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Hadronic contributions to $a_μ$ within Resonance Chiral Theory

Emilio J. Estrada, Alejandro Miranda, Pablo Roig

TL;DR

The paper reviews progress in computing hadronic contributions to the muon anomalous magnetic moment $a_\mu$ within Resonance Chiral Theory (R$\chi$T), focusing on hadronic vacuum polarization (HVP) and hadronic light-by-light scattering (HLBL). By combining tau and $e^+e^-$ input with short-distance QCD constraints, the authors provide information-rich predictions for LO-HVP and the various HLBL components, including pseudoscalar poles/boxes, axial, scalar, and tensor contributions. The R$\chi$T-based results for HVP are broadly consistent with lattice QCD and WP2 expectations, though differences between tau- and $e^+e^-$-driven analyses remain unresolved due to data tensions. For HLBL, pseudoscalar contributions are well constrained, while tensor and axial sectors carry larger uncertainties and show tensions with dispersive/holographic approaches, underscoring the need for improved form-factor data, especially for double-virtual transitions. Overall, the work demonstrates the viability of R$\chi$T as a predictive framework for hadronic contributions, while highlighting pivotal measurements and theoretical developments required to sharpen the SM prediction and interpret any potential deviations in $a_\mu$.

Abstract

We review the recent progress achieved, using Resonance Chiral Theory, in the hadronic contributions to the muon anomalous magnetic moment. These include the hadronic vacuum polarization, either using $e^+e^-$ or $τ$ decays into hadron final states as input; and the hadronic light-by-light part, where in addition to previous results on the lightest pseudoscalar and tensor-poles contributions, we first present the evaluation of the pseudoscalar box using this formalism. We also discuss the scalar, axial-pole and other subleading pieces. The results obtained are consistent with the White Paper 2 values, with comparable precision.

Hadronic contributions to $a_μ$ within Resonance Chiral Theory

TL;DR

The paper reviews progress in computing hadronic contributions to the muon anomalous magnetic moment within Resonance Chiral Theory (RT), focusing on hadronic vacuum polarization (HVP) and hadronic light-by-light scattering (HLBL). By combining tau and input with short-distance QCD constraints, the authors provide information-rich predictions for LO-HVP and the various HLBL components, including pseudoscalar poles/boxes, axial, scalar, and tensor contributions. The RT-based results for HVP are broadly consistent with lattice QCD and WP2 expectations, though differences between tau- and -driven analyses remain unresolved due to data tensions. For HLBL, pseudoscalar contributions are well constrained, while tensor and axial sectors carry larger uncertainties and show tensions with dispersive/holographic approaches, underscoring the need for improved form-factor data, especially for double-virtual transitions. Overall, the work demonstrates the viability of RT as a predictive framework for hadronic contributions, while highlighting pivotal measurements and theoretical developments required to sharpen the SM prediction and interpret any potential deviations in .

Abstract

We review the recent progress achieved, using Resonance Chiral Theory, in the hadronic contributions to the muon anomalous magnetic moment. These include the hadronic vacuum polarization, either using or decays into hadron final states as input; and the hadronic light-by-light part, where in addition to previous results on the lightest pseudoscalar and tensor-poles contributions, we first present the evaluation of the pseudoscalar box using this formalism. We also discuss the scalar, axial-pole and other subleading pieces. The results obtained are consistent with the White Paper 2 values, with comparable precision.

Paper Structure

This paper contains 13 sections, 42 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. A brief introduction to Resonance Chiral Theory
  3. HVP contributions to Lg
  4. Using tau decay input
  5. Using Lg input
  6. HLBL contributions to Lg
  7. Pseudoscalar pole contributions
  8. Pseudoscalar box contributions
  9. Axial pole contributions
  10. Scalar pole contributions
  11. Tensor pole contributions
  12. Other contributions
  13. Conclusions and outlook

Figures (1)

  • Figure 1: Leading order (LO) hadronic contributions to $a_\mu$: of vacuum polarization (HVP) and Hadronic light-by-light (HLBL) type. The blob represents all QCD interactions among the quark and anti-quark, dominated by the low-energy hadronic effects.