The Proton-Box Contribution to the Hadronic Light-by-Light Part of the Muon's Anomalous Magnetic Moment

Core Concepts

The proton-box contribution to the hadronic light-by-light scattering part of the muon's anomalous magnetic moment is smaller than initially predicted by the Heavy Mass Expansion method, primarily due to the damping effect of proton form factors at relevant energy scales.

Abstract

• Bibliographic Information: Estrada, E.J., Márquez, J.M., Portillo-Sánchez, D., & Roig, P. (2024). Proton-box contribution to $a_{\mu}^{\rm{HLbL}}$. arXiv:2411.07115v1 [hep-ph].

• Research Objective: This research paper aims to calculate the proton-box contribution to the hadronic light-by-light (HLbL) scattering component of the muon's anomalous magnetic moment (g-2). This is the first study to investigate a baryonic contribution to this specific component.

• Methodology: The researchers employed a master formula based on unitarity, analyticity, crossing symmetry, and gauge invariance to evaluate the HLbL contributions. They incorporated data-driven and lattice-calculated proton form factors into their analysis, going beyond the limitations of the Heavy Mass Expansion (HME) method.

• Key Findings: The study reveals that the proton-box contribution to the muon g-2 anomaly is significantly smaller than the preliminary estimate obtained using the HME method. The data-driven approach yielded a value of ap−box µ = 1.82(7) × 10−12, two orders of magnitude smaller than the HME prediction. This discrepancy is attributed to the damping effect of proton form factors in the momentum regions where the integral kernel peaks.

• Main Conclusions: The proton-box contribution to the HLbL scattering component of the muon g-2 is negligible compared to the total expected uncertainty of future experimental measurements and Standard Model predictions.

• Significance: This research provides a more accurate calculation of the proton-box contribution to the muon g-2 anomaly, contributing to the ongoing efforts to resolve the discrepancy between experimental measurements and theoretical predictions within the Standard Model.

• Limitations and Future Research: The authors acknowledge that a more comprehensive analysis incorporating the tensor vertex contribution and the F2(Q2) form factor would further refine the results. Future research could extend this approach to other baryons with well-defined form factors, such as the neutron.

Stats

∆aµ = aexp µ −aSM µ = 249(48) × 10−11 (The discrepancy between the experimental measurement and the theoretical prediction of the muon's anomalous magnetic moment).
ap−box µ = 9.7 × 10−11 (Preliminary result from the Heavy Mass Expansion method).
ap−box µ = 1.82(7) × 10−12 (Result using data-driven proton form factors).
ap−box µ = 2.38(16) × 10−12 (Result using lattice QCD proton form factors).

Quotes

"The anomalous magnetic moment of the muon has attracted significant attention in particle physics due to the persistent discrepancy between its experimental measurement and the theoretical predictions of the Standard Model (SM)."
"As the uncertainty in aexp µ is expected to decrease further as more data is analyzed, a significant improvement of the theoretical calculation is essential to determine whether this discrepancy can be attributed to New Physics (NP)."
"Although the heavy mass expansion would yield a contribution of O(10−10), the damping of the form factors in the regions where the kernel peaks, explains our finding ap−box µ = 1.82(7) × 10−12, two orders of magnitude smaller than the forthcoming uncertainty on the aµ measurement and on its Standard Model prediction."

Key Insights Distilled From

Proton-box contribution to $a_{\mu}^{\rm{HLbL}}$

by Emil... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.07115.pdf

Deeper Inquiries

How might future advancements in lattice QCD calculations further impact the precision of the proton-box contribution to the muon g-2 anomaly?

Answer:
Future advancements in lattice QCD calculations hold significant potential to enhance the precision of the proton-box contribution to the muon g-2 anomaly ($a_\mu$). Here's how:

Improved Form Factor Determinations: Lattice QCD provides a first-principles approach to calculating the proton's electromagnetic form factors, which are crucial inputs for evaluating the proton-box diagram. Current lattice calculations still have limitations, particularly at low momentum transfer (Q2), where the proton's internal structure is most complex. Advancements in lattice techniques, such as:

Finer Lattice Spacings: Smaller lattice spacings reduce discretization errors, leading to more accurate form factor calculations, especially at higher Q2 values.
Larger Lattice Volumes: Larger lattice volumes minimize finite-size effects, improving the reliability of form factor extractions at low Q2.
Physical Quark Masses: Simulations performed directly at the physical masses of up, down, and strange quarks reduce uncertainties associated with extrapolations from heavier quark masses.
Controlled Systematics: Rigorous quantification and reduction of systematic uncertainties arising from lattice artifacts, chiral extrapolations, and excited-state contaminations are essential.

Direct Calculation of the HLbL Contribution: In the future, it might become feasible to directly compute the Hadronic Light-by-Light (HLbL) scattering amplitude on the lattice, including contributions from the proton-box diagram. This would bypass the need to rely on form factor parametrizations and potentially lead to a more precise determination of the proton-box contribution.

Addressing Tensor Coupling: Current calculations often neglect the contribution from the proton's tensor coupling, which is suppressed at low Q2 but could become relevant at higher virtualities. Improved lattice QCD calculations can provide more reliable estimates of the tensor form factor F2(Q2), allowing for a more complete evaluation of the proton-box diagram.
By addressing these challenges, future lattice QCD calculations can significantly reduce the uncertainties associated with the proton-box contribution to $a_\mu$, leading to a more stringent test of the Standard Model and potentially shedding light on new physics.

Could the observed discrepancy between the experimental measurement and theoretical prediction of the muon's anomalous magnetic moment be attributed to factors other than new physics, such as unaccounted-for systematic uncertainties in experiments or theoretical calculations?

Answer:
While the possibility of new physics is an exciting prospect, it's crucial to thoroughly examine potential Standard Model explanations for the muon g-2 anomaly before claiming a definitive discovery. Unaccounted-for systematic uncertainties in experiments or theoretical calculations could indeed contribute to the observed discrepancy. Here are some key considerations:
Experimental Uncertainties:

Muon Beam Dynamics: Precise control and understanding of the muon beam's properties (e.g., momentum spread, polarization) are essential for accurate measurements. Uncertainties in these areas could potentially shift the extracted value of $a_\mu$.
Magnetic Field Measurement: The muon g-2 experiment relies on an exquisitely precise measurement of the magnetic field experienced by the muons. Even small, unaccounted-for variations in the field could affect the results.
Detector Effects: Systematic biases in the detectors used to measure the muon decay products could introduce uncertainties in the determination of $a_\mu$.
Theoretical Uncertainties:

Hadronic Vacuum Polarization (HVP): The HVP contribution is the dominant source of uncertainty in the theoretical prediction of $a_\mu$. While data-driven approaches and lattice QCD calculations have made significant progress, uncertainties remain, particularly in the low-energy region.
Higher-Order Hadronic Corrections: Contributions from higher-order hadronic effects, beyond the leading HLbL scattering, are challenging to calculate precisely. These uncertainties could potentially account for part of the discrepancy.
Missing Standard Model Contributions: It's conceivable that there are small, yet unaccounted-for, contributions from known Standard Model processes that have not been fully considered in the theoretical calculations.
Addressing Uncertainties:
Both experimental and theoretical collaborations are actively working to address these uncertainties. On the experimental side, efforts are focused on improving beam control, magnetic field measurements, and detector calibrations. On the theoretical front, researchers are pursuing more precise HVP calculations, refining estimates of higher-order hadronic corrections, and exploring potential missing Standard Model contributions.
Conclusion:
While the muon g-2 anomaly is a tantalizing hint of new physics, it's essential to exercise caution and thoroughly investigate all potential sources of uncertainty before drawing definitive conclusions. Ongoing and future efforts to improve both experimental measurements and theoretical calculations will be crucial in determining whether the anomaly truly points towards physics beyond the Standard Model.

What are the broader implications for our understanding of fundamental physics if the muon g-2 anomaly persists even after accounting for all known Standard Model contributions with even higher precision?

Answer:
If the muon g-2 anomaly persists even after accounting for all known Standard Model contributions with even higher precision, it would have profound implications for our understanding of fundamental physics, potentially revolutionizing our view of the universe:
Clear Evidence for New Physics:

Beyond the Standard Model: The most straightforward implication is the existence of new particles or forces beyond the Standard Model. The muon's anomalous magnetic moment is incredibly sensitive to the presence of new physics, as virtual particles from these unknown sectors can contribute to the muon's interactions.
New Interactions and Symmetries: The new physics responsible for the anomaly could involve new fundamental interactions or symmetries that are not present in the Standard Model. This could lead to a deeper understanding of the fundamental building blocks of matter and the forces that govern their behavior.
Reshaping Our Understanding of the Universe:

Dark Matter and Dark Energy: The new particles or forces could provide insights into the nature of dark matter and dark energy, which constitute the vast majority of the universe's energy density but remain shrouded in mystery.
Hierarchy Problem: The muon g-2 anomaly could be related to the hierarchy problem, which questions why the Higgs boson mass is so much smaller than the Planck scale, the fundamental energy scale of gravity. New physics at the TeV scale, motivated by the anomaly, could offer solutions to this puzzle.
Grand Unified Theories: The discovery of new particles or forces could provide evidence for grand unified theories (GUTs), which attempt to unify the electromagnetic, weak, and strong forces into a single framework.
Experimental and Theoretical Revolution:

Search for New Particles: A confirmed muon g-2 anomaly would trigger an intense experimental program at high-energy colliders, such as the Large Hadron Collider (LHC), to directly search for the new particles responsible for the discrepancy.
Theoretical Model Building: Theorists would be challenged to develop new models that can accommodate the observed anomaly while remaining consistent with all other experimental data. This would lead to a flurry of activity in theoretical particle physics.
Conclusion:
The persistence of the muon g-2 anomaly would be a groundbreaking discovery, signaling a paradigm shift in our understanding of fundamental physics. It would open up new avenues of exploration, potentially leading to a more complete and profound picture of the universe and its underlying laws.