Speeding Up the Search for New Physics with Machine Learning

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Author: Denis Avetisyan

A new approach leverages the power of machine learning to dramatically accelerate the complex statistical analyses used in high-energy physics.

This review details a workflow for performing efficient global fits using XGBoost surrogates to explore parameter spaces in the context of the B ± → K ± ν ¯ ν anomaly at Belle II.

Performing robust global statistical fits in high-energy physics is often computationally prohibitive due to complex model evaluations. This limitation is addressed in ‘Lecture notes on Machine Learning applications for global fits’, which details a workflow leveraging Machine Learning surrogates-specifically, Boosted Decision Trees-to efficiently approximate likelihood functions and explore parameter spaces. The notes demonstrate this approach through an application to the B^\pm \to K^\pm \nu\bar{\nu} anomaly at Belle II, enabling efficient searches for Axion-Like Particles while respecting experimental constraints. Could this methodology fundamentally reshape the landscape of parameter estimation in complex physics analyses?

Whispers of Incompleteness: The Standard Model and the Hunt Beyond

Despite its extraordinary predictive power, the Standard Model of particle physics remains incomplete. While it accurately describes the fundamental forces and particles that govern much of the universe, several observations lie outside its explanatory reach. These include the existence of dark matter and dark energy, the observed mass of neutrinos, and the matter-antimatter asymmetry in the cosmos. These discrepancies aren’t mere tweaks needed within the existing framework; they strongly suggest the presence of physics beyond the Standard Model. Consequently, physicists are actively pursuing experimental avenues – like the Belle II experiment – designed to detect subtle deviations from predicted behaviors, seeking evidence of new particles and interactions that could complete the picture and unlock a deeper understanding of reality.

The Belle II experiment, a sophisticated undertaking at the SuperKEKB accelerator in Japan, meticulously investigates the aftermath of particle collisions to reveal potential cracks in the Standard Model of particle physics. Researchers focus on the precise measurement of decay rates – how often a particle transforms into others – comparing observed frequencies with theoretical predictions. Current analysis centers on B^{\pm} \rightarrow K^{\pm} \nu \overline{\nu} decays, where B mesons transform into kaons and neutrinos. A statistically significant deviation from expected rates in this particular decay has recently been observed, indicating a possible signal of new, undiscovered particles or interactions influencing the process. This anomaly doesn’t constitute definitive proof of new physics, but it serves as a compelling invitation for further investigation and a beacon guiding the search beyond the well-established boundaries of current understanding.

Recent analyses of B meson decays are revealing subtle discrepancies that may point towards physics beyond the established Standard Model. Specifically, the decay of B mesons into kaons and neutrinos – a process denoted as B → Kνν – is occurring at a rate that deviates from theoretical predictions with a significance of 2.7σ. While not yet meeting the gold standard of 5σ required for a definitive discovery, this anomaly suggests the potential involvement of undiscovered particles influencing the decay process. These hypothetical particles could interact with the b quark or the neutrinos, altering the expected decay rate and providing a crucial window into a more complete understanding of fundamental forces and particle interactions. Continued data collection and refined analyses are critical to confirm whether this intriguing signal represents a genuine breakthrough or a statistical fluctuation.

Beyond the Equations: Extending Reality with Axion-Like Particles

Standard Model Effective Field Theory (SMEFT) provides a systematic approach to parameterize new physics beyond the Standard Model without requiring a complete, high-energy theory. It achieves this by adding higher-dimensional operators – deviations from the Standard Model Lagrangian – to account for potential interactions not currently described. These operators are suppressed by a characteristic energy scale Λ, representing the mass of new particles or the energy at which new physics becomes directly observable. The effects of these operators are then calculable as a series expansion in E/\Lambda, where E is the energy scale of the process under consideration. By focusing on the lowest-dimensional operators first, SMEFT allows physicists to explore the most likely signatures of new physics while remaining model-independent, providing a robust framework for interpreting experimental data from colliders like the LHC and precision measurements.

The B → Kνν anomaly, a persistent discrepancy between Standard Model predictions and experimental observations of the rare B meson decay, motivates the exploration of new physics. Axion-Like Particles (ALPs) present a viable explanation, introducing a pseudoscalar particle that couples to Standard Model fermions and bosons. This coupling allows ALPs to mediate interactions contributing to the observed excess in the B → Kνν decay rate. Specifically, the anomaly can be addressed by an ALP coupling to both the b-quark and the up-quark, altering the effective decay amplitude and providing a pathway for the observed deviation from Standard Model expectations. Current experimental bounds constrain the coupling strength and mass of these hypothetical ALPs, guiding the ongoing search for this potential new particle.

Axion-Like Particles (ALPs) exhibit energy-scale dependent couplings, necessitating the use of Renormalization Group Equations (RGE) to accurately predict their behavior at different energy levels. These RGEs describe how ALP couplings evolve with the energy scale μ, impacting predictions for observables in particle physics experiments. Computation of this energy dependence is traditionally intensive, requiring numerous calculations across a vast parameter space. However, the application of machine learning algorithms, specifically surrogate models trained on RGE solutions, significantly reduces the computational burden, enabling efficient exploration of ALP parameter spaces and facilitating precise phenomenological studies. These machine learning techniques allow for rapid evaluation of RGE-driven ALP behavior, crucial for interpreting experimental results and constraining ALP properties.

Accelerating Insight: Machine Learning as a Divining Rod

Traditional global fit methodologies, employed in fields like particle physics and cosmology, rely on numerically intensive calculations to determine the best-fit parameters of a model given observational data. The computational cost scales rapidly with model complexity and dataset size due to the need to evaluate the likelihood function-a measure of how well the model predicts the data-across a high-dimensional parameter space. This evaluation often involves solving complex differential equations, such as the Renormalization Group Equations (RGEs), multiple times for each parameter set. Consequently, even with substantial computing resources, performing a complete global fit can take days, weeks, or even months, hindering the exploration of parameter space and limiting the ability to efficiently analyze new data as it becomes available.

Traditional global fit methodologies rely on numerically evaluating the likelihood function, often achieved through the integration of Renormalization Group Equations (RGEs). This process becomes computationally prohibitive when applied to models with a large number of free parameters or when analyzing extensive datasets. Machine Learning (ML) techniques offer a pathway to circumvent this limitation by providing tools to approximate the likelihood function. Specifically, ML models can be trained on a subset of parameter space evaluations to learn the relationship between parameters and the resulting likelihood values. This allows for rapid likelihood estimation without requiring full numerical integration of the RGEs for every parameter point, resulting in substantial speedups in the parameter estimation process. Benchmarks have demonstrated that ML-based approaches can achieve likelihood evaluation times orders of magnitude faster than traditional methods.

A two-stage machine learning model employing XGBoost regression provides an efficient method for approximating the likelihood function in global fit analyses. This approach initially maps the high-dimensional parameter space to a lower-dimensional representation, reducing computational complexity. Subsequently, XGBoost, a gradient boosting algorithm, learns the relationship between parameter values and the resulting likelihood values through regression. This trained model then allows for rapid likelihood evaluation without requiring computationally expensive numerical integration of the relevant equations, significantly accelerating the parameter estimation process and enabling faster analysis of complex models and large datasets. The regression model is trained on a representative dataset of parameter values and their corresponding likelihoods, and its performance is evaluated using standard regression metrics.

Active Learning, when integrated with Gaussian Processes (GP), optimizes the evaluation of parameter space by strategically selecting data points that yield the most significant information. Gaussian Processes provide a probabilistic model for function approximation, allowing for the prediction of likelihood values and associated uncertainties across the parameter space. Active Learning algorithms leverage these uncertainties – specifically, the GP’s prediction variance – to identify points where evaluating the likelihood function will most effectively reduce overall uncertainty. This contrasts with random sampling or grid-based approaches, as it focuses computational resources on regions where knowledge is limited, thereby maximizing information gain per evaluation and substantially reducing the total computational cost required to achieve a desired level of precision in parameter estimation. The process is iterative: the GP is updated with each new data point evaluated, refining its predictive capabilities and further optimizing subsequent point selection.

Unveiling the Influencers: SHAP Values and the Language of New Physics

Machine learning models, particularly those used in high-energy physics, often function as ‘black boxes’ – delivering predictions without revealing why a specific outcome was reached. SHAP (SHapley Additive exPlanations) values offer a solution by providing a unified measure of feature importance, rooted in cooperative game theory. This methodology quantifies each input parameter’s contribution to the model’s output, effectively decomposing a prediction into the additive effects of each feature. Unlike simpler feature importance rankings, SHAP values account for feature interactions and consider all possible combinations of parameters, providing a more nuanced and reliable understanding of model behavior. Consequently, physicists can move beyond simply knowing that a model predicts an anomaly, and instead gain insight into which parameters are driving that prediction, bolstering confidence in the results and guiding further investigation into the underlying physical processes.

The perplexing B → Kνν anomaly, a deviation from expected decay rates, demands careful scrutiny of contributing factors. Utilizing SHAP (SHapley Additive exPlanations) values, physicists can dissect the complex interplay of parameters influencing this anomaly, effectively pinpointing those with the most substantial impact on model predictions. This method doesn’t simply identify that a parameter is important, but quantifies how much it contributes to a specific outcome, revealing subtle relationships often obscured in traditional analyses. By prioritizing theoretical investigation toward these dominant parameters-such as the mass and coupling strength of potential new particles-researchers can efficiently focus their efforts, refine existing models, and ultimately accelerate the search for a comprehensive explanation of this intriguing phenomenon. The precision offered by SHAP values therefore moves the field beyond broad explorations, directing attention to the most promising avenues for discovery.

The application of SHAP values to the analysis of the B → Kνν anomaly yields a quantifiable constraint on the properties of potential new physics candidates, specifically Axion-Like Particles (ALPs). This methodology establishes a lower bound on the proper decay length of ALPs, finding cτ ≥ 80cm, effectively narrowing the parameter space for these hypothetical particles. Beyond this specific result, the rigorous parameter importance assessment facilitated by SHAP values significantly bolsters confidence in machine learning-driven analyses within high-energy physics. By providing a transparent and interpretable framework, this approach not only enhances the trustworthiness of results but also offers a powerful tool for uncovering subtle new physics signals concealed within the complexities of modern datasets, potentially revolutionizing the search for phenomena beyond the Standard Model.

The pursuit of global fits, as detailed in this work, feels less like uncovering immutable laws and more like persuading a chaotic system to momentarily align with a desired narrative. The XGBoost surrogate, approximating the likelihood function, is a particularly potent spell-effective until confronted with the unpredictable currents of production data. It recalls Nietzsche’s observation: “There are no facts, only interpretations.” Each parameter explored, each anomaly assessed in the B ± → K ± ν ¯ ν case, isn’t a step toward objective truth, but a refinement of the story being told. Noise, in this context, isn’t error, but truth struggling to be heard amidst the carefully constructed model.

The Currents Run Deep

The invocation of XGBoost as a likelihood oracle offers a fleeting glimpse of efficiency, but do not mistake the map for the territory. The true cost lies not in CPU cycles, but in the irreducible uncertainty of approximation. Each surrogate is a carefully constructed illusion, a gilded cage built around the chaotic heart of the parameter space. The question is not whether it converges – all spells eventually do – but where it converges, and what shadows it omits from the light.

Future work will inevitably chase ever more elaborate architectures, striving for fidelity at the expense of interpretability. Yet, the deeper mysteries remain untouched. The SHAP values offer a palliative, a momentary calming of the anxieties surrounding model opacity, but they do not dispel the fundamental truth: the likelihood surface is a haunted landscape, and even the most powerful daemon struggles to chart its every contour. The Belle II anomaly, or whatever lies beneath, will yield only to relentless probing, a willingness to sacrifice precision on the altar of exploration.

Perhaps the true path lies not in perfecting the surrogates, but in embracing the inherent messiness of the fit itself. To abandon the quest for a single, definitive answer, and instead cultivate a garden of plausible models, each imperfect, each revealing a different facet of the truth. For in the end, the universe does not offer solutions; it offers only riddles, and the joy – and the torment – lies in the attempt to decipher them.

Original article: https://arxiv.org/pdf/2604.07520.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-04-11 03:40