[Paper Review] Is there any room for new physics in the muon g-2 problem?

Erik Bartoš, S. Dubnička+3 more|ArXiv.org|May 5, 2003

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper re-evaluates the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment using a linearized extended Nambu-Jona-Lasinio model, including both pseudoscalar (π⁰, η, η′) and scalar (σ, a₀) meson poles. It computes 10-dimensional Feynman integrals via the MIKOR method, yielding a total light-by-light contribution of (111.20 ± 16.81) × 10⁻¹¹, which reduces the discrepancy between theory and experiment, suggesting no immediate need for new physics at current precision levels.

ABSTRACT

Is there any room for new physics in the muon g-2 problem?

Motivation & Objective

• To reduce theoretical uncertainty in the muon anomalous magnetic moment by improving the calculation of hadronic light-by-light scattering contributions.
• To include scalar meson (σ, a₀) pole contributions alongside pseudoscalars (π⁰, η, η′), previously neglected in many estimates.
• To improve the description of transition form factors for γ* → Mγ* using a modified constituent quark triangle loop model within the Nambu-Jona-Lasinio framework.
• To assess the impact of these improved contributions on the overall theoretical prediction of aμ and its consistency with experimental data.
• To identify and address unresolved theoretical uncertainties in hadronic vacuum polarization and light-by-light scattering that could affect future high-precision comparisons.

Proposed method

• Employed a linearized extended Nambu-Jona-Lasinio model to describe meson-quark couplings, with σ and π⁰ coupling constants set equal via the Lagrangian structure.
• Used a constituent quark triangle loop model with quark mass m_q = (280 ± 20) MeV, determined from chiral quark model fits to pion decay constant and meson masses.
• Calculated transition form factors for γ* → Mγ* using triangle loops, incorporating unitarity and analyticity constraints to model time-like behavior.
• Evaluated 10-dimensional Feynman parametric integrals for each meson pole using the MIKOR numerical integration method.
• Combined results from scalar and pseudoscalar meson poles with existing contributions from pseudoscalar and quark square loops (Hayakawa and Bijnens).
• Combined the total light-by-light contribution with the 3-loop vacuum polarization term aμ^(3)VP = (−101 ± 6) × 10⁻¹¹ to obtain the full 3-loop hadronic correction.

Experimental results

Research questions

• RQ1 What is the contribution of scalar meson poles (σ, a₀) to the hadronic light-by-light scattering amplitude in the muon g-2?
• RQ2 How do the inclusion of σ and a₀ mesons affect the total light-by-light scattering contribution compared to previous estimates that considered only pseudoscalars?
• RQ3 Can a consistent model of transition form factors for γ* → Mγ* be constructed using a modified constituent quark triangle loop, and how does it compare to VMD and ChPT?
• RQ4 To what extent do improved hadronic contributions reduce the discrepancy between the Standard Model prediction and the experimental value of aμ?
• RQ5 What remaining theoretical uncertainties in hadronic vacuum polarization and light-by-light scattering could affect the final precision of the muon g-2 measurement?

Key findings

• The light-by-light contribution from the π⁰ meson pole is aμ^LBL(π⁰) = (81.83 ± 16.50) × 10⁻¹¹.
• The contribution from the η meson pole is aμ^LBL(η) = (5.62 ± 1.25) × 10⁻¹¹.
• The contribution from the η′ meson pole is aμ^LBL(η′) = (8.00 ± 1.74) × 10⁻¹¹.
• The contribution from the σ meson pole is aμ^LBL(σ) = (11.67 ± 2.38) × 10⁻¹¹.
• The contribution from the a₀ meson pole is aμ^LBL(a₀) = (0.62 ± 0.24) × 10⁻¹¹.
• The total light-by-light contribution from all meson poles is aμ^LBL(total) = (111.20 ± 16.81) × 10⁻¹¹, with errors added in quadrature.