Author: Denis Avetisyan
A comprehensive global analysis of particle physics data yields a precise determination of αs, a fundamental parameter governing the strong nuclear force.
This study presents a new determination of the strong coupling constant, αs(MZ) = 0.1183 ± 0.0020, from the CT25 global QCD analysis, highlighting the role of robust uncertainty quantification and data clustering methods.
Precisely determining the strong coupling constant, αs, remains a fundamental challenge in quantum chromodynamics despite decades of research. This paper, ‘Strong Coupling Constant Determination from the new CTEQ-TEA Global QCD Analysis’, presents a novel determination of αs(MZ) derived from the CT25 global analysis of parton distribution functions, incorporating recent high-precision data from the LHC and beyond. We find a value of αs(MZ) = 0.1183 ± 0.0020, while critically evaluating the robustness of uncertainty quantification methods and the impact of data clustering on the final result. How can we further refine these analyses to achieve even more precise and reliable determinations of this crucial parameter, and what implications will this have for our understanding of the strong force?
Unveiling the Strong Force: Precision Determination of αs(MZ)
The strong coupling constant, denoted \alpha_s(M_Z), represents the strength of the strong force – one of the four fundamental forces governing the universe. As a cornerstone parameter within the Standard Model of particle physics, its precise value is critical for accurately predicting the outcomes of high-energy particle collisions and understanding the interactions of quarks and gluons. This constant doesn’t simply dictate the presence of the strong force, but rather its intensity; even slight variations in \alpha_s(M_Z) can significantly alter calculations concerning particle decay rates, cross-sections, and the behavior of matter at the most fundamental levels. Consequently, refining the determination of this constant isn’t merely an exercise in numerical precision; it’s a vital step toward validating the Standard Model and searching for potential new physics beyond its current framework, as inconsistencies between predicted and observed values could signal the presence of undiscovered particles or interactions.
Current calculations of the strong coupling constant, \alpha_s(M_Z), are not purely derived from experimental observation but necessitate reliance on theoretical approximations – specifically, perturbative calculations within the Standard Model. These approximations, while powerful, introduce inherent uncertainties due to the complexities of quantum chromodynamics and the limitations of expanding in powers of \alpha_s. Consequently, the precision with which \alpha_s(M_Z) is known directly constrains the accuracy of predictions for a wide range of particle physics processes, including Higgs boson production and decay, as well as searches for physics beyond the Standard Model. A more precise determination of this fundamental parameter is therefore crucial for rigorously testing the Standard Model and unlocking new discoveries at the energy frontier.
Recent data gathered during the LHC Run-2 period presents an unprecedented chance to precisely determine the strong coupling constant, \alpha_s(M_Z). This refinement stems from the sheer volume and accuracy of particle interactions recorded, allowing for a more robust analysis than previously possible. The culmination of this work yields a new determination of \alpha_s(M_Z) with a value of 0.1183−0.0020+0.0023, representing a significant reduction in uncertainty compared to prior calculations. This improved precision is crucial, as \alpha_s(M_Z) directly impacts the reliability of Standard Model predictions and, consequently, the interpretation of experimental results at the energy frontier, offering a pathway to unveil potential new physics beyond our current understanding.
Refining the Calculation: A High-Order Approach with Global Analysis
A new determination of the strong coupling constant, \alpha_s(M_Z), has been calculated to Next-to-Next-Leading Order (NNLO) precision. This calculation incorporates proton-proton collision data collected during LHC Run-2, representing the most recent and comprehensive dataset available from this energy frontier. The NNLO calculation includes all available theoretical predictions at this order, and the analysis leverages the increased luminosity and improved detector performance of the LHC to reduce statistical uncertainties and constrain the value of \alpha_s(M_Z). The resulting value represents an updated determination of this fundamental parameter of the Standard Model, using the latest experimental input.
The determination of \alpha_s(M_Z) presented utilizes a global fit strategy, meaning data from numerous experiments – including those at the Tevatron and the LHC – are simultaneously analyzed to constrain the fitted parameters. This approach contrasts with individual experiment analyses, and is essential for optimizing statistical power. By combining datasets, the global fit effectively increases the total event yield and reduces the impact of individual experiment uncertainties, leading to a more precise and reliable determination of \alpha_s(M_Z). The methodology accounts for the correlations between measurements from different experiments, ensuring that uncertainties are not underestimated.
The determination of \alpha_s(M_Z) required a comprehensive evaluation of correlated systematic uncertainties across multiple experiments. These correlations, arising from shared data sources or analysis techniques, were carefully modeled and accounted for in the global fit. Failure to address these correlations would lead to an underestimation of the total uncertainty. Through this detailed assessment and mitigation, the final result achieved a combined uncertainty of \pm 0.0020 to +0.0023 on the value of \alpha_s(M_Z) , representing a significant improvement in precision.
Validating Robustness: Data Reclustering and Uncertainty Quantification
Data Reclustering is employed to assess the influence of data grouping on uncertainty quantification. This technique involves iteratively re-assigning data points to different clusters and observing the resulting changes in uncertainty estimates. By repeatedly clustering the data using varied initial conditions or algorithms, the stability of the uncertainty values can be evaluated. Significant variations in uncertainty following reclustering indicate a sensitivity to the specific data grouping, suggesting potential limitations in the reliability of the initial uncertainty assessment. This process allows for a systematic investigation of how the chosen clustering method impacts the overall confidence in the derived results and provides a means of characterizing the robustness of the analysis to different data partitioning schemes.
Sensitivity to data grouping was evaluated using both a ‘Global Tolerance’ and a ‘Dynamic Tolerance’ method. The ‘Global Tolerance’ approach applies a uniform tolerance level across all data points when assessing cluster stability. In contrast, the ‘Dynamic Tolerance’ method utilizes \chi² profiles to inform tolerance levels; these profiles are derived from the observed data and allow for varying degrees of tolerance based on the data’s distribution and inherent uncertainty. This approach permits a more nuanced assessment of result sensitivity, as tolerance is not fixed but adapts to the characteristics of each data grouping, providing a more accurate representation of uncertainty propagation.
A Bayesian Hierarchical Model, integrated with a Gaussian Mixture Model, was utilized to quantify uncertainties within the data. Model selection was performed using the Akaike Information Criterion (AIC); the AIC was minimized at K=2, indicating that a Gaussian Mixture Model with two components provides the optimal balance between model fit and complexity for this dataset. This suggests the data is best represented by two distinct Gaussian distributions, and the hierarchical Bayesian framework facilitates a rigorous assessment of the uncertainty associated with parameter estimation for each Gaussian component, accounting for potential dependencies and shared information across the mixture.
Implications and Future Pathways in Particle Physics
A more precise value for the strong coupling constant, \alpha_s, at the Z boson mass scale, M_Z, significantly sharpens the accuracy of predictions within the Standard Model of particle physics. This refinement isn’t merely a technical improvement; it directly impacts calculations crucial for understanding fundamental particle interactions. By reducing the uncertainty surrounding key parameters, physicists can more reliably predict the probabilities of processes like Higgs boson production and decay, and more sensitively search for deviations that might signal the presence of new particles or forces beyond the current theoretical framework. This enhanced precision is vital for interpreting experimental results from the Large Hadron Collider and future colliders, allowing for more stringent tests of the Standard Model and opening pathways to potential discoveries.
The refined determination of the strong coupling constant \alpha_s(M_Z) directly influences the precision of calculations pertaining to fundamental particle interactions. Specifically, predictions for the production and subsequent decay of the Higgs boson – a cornerstone of the Standard Model – become more accurate, allowing for increasingly stringent tests of theoretical frameworks. Beyond confirming existing models, this improved precision is crucial for the search for new physics. Subtle deviations from Standard Model predictions, potentially indicative of undiscovered particles or forces, are more easily identified with reduced theoretical uncertainty, opening avenues for exploration beyond our current understanding of the universe and pushing the boundaries of particle physics research.
The precision of determining the strong coupling constant, \alpha_s, is poised for continued advancement through the confluence of increased data from future high-luminosity runs of the Large Hadron Collider and ongoing refinements to the complex theoretical calculations underpinning its determination. This analysis reveals a remarkably low sensitivity to variations in the charm quark mass, bolstering confidence in the result and demonstrating a level of uncertainty in \alpha_s(MZ) – specifically 0.0017 – now comparable to that established by the Particle Data Group. These improvements will not only sharpen predictions within the Standard Model, crucial for understanding processes like Higgs boson decay, but also enhance the sensitivity of searches for physics beyond our current understanding, paving the way for potential discoveries at the energy frontier.
The determination of the strong coupling constant, αs, as detailed in this global QCD analysis, highlights a fundamental principle of systemic behavior. Just as a living organism responds holistically to change, the analysis demonstrates how precise values-like αs(MZ)-are not isolated data points, but emerge from the interconnectedness of data and methodology. As Georg Wilhelm Friedrich Hegel observed, “The truth is the whole.” This pursuit of a precise value for αs necessitates a comprehensive approach, accounting for tolerance methods, data clustering, and robust uncertainty quantification. The entire analytical structure dictates the reliability of the result, reinforcing the idea that understanding the whole system is paramount to interpreting any single component.
The Road Ahead
The determination of αs, while seemingly a numerical exercise, consistently reveals the fragility of the assumptions underpinning perturbative QCD. This work, achieving a precise value with quantified uncertainty, does not eliminate the underlying tension: the dependence of results on the chosen framework for Parton Distribution Function determination. The refinement of tolerance methods and the investigation of data clustering represent steps towards acknowledging, rather than masking, these dependencies. It is not simply about shrinking error bars, but about understanding what those errors signify.
Future progress necessitates a move beyond treating PDFs as merely input parameters. A complete picture demands exploration of the information lost during the discretization inherent in PDF fitting, and a careful assessment of how sensitivity to initial conditions propagates through the evolution equations. The true cost of freedom in choosing a functional form for the PDF-the implicit biases introduced-remains largely unaddressed. Good architecture, in this context, is invisible until it breaks, and the current reliance on specific functional forms may be precisely such a hidden fragility.
Ultimately, the pursuit of increasingly precise αs values will yield diminishing returns without a corresponding effort to build a more robust theoretical foundation. The field will benefit less from cleverness-from increasingly complex fitting procedures-and more from simplicity. A simpler, more transparent framework, even if initially less precise, will scale more effectively as both data volume and theoretical understanding advance.
Original article: https://arxiv.org/pdf/2512.23792.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2026-01-04 16:03