[Paper Review] Hadronic Light-by-Light Contribution to Muon g-2

Joaquím Prades|ArXiv.org|May 19, 2009

Particle physics theoretical and experimental studies5 references3 citations

TL;DR

This paper presents a refined theoretical estimate of the hadronic light-by-light (HLbL) contribution to the muon anomalous magnetic moment, yielding $ a^{\text{HLbL}}_{\mu} = (10.5 \pm 2.6) \times 10^{-10} $, using an $1/N_c$ expansion and constraints from short-distance QCD. The work emphasizes model dependence reduction through future KLOE2 two-photon experiments on $\pi^0$ and other meson transitions.

ABSTRACT

I present the main results obtained in a recent work together with Eduardo de Rafael and Arkady Vainshtein on the hadronic light-by-light contribution to muon g-2. We came to the estimate a^{HLbL}_μ= (10.5 +- 2.6) x 10^{-10}. Here, some emphasis is put in pointing out where the future KLOE2 two-photon experimental program can help to reduce the present model dependence of a^{HLbL}_μ.

Motivation & Objective

• To improve the theoretical uncertainty in the hadronic light-by-light (HLbL) contribution to the muon anomalous magnetic moment $a_\mu^{\text{HLbL}}$.
• To reduce model dependence in existing HLbL calculations by incorporating short-distance QCD constraints and experimental inputs.
• To identify key experimental measurements—particularly from the KLOE2 two-photon program—that can constrain and improve HLbL amplitude models.
• To assess the numerical impact of different hadronic contributions: $\pi^0$, $\eta$, $\eta'$, pseudo-scalars, scalars, and pion loops.
• To provide a conservative, error-robust estimate of $a_\mu^{\text{HLbL}}$ by combining results from multiple models with error propagation.

Proposed method

• Uses an $1/N_c$ expansion to organize contributions from light-quark hadronic states, including $\pi^0$, $\eta$, $\eta'$, and higher resonances.
• Applies operator product expansion (OPE) constraints to refine the neutral pion exchange model, improving consistency with QCD short-distance behavior.
• Combines results from the ENJL model and OPE-based models, taking the central value from the OPE result and conservative error from the ENJL model to account for uncertainties.
• Incorporates contributions from pseudo-vector mesons, scalar resonances, and dressed pion loops using model-dependent estimates with enlarged error bars to reflect model dependence.
• Treats charm quark contributions as a small, fixed correction: $+0.23 \times 10^{-10}$.
• Performs quadrature addition of all contributions and errors to obtain the final estimate, ensuring error propagation accounts for model and theoretical uncertainties.

Experimental results

Research questions

• RQ1 What is the most reliable estimate of the hadronic light-by-light contribution to the muon $g-2$, given current theoretical and experimental constraints?
• RQ2 How can short-distance QCD constraints be used to reduce model dependence in HLbL amplitude calculations?
• RQ3 Which experimental measurements—particularly from two-photon processes—can most effectively reduce uncertainty in $a_\mu^{\text{HLbL}}$?
• RQ4 How do contributions from different hadronic states (e.g., $\pi^0$, $\eta$, $\eta'$, $\rho$, $\sigma$) compare in magnitude and uncertainty?
• RQ5 To what extent do existing models satisfy the full set of QCD short-distance constraints, and how can this be improved?

Key findings

• The central estimate for the hadronic light-by-light contribution is $ a^{\text{HLbL}}_{\mu} = (11.4 \pm 1.3) \times 10^{-10} $, primarily driven by $\pi^0$, $\eta$, and $\eta'$ exchanges.
• The contribution from pseudo-vector mesons is estimated as $ (1.5 \pm 1.0) \times 10^{-10} $, with significant uncertainty due to model dependence.
• Scalar resonance contributions are estimated as $ -(0.7 \pm 0.7) \times 10^{-10} $, indicating a small but negative contribution with large error.
• The dressed charged pion loop contributes $ -(1.9 \pm 1.9) \times 10^{-10} $, with high uncertainty due to model instability.
• The total estimate, combining all contributions and errors in quadrature, is $ (10.5 \pm 2.6) \times 10^{-10} $, with the charm quark contribution adding $ +0.23 \times 10^{-10} $.
• The paper identifies KLOE2 two-photon experiments on $\pi^0 \to \gamma\gamma^*$, $\pi^0 \to \gamma^*\gamma^*$, and $\pi^+\pi^- \to \gamma^*\gamma^*$ as critical for reducing model dependence.