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Symbolic Classification-Enabled LHC Limits Online BSM Global Fits
Shehu AbdusSalam
TL;DR
LHC limits are difficult to evaluate online in high-dimensional BSM global fits because conventional collider-limit calculations are computationally expensive. The paper uses symbolic regression on ATLAS Run-2 electroweakino data to derive a pMSSM exclusion classifier and applies it during global-fit sampling. The resulting approach achieves approximately 97% ROC AUC and illustrates online incorporation of ATLAS constraints into pMSSM fits.
Problem
Directly evaluating LHC exclusion limits during BSM global-fit scans is computationally prohibitive because collider-limit calculations can require expensive simulation and recasting pipelines.
Method
Symbolic regression is applied to ATLAS electroweakino constraints to derive a mathematical pMSSM classifier, which is then used dynamically during global-fit sampling.
Results
AUC: approximately 97% for the symbolic classifier, which is integrated into a pMSSM global fit using ATLAS constraints during posterior-sample generation.
Takeaways & Limitations
The framework provides an efficient route for incorporating ATLAS LHC constraints online rather than evaluating collider limits through costly post-processing calculations.
Abstract
from arXiv · showhide
Global fits of Beyond the Standard Model (BSM) physics often involve a two-way interplay between theory and experiment. Theoretical models provide guidance for experimental searches, while experimental results, in turn, constrain theoretical frameworks. A crucial aspect of this feedback loop is the direct inclusion of measurements and exclusion limits ``online'' global fits, i.e. during the parameter scans aspects of the global fits. However, incorporating the Large Hadron Collider (LHC) limits into such analyses has been computationally prohibitive, often due to time taken per parameter point exceeding the scales acceptable for global fit frameworks. In this study, we show that LHC limits can be incorporated ``online'' global fits by leveraging approximations derived from symbolic regression techniques. We utilize a dataset of ATLAS constraints from searches for electroweakino productions to derive a mathematical expression capable of classifying the phenomenological Minimal Supersymmetric Standard Model (pMSSM) parameter space as allowed or excluded. This is subsequently incorporated for making a global fit of the pMSSM to data, including the LHC Run-2 limits.
I. INTRODUCTION
The study addresses the computational cost of incorporating LHC exclusion limits directly into BSM global fits. It uses symbolic regression to approximate ATLAS electroweakino constraints and integrate their classification into a pMSSM global-fit framework.
- Motivation: LHC recasting pipelines require event generation, detector simulation, reconstruction, cross-section calculations, and analysis selections for each parameter point.This makes direct incorporation into global fits prohibitively time-consuming, so collider constraints are often applied after sampling.
- Motivation: Simplified-model tools do not generally capture realistic BSM scenarios with extensive cascade decays and multiple mass scales.
- Related approaches: Machine-learning alternatives can evaluate points rapidly, but SUSY-AI is restricted to LHC Run-1 analyses and is cumbersome to integrate into global-fit pipelines.
- Contribution: Symbolic regression approximates LHC direct-search limits as mathematical functions of model parameters, providing computationally efficient experimental constraints.
- Contribution: The resulting symbolic expression classifies pMSSM parameter space using ATLAS Run-2 electroweakino constraints and is incorporated into a global fit with three representative measurements.
II. SYMBOLIC EXPRESSIONS OF LHC LIMITS
The paper uses symbolic regression to derive analytic approximations of ATLAS exclusion limits. The expressions prioritize accurate classification and efficient evaluation within global-fit pipelines.
- Approach: Symbolic regression searches mathematical-formula space for expressions that reproduce complex numerical computations such as ATLAS exclusion limits.
- Purpose: These analytic expressions serve as efficient approximations to full particle-physics simulation outputs, substantially improving computational speed.
- Implementation: The analysis employs the Feyn symbolic-regression package, while PyOperon and PySR are identified as alternative frameworks.
- Implementation: Feyn represents candidate expressions as operator trees whose fitness is determined by their ability to reproduce the supplied dataset, typically through a loss function.
- Dataset: The dataset for symbolic regression consists of ATLAS electroweakino exclusion limits.
A. Summary of ATLAS limits considered
The ATLAS dataset combines eight Run-2 electroweakino searches probing complementary regions of the LSP–NLSP mass plane. Each pMSSM point receives a binary exclusion label from its combined CLs value.
- Search program: Eight ATLAS Run-2 analyses probe complementary regions of the lightest- versus next-to-lightest-supersymmetric-particle mass plane.
- Search channels: The search program covers multiple electroweakino production and decay topologies, including leptonic, hadronic, compressed-spectrum, and disappearing-track signatures.
- Dataset construction: 12,280 of 20,000 generated pMSSM electroweakino models passed ATLAS preselection, and 2,263 were classified as excluded.
- Classification labels: Each model is represented by pMSSM parameters x_i and a binary label y_i, with y_i = 0 for “Final” CLs < 0.05 and y_i = 1 otherwise.
- Pipeline: The symbolic-classification pipeline derives an analytic function y(x) that approximates the ATLAS classifier across pMSSM parameter space for dynamic global-fit use.
B. ATLAS limits as symbolic expressions
The workflow trains a symbolic classifier to predict ATLAS exclusion labels from pMSSM parameters. A multi-stage search selects an expression whose discrimination reaches an AUC of about 0.97.
- Workflow: The workflow derives a compact functional form that predicts the exclusion label y(x) from pMSSM parameters x.
- Training procedure: The dataset is randomly split with 30% reserved for testing, while inverse-frequency event weights address the imbalance between excluded and allowed points.
- Optimization: Binary cross-entropy guides classification, Akaike Information Criterion penalizes expression complexity, and evaluations run in parallel across 28 threads.
- Optimization: Six iterative Feyn runs explored approximately 10^7 symbolic models over roughly 840 CPU core-hours before selecting the top-ranked expression for the global-fit pipeline.
- Performance: AUC: about 0.97, indicating strong discrimination between the evaluated classes.
- Classification: The classifier outputs a continuous allowed-class score and uses a Youden threshold of 0.506 to obtain binary classifications.
III. LHC LIMITS ONLINE GLOBAL FITS
The pMSSM global fit combines ATLAS Run-2 limits with three representative measurements, applying the learned LHC classifier during parameter sampling. The fit samples pMSSM parameters under stated assumptions and uses the classifier as an allowed/excluded likelihood factor.
- pMSSM setup: The pMSSM parameters θ define the gaugino masses, sfermion masses, trilinear couplings, and Higgs-sector parameters used in the fit.The Higgs sector is specified by mA, µ, and tan β, while M1, M2, and M3 are gaugino mass parameters.
- pMSSM setup: The fit assumes real supersymmetry-breaking parameters, zero off-diagonal sfermion mass and trilinear terms, and degenerate first- and second-generation soft masses.These assumptions are imposed to maintain compatibility with observed CP-violation and flavor-changing-neutral-current constraints.
- Sampling and constraints: pMSSM points are sampled from uniform priors within specified ranges, while selected first-, second-, and third-generation sfermion masses are fixed at 10 TeV.The high-scale fixing follows the electroweakino focus of the ATLAS analyses and their current LHC-limit consistency.
- Sampling and constraints: For each sampled point, spectrum and observable predictions are computed, and the symbolic formula supplies the ATLAS compatibility flag.Points can be discarded for unphysical spectra, including failed electroweak symmetry breaking, tachyonic states, or an unsuitable LSP.
- Data and likelihood: The likelihood assigns L(dLHC|θ) = 1 to points flagged allowed by the learned formula and 0 to points flagged otherwise.Two global fits are performed: one without ATLAS limits and one incorporating them through symbolic expressions, enabling comparison of posterior impacts.
IV. RESULTS AND DISCUSSION
The ATLAS electroweakino limits alter pMSSM posterior distributions and correlations when incorporated online, tightening viable regions alongside naturalness constraints. The symbolic-classification approach provides an efficient route for including these limits during global-fit scans.
- Posterior impact: Online ATLAS limits modify marginalized posteriors for the electroweakino-relevant pMSSM parameters M1, M2, µ, and At.Figure 3 compares posteriors without the limits against those obtained with them incorporated during the global fit.
- Posterior impact: The ATLAS limits visibly push posterior samples into tighter corners of pMSSM parameter space.
- Correlated observables: With ATLAS limits applied, the proportionality δ(g −2)µ ∝tan β is pronounced, unlike in the moderate-to-high tan β region without those limits.The comparison is shown through the posterior in the (tan β, δ(g −2)µ) plane.
- Naturalness interplay: The ATLAS limits remove anomalous posterior points that spoil the δ(g −2)µ ∝tan β relation when the naturalness line cut is applied.Figure 5 compares samples without and with ATLAS limits under the naturalness-line condition.
- Naturalness interplay: The naturalness line bounds mA from above, while the ATLAS limit raises its lower bound, squeezing the allowed region from opposite directions.For tan β ∈[1, 60], the naturalness line requires mA less than 4 TeV; with ATLAS limits and the line applied, mA must exceed 500 GeV, versus 100 GeV without ATLAS limits.
- Computational implication: The study concludes that symbolic classification enables fast online inclusion of LHC constraints instead of computationally expensive post-processing.The method encodes exclusion boundaries as explicit mathematical expressions usable during pMSSM sampling.