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Testing Local Realism at the LHC with a New Bell Inequality for Gauge Bosons


Core Concepts
This paper proposes a new Bell-like inequality, the Spin-Squared-Bell (SS-Bell) inequality, specifically designed for gauge bosons, and demonstrates its potential to detect Bell violation in proton-proton collisions at the LHC, particularly in the production of ZZ and W+b¯b pairs.
Abstract
  • Bibliographic Information: Grabarczyk, R. (2024, October 24). An improved Bell-CHSH observable for gauge boson pairs. arXiv:2410.18022v1 [hep-ph].

  • Research Objective: This paper aims to extend the study of Bell inequality violations to particle decays and splittings beyond weak interactions, focusing on processes involving gauge bosons at the LHC.

  • Methodology: The author introduces a new Bell-like inequality, the SS-Bell inequality, based on squares of spin operators. This inequality is parity-invariant, making it suitable for studying decays and splittings not governed by weak interactions. The author calculates the expected values of the SS-Bell observable for specific processes (ZZ and W+b¯b production) at the LHC using leading-order calculations and simulations.

  • Key Findings: The SS-Bell inequality shows promising results for detecting Bell violation in both ZZ and W+b¯b production at the LHC. It outperforms the previously used LP-Bell inequality in terms of the phase space volume where violation occurs, particularly for the ZZ process. The study suggests that observing Bell violation with the SS-Bell inequality is statistically feasible at the HL-LHC.

  • Main Conclusions: The SS-Bell inequality offers a new and potentially powerful tool for testing local realism in high-energy physics. It opens up possibilities for studying Bell violation in a wider range of processes, including those involving strong interactions. The findings suggest that the HL-LHC might have the sensitivity to observe Bell violation in gauge boson pairs, providing a significant test of quantum mechanics in a new regime.

  • Significance: This research significantly contributes to the field of quantum foundations by proposing a practical method for testing Bell inequalities in high-energy collisions. It paves the way for exploring the quantum nature of fundamental particles and interactions at unprecedented energy scales.

  • Limitations and Future Research: The study acknowledges the need to investigate the impact of higher-order corrections on the SS-Bell observable. Further research should address the experimental challenges associated with reconstructing gauge boson states, particularly in the presence of jets and background processes.

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Stats
The estimated number of ZZ → leptons events at the LHC is approximately 3100 for an integrated luminosity of 140 fb−1. For the SS-Bell inequality applied to ZZ production, a significance of 1.1σ and 3.5σ is projected for integrated luminosities of 300 fb−1 and 3000 fb−1, respectively. In the W+b¯b process, an estimated 5000 events are expected at the LHC for an integrated luminosity of 300 fb−1, increasing to 50000 events for 3000 fb−1. The projected significance for observing SS-Bell violation in the W+b¯b channel is less than 1σ for 300 fb−1 and 3.1σ for 3000 fb−1.
Quotes
"This makes the measurement promising, especially for the High-Luminosity LHC (HL-LHC)." "Using our Bell operator in this process constitutes the first proposal involving a Bell-like observable for a quantum state containing gauge bosons mediating different fundamental interactions." "Our new SS-Bell inequality greatly improves Bell violation prospects for states present in the pp →ZZ process compared to the CGLMP inequality."

Key Insights Distilled From

by Rado... at arxiv.org 10-24-2024

https://arxiv.org/pdf/2410.18022.pdf
An improved Bell-CHSH observable for gauge boson pairs

Deeper Inquiries

How might the understanding of quantum entanglement change if Bell violation is definitively observed in high-energy collisions, particularly involving particles governed by the strong force?

Answer: Definitive observation of Bell violation in high-energy collisions, especially those involving strongly interacting particles like gluons, would be a groundbreaking achievement with profound implications for our understanding of quantum entanglement. Here's how: Confirmation of Entanglement at Unprecedented Energy Scales: Currently, entanglement has been primarily studied and confirmed in systems at relatively low energies. Observing it in the highly energetic environment of the LHC, where the strong force dominates, would demonstrate the universality of entanglement and its relevance across a vast range of energy scales. This would solidify our understanding of entanglement as a fundamental principle of nature, not limited to specific systems or energy regimes. New Insights into the Strong Force and Quantum Chromodynamics (QCD): The strong force, responsible for binding quarks within protons and neutrons, is notoriously complex. Observing entanglement in systems governed by the strong force could provide novel tools to probe its intricacies. It might reveal unexpected quantum correlations between quarks and gluons, leading to a deeper understanding of QCD and potentially uncovering new physics beyond the Standard Model. Bridging the Gap Between Quantum Mechanics and Gravity: One of the biggest challenges in modern physics is unifying quantum mechanics with general relativity, Einstein's theory of gravity. Entanglement, a cornerstone of quantum mechanics, is hypothesized to play a role in the quantum nature of spacetime itself. Observing entanglement at the highest energy scales achievable in colliders could offer hints about this connection and potentially guide the development of a unified theory of quantum gravity. Rethinking Locality in Quantum Field Theory: Bell violation challenges our intuitive notions of locality, suggesting that quantum correlations can persist over large distances without violating the speed of light limit. Observing such violations in high-energy collisions, where particles are created and interact at extremely short distances and timescales, would further challenge our understanding of locality in the context of quantum field theory. It might necessitate a paradigm shift in how we think about the relationship between quantum mechanics, spacetime, and the fundamental forces. Overall, definitively observing Bell violation in high-energy collisions involving the strong force would be a major milestone in physics. It would not only confirm the universality of entanglement but also open up new avenues for exploring the fundamental nature of quantum mechanics, the strong force, and potentially even the unification of quantum mechanics and gravity.

Could there be alternative explanations, beyond quantum entanglement, for the observed correlations in gauge boson pairs at the LHC, and how might those be tested?

Answer: While quantum entanglement is the leading explanation for the observed correlations in gauge boson pairs at the LHC, it's crucial to consider alternative explanations to ensure the robustness of the interpretation. Here are some possibilities and ways to test them: Hidden Variables and Local Realism: Bell's theorem famously rules out local hidden variable theories, which attempt to explain quantum correlations through pre-existing, unknown properties of particles. However, more sophisticated hidden variable models, like those involving superdeterminism or non-locality weaker than quantum entanglement, might still be compatible with the observations. Testing: These alternative models often make specific predictions about the statistical distribution of measurement outcomes that differ subtly from quantum mechanics. Performing more precise measurements of Bell observables and analyzing the data for deviations from quantum mechanical predictions could potentially rule out or support these alternative explanations. Detector Loopholes and Experimental Biases: Experimental setups are never perfect, and subtle biases or loopholes in the detection and analysis of particle collisions could, in principle, lead to spurious correlations that mimic entanglement. Testing: Rigorously characterizing and minimizing systematic uncertainties in the detectors, data acquisition, and analysis procedures are crucial. This involves conducting independent cross-checks, blinding analyses, and carefully studying potential sources of bias. Additionally, repeating the experiments with different detector configurations and analysis techniques can help identify and mitigate systematic effects. New Physics Beyond the Standard Model: It's conceivable, though less likely, that unknown particles or interactions beyond the Standard Model could mediate correlations between gauge bosons that appear entangled but arise from a different mechanism. Testing: This would likely require observing other deviations from Standard Model predictions in addition to the Bell correlations. For example, new particles might be directly produced or indirectly inferred through their effects on other processes. Careful analysis of a wide range of LHC data, including searches for new particles and deviations in other observables, is essential to explore this possibility. Undiscovered Properties of Gauge Bosons: While less probable, it's not entirely impossible that gauge bosons possess undiscovered properties or interactions that could lead to the observed correlations without invoking entanglement. Testing: This would require a thorough theoretical and experimental investigation of gauge boson properties. Precision measurements of their properties, such as their masses, decay rates, and interactions with other particles, could reveal any inconsistencies with the Standard Model and hint at new physics or undiscovered properties. In conclusion, while quantum entanglement is the most plausible explanation for the observed correlations in gauge boson pairs at the LHC, it's essential to rigorously rule out alternative explanations. This requires a combination of improved experimental precision, careful analysis to minimize biases, and a comprehensive search for any additional deviations from Standard Model predictions.

If the universe can be considered a quantum system, what are the implications of these findings for understanding the potential "entanglement" of distant galaxies?

Answer: The idea of the universe as a single, interconnected quantum system is a captivating one, and the findings regarding potential entanglement at the LHC raise intriguing questions about the implications for distant galaxies. However, directly applying these findings to cosmological scales requires careful consideration: Extrapolation Challenges: The energy scales probed at the LHC, while immense, are still vastly smaller than those involved in the early universe or in processes governing the large-scale structure of spacetime. Extrapolating findings from these relatively "low-energy" experiments to cosmological distances and energies requires caution, as new physics or unknown effects could emerge at those scales. Quantum Gravity and Spacetime Entanglement: A major challenge lies in our incomplete understanding of quantum gravity. If spacetime itself is subject to quantum effects, as many theories suggest, then the very notion of "distance" and the separation between galaxies might need to be redefined in a quantum framework. Entanglement between distant galaxies could be fundamentally different from the entanglement we observe in laboratory settings. Cosmic Inflation and Entanglement Generation: The inflationary epoch, a period of rapid expansion in the very early universe, is thought to have stretched quantum fluctuations to cosmological scales, potentially creating entanglement between distant regions. However, the exact mechanisms of entanglement generation during inflation and its subsequent evolution are still active areas of research. Observational Constraints: Directly observing entanglement between distant galaxies is an immense challenge. Unlike controlled laboratory experiments, we cannot manipulate galaxies or perform Bell tests on them. Inferring entanglement at such scales would likely require indirect methods, such as searching for subtle correlations in cosmological observables like the cosmic microwave background radiation or the distribution of galaxies. Implications for Our Understanding of the Universe: If entanglement between distant galaxies is confirmed, it would have profound implications for our understanding of the universe's origin, evolution, and interconnectedness. It could provide evidence for the holographic principle, which suggests that the information content of a region of space is encoded on its boundary, potentially linking distant parts of the universe in unexpected ways. In conclusion, while the LHC findings provide tantalizing hints about the potential for entanglement at cosmological scales, directly applying them to distant galaxies is not straightforward. A deeper understanding of quantum gravity, the early universe, and the evolution of entanglement is crucial. Nevertheless, the possibility of a universe woven together by quantum entanglement remains a captivating area of exploration, pushing the boundaries of our understanding of the cosmos and the fundamental laws governing it.
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