This assessment is based on version 1 of this paper. Version 2 is now available on arXiv — the authors may have revised their methods, results, or conclusions.
The running of the electroweak gauge couplings from first principles
Alessandro Conigli, Dalibor Djukanovic, Georg von Hippel, Simon Kuberski, Harvey B. Meyer, Kohtaroh Miura, Konstantin Ottnad, Andreas Risch
Abstract
We present a high-precision calculation of the hadronic running of electroweak gauge couplings from first principles. Employing lattice QCD in the low-energy regime, we achieve permille precision for virtualities . At , our determination deviates by up to from estimates based on measurements. Combining lattice QCD with perturbative QCD via the Euclidean split technique, we obtain for the electromagnetic coupling , which is more than twice as precise as recent phenomenological determinations. We assess improvement scenarios by which the precision target for next-generation electroweak measurements could be reached.
AI Impact Assessments
(1 model)Scientific Impact Assessment
Core Contribution
This paper delivers a first-principles lattice QCD determination of the hadronic vacuum polarization (HVP) contribution to the running of the electromagnetic coupling constant and the electroweak mixing angle. The headline result, Δα⁽⁵⁾_had(M²_Z) = 0.027821(34)_lat(35)_pQCD, achieves 0.17% relative precision — more than twice as precise as the best phenomenological (data-driven) determinations based on e⁺e⁻ cross-section measurements. This represents a landmark in the program of computing fundamental Standard Model parameters from first principles.
The paper solves a critical problem: the hadronic contribution to the running of α is the dominant source of uncertainty in electroweak precision tests, and traditional dispersive evaluations suffer from unresolved tensions in e⁺e⁻ → π⁺π⁻ data. By providing an independent, ab initio determination, this work circumvents the data-driven controversies that have plagued the field, particularly those highlighted by the CMD-3 measurement's tension with earlier BaBar and KLOE results.
Methodological Rigor
The calculation rests on a substantial computational infrastructure: 27 CLS ensembles spanning lattice spacings from 0.039 to 0.085 fm with pion masses reaching the physical point. Several methodological innovations strengthen the result:
1. Telescopic window decomposition: The HVP is split into high-, mid-, and low-virtuality components, each with distinct systematic profiles, enabling optimized treatment of discretization effects and long-distance noise.
2. Noise reduction: Low-mode averaging and spectral reconstruction techniques are employed in the long-distance Euclidean regime where signal-to-noise degradation is most severe.
3. Finite-volume corrections: A hybrid Hansen-Patella and Meyer-Lellouch-Lüscher framework provides controlled treatment of finite-volume effects.
4. Systematic uncertainty quantification: Model averaging with AIC weights across multiple fit ansätze and ensemble cuts provides a disciplined approach to systematic errors.
5. Euclidean split technique: Matching lattice QCD to perturbative QCD at Q² = 9 GeV² via the Adler function, with cross-checks between two independent pQCD codes (AdlerPy and pQCDAdler).
The isospin-breaking corrections are estimated to be small (sub-10⁻⁵ level), with conservative uncertainty assignments. The treatment appears thorough, though full QED corrections remain a target for future work.
Significance of the Tension with Data-Driven Results
The up to 7σ deviation from phenomenological estimates at Q² ≃ 1 GeV² is a striking finding. This tension mirrors and reinforces similar discrepancies observed in the HVP contribution to the muon g−2, where lattice results (notably from BMW) have been systematically higher than traditional e⁺e⁻-based evaluations. The fact that the tension diminishes at higher virtualities (to ~4.5σ at Q² = 9 GeV²) but persists is significant, as it suggests the discrepancy is concentrated in the low-energy hadronic regime where non-perturbative effects are largest and e⁺e⁻ data tensions are most acute.
Potential Impact
Electroweak precision physics: This result directly improves the precision of α(M²_Z), a critical input to global electroweak fits. The achieved precision already approaches the upper bound of what FCC-ee will require (1.7‰ vs. 1.0-1.7‰ target).
Muon g−2 connection: The HVP enters both Δα_had and a^hvp_μ. The consistency of lattice results for both quantities strengthens the case that the e⁺e⁻ data may harbor systematic issues, with profound implications for whether the muon g−2 anomaly constitutes evidence for BSM physics.
Future collider program: The roadmap analysis in Figure 3 is particularly valuable, demonstrating that a 50% lattice improvement combined with matching at Q²₀ ~ 20 GeV² could reach the 3×10⁻⁵ precision target for FCC-ee. This provides concrete guidance for resource allocation in the lattice QCD community.
Weak mixing angle: The simultaneous determination of (Δsin²θ_W)_had provides direct input for interpreting upcoming P2 and MOLLER parity-violation experiments.
Timeliness & Relevance
The timing is highly relevant. The muon g−2 theory community recently acknowledged the data-driven tensions by omitting e⁺e⁻-based estimates from their consensus. This paper provides independent corroboration of the lattice perspective at a precision level that commands attention. With FCC-ee planning advancing and low-energy parity-violation experiments on the horizon, this calculation addresses an immediate and pressing need.
Strengths & Limitations
Key Strengths:
Notable Limitations:
Overall Assessment
This paper represents a major advance in precision electroweak physics from lattice QCD. It establishes lattice methods as the most precise approach for determining the hadronic running of electroweak couplings, surpassing decades of data-driven phenomenology. The 7σ tension with e⁺e⁻-based determinations, if confirmed, has far-reaching implications for our understanding of hadronic physics and the interpretation of precision tests of the Standard Model.
Generated Jul 7, 2026
Comparison History (21)
Paper 1 presents a fundamental breakthrough in precision particle physics, achieving unprecedented accuracy in the hadronic running of electroweak gauge couplings. By revealing a 7-sigma deviation from empirical estimates and doubling the precision of phenomenological methods, it carries profound implications for Standard Model tests and searches for new physics. While Paper 2 introduces an innovative and timely AI-driven workflow tool for lattice QCD, Paper 1's highly rigorous, field-shifting physical result will directly and immediately impact a vast range of theoretical and experimental high-energy physics research.
Paper 1 presents a landmark lattice QCD calculation of the hadronic running of electroweak gauge couplings with unprecedented precision, finding a significant 7σ deviation from e+e- based estimates. This directly impacts the Standard Model's precision electroweak program, including the muon g-2 anomaly and Higgs/Z-pole physics. Its implications for fundamental physics are immediate and far-reaching. Paper 2, while methodologically interesting in applying diffusion models to lattice field theory sampling with cross-volume generalization, addresses a computational methodology question with narrower immediate impact on fundamental physics results.
Paper 2 presents a first-principles lattice QCD calculation of the hadronic running of electroweak gauge couplings achieving unprecedented precision, with a striking 7σ deviation from e+e- measurements at low Q². This has immediate, profound implications for precision electroweak physics, the anomalous magnetic moment of the muon, and potential BSM physics interpretation. Its twice-improved precision over phenomenological methods and direct relevance to next-generation experiments (FCC-ee, CEPC) ensure broad, lasting impact. Paper 1, while methodologically innovative for lattice sampling, addresses a more specialized computational problem with demonstrated results limited to 2D φ⁴ theory.
Paper 2 delivers a breakthrough in precision physics, achieving permille accuracy for electroweak gauge couplings and revealing a massive 7-sigma deviation from phenomenological estimates. This result directly impacts Standard Model tests and experimental particle physics, likely triggering immediate, widespread investigations. While Paper 1 introduces an innovative machine learning methodology for lattice field theory, Paper 2's direct extraction of fundamental parameters with unprecedented precision and its discovery of a major discrepancy give it substantially higher immediate and broad scientific impact.
Paper 2 has higher potential impact due to its direct relevance to precision electroweak physics and global Standard Model fits. A first-principles, high-precision lattice determination of the hadronic running of α and electroweak couplings at MZ affects many observables (MW, sin²θW, g−2, new-physics constraints) and is timely given upcoming precision experiments. The reported permille precision and a 7σ tension with e+e−-based estimates indicate strong novelty and broad implications. Paper 1 is valuable for finite-T QCD and chiral restoration, but its applications and cross-field reach are narrower and methodological limitations (truncation/statistics) likely reduce impact.
While Paper 1 reports a crucial 7-sigma anomaly in the Standard Model, Paper 2 provides a transformative methodological breakthrough. By using machine learning to achieve up to a 1000-fold variance reduction in lattice QCD, Paper 2 solves a major computational bottleneck. This novel approach scales across multiple quantum field theories, offering broader cross-disciplinary impact and enabling previously intractable physics computations, giving it a higher potential for widespread, long-term scientific impact.
Paper 1 likely has higher scientific impact: it delivers a first-principles, permille-level lattice-QCD determination of electroweak gauge-coupling running and a significantly improved Δα_had^(5)(M_Z^2), directly affecting precision SM tests, global electroweak fits, and new-physics sensitivity at current/next colliders. The reported 7σ tension with e+e−-based estimates could reshape key inputs. Methodological rigor and broad relevance to HEP phenomenology are strong. Paper 2 is novel and timely for ML-for-lattice, but its immediate impact is narrower and more methodological.
Paper 1 pioneers the quantum simulation of non-Abelian gauge theories on a 156-qubit processor, addressing classically intractable real-time dynamics of strongly interacting matter. This represents a major methodological breakthrough bridging quantum computing and particle physics. While Paper 2 offers high-precision Standard Model calculations and a notable 7-sigma tension, Paper 1's scalable, physics-native encoding introduces a paradigm-shifting approach with broader interdisciplinary impact, laying the foundational groundwork for solving previously insurmountable problems in fundamental physics using near-term quantum hardware.
Paper 2 presents a first-principles lattice QCD calculation of the hadronic running of electroweak gauge couplings with unprecedented precision, revealing a significant 7σ tension with e+e- measurements. This has major implications for precision electroweak physics, the muon g-2 puzzle, and future collider programs. Its methodological rigor (permille precision), direct relevance to unresolved experimental tensions, and importance for next-generation experiments give it substantially broader and more immediate scientific impact than Paper 1, which is a more theoretical exploration of the relationship between gluon and quark condensates.
Paper 2 presents a first-principles calculation of fundamental Standard Model parameters with unprecedented precision, revealing a significant 7-sigma deviation from previous phenomenological estimates. This result directly impacts electroweak precision tests, addresses anomalies in high-energy physics, and sets a new standard for next-generation collider targets. While Paper 1 introduces a highly rigorous and novel methodological advancement for lattice QFT, Paper 2's direct, high-precision challenge to existing experimental estimates promises immediate, profound, and broad impact across the entire particle physics community.