical observables in BSM models?
• RQ3 To what extent does the inclusion of lepton flavor-violating processes improve the constraint of BSM parameter spaces in 2HDM models?
• RQ4 How do the results from SpaceMath v.2.0 compare with those from the Gfitter group, especially in the cos(β−α)–tanβ plane?
• RQ5 Can the package’s symbolic interface and machine learning integration significantly reduce the learning curve for non-expert users in BSM phenomenology?

Key findings

• SpaceMath v.2.0 reproduces Higgs branching ratios in the 2HDM-I model with full agreement to HDecay, including BR(h→bb̄)=0.6080 and BR(h→γγ)=0.2126×10⁻².
• The package generates plots and tables of allowed parameter regions that are consistent with current LHC data, including signal strength modifiers and coupling deviations.
• The machine learning module successfully generates benchmark points for physical observables, enabling direct use in further numerical calculations.
• Results in the cos(β−α)–tanβ plane show high similarity to Gfitter group results, with minor differences due to updated data and exclusive use of gluon fusion in SpaceMath.
• The validation confirms that SpaceMath v.2.0 correctly implements theoretical expressions for Higgs decays and LFV processes, ensuring reliability for BSM model studies.
• The package’s symbolic interface allows users to explore complex BSM models with minimal programming knowledge, significantly lowering the barrier to entry.