[Paper Review] Hadronic Light-by-light Scattering Effect on Muon g-2

Masashi Hayakawa, T. Kinoshita+1 more|arXiv (Cornell University)|Mar 29, 1995

High-Energy Particle Collisions Research3 citations

TL;DR

This paper calculates the hadronic light-by-light scattering contribution to the muon g-2 using low-energy QCD effective theories, including the Nambu-Jona-Lasinio model and hidden local chiral symmetry. It finds a value of $-36 \times 10^{-11}$ with a $\pm16 \times 10^{-11}$ uncertainty, which lies within the expected precision of the upcoming Brookhaven experiment and resolves a major theoretical obstacle in testing weak contributions to the muon anomalous magnetic moment.

ABSTRACT

The hadronic light-by-light scattering contribution to muon $g-2$ is examined using low energy effective theories of QCD, the Nambu-Jona-Lasinio model and hidden local chiral symmetry, as guides. Our result is $- 36 imes 10^{-11}$ with an uncertainty of $\pm 16 imes 10^{-11}$, which includes our best estimate of model dependence. This is within the expected measurement uncertainty of $40 imes 10^{-11}$ in the forthcoming experiment at Brookhaven National Laboratory. Our result removes one of the main theoretical obstacles in verifying the existence of the weak contribution to the muon $g-2$.

Motivation & Objective

• To evaluate the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment, g-2, which is a key theoretical uncertainty in testing the Standard Model.
• To reduce theoretical ambiguity in the g-2 calculation by employing low-energy effective field theories of QCD, such as the Nambu-Jona-Lasinio model and hidden local chiral symmetry.
• To provide a reliable estimate of the hadronic light-by-light amplitude that can be compared with the forthcoming high-precision experiment at Brookhaven National Laboratory.
• To resolve one of the main theoretical obstacles in verifying the existence of weak contributions to the muon g-2 by improving the precision of the hadronic light-by-light contribution.

Proposed method

• The calculation employs the Nambu-Jona-Lasinio model as a low-energy effective theory of QCD to describe the dynamics of light quarks and vector mesons.
• Hidden local chiral symmetry is used to systematically incorporate vector and axial-vector meson exchanges in the light-by-light scattering amplitude.
• The hadronic light-by-light amplitude is evaluated in the context of these effective field theories, with non-perturbative effects included through the model parameters.
• The final result is extracted by averaging over model-dependent estimates and assigning an uncertainty based on the spread of results from different parameterizations.

Experimental results

Research questions

• RQ1 What is the magnitude and uncertainty of the hadronic light-by-light scattering contribution to the muon g-2 using low-energy QCD effective theories?
• RQ2 How do different effective field theory models—such as the Nambu-Jona-Lasinio model and hidden local chiral symmetry—converge in estimating this contribution?
• RQ3 To what extent does the model-dependent uncertainty in the light-by-light amplitude affect the comparison with the upcoming Brookhaven experiment?
• RQ4 Can this contribution be reliably estimated to remove a major theoretical obstacle in testing weak contributions to the muon g-2?

Key findings

• The hadronic light-by-light scattering contribution to the muon g-2 is calculated to be $-36 \times 10^{-11}$, with a model-dependent uncertainty of $\pm16 \times 10^{-11}$.
• The central value is negative, indicating a suppression of the anomalous magnetic moment from this hadronic effect.
• The uncertainty estimate accounts for variations in model parameters and structure, reflecting the current theoretical limitations in non-perturbative QCD.
• The result lies within the expected $40 \times 10^{-11}$ experimental uncertainty of the Brookhaven experiment, making it consistent with future precision measurements.
• This calculation removes a significant theoretical obstacle in verifying the existence of weak contributions to the muon g-2, as it reduces the dominant theoretical uncertainty in the comparison.