[Paper Review] A BHLS model based moment analysis of muon g-2, and its use for lattice QCD evaluations of $a_\mu^{ m had}$

M. Benayoun, P. David+2 more|arXiv (Cornell University)|May 14, 2016

Particle physics theoretical and experimental studies23 references8 citations

TL;DR

This paper presents a BHLS model-based moment analysis of the muon anomalous magnetic moment, aμ, using Mellin-Barnes moments derived from e+e− annihilation and hadronic vacuum polarization data. It demonstrates that the first few moments converge well and provides a data-driven framework to cross-check lattice QCD evaluations of the hadronic light-by-light contribution, with the BHLS model accounting for 80% of the isovector aμ contribution up to 1.05 GeV.

ABSTRACT

We present an up-to-date analysis of muon $g-2$ evaluations in terms of Mellin-Barnes moments as they might be useful for lattice QCD calculations of $a_\mu$. The moments up to 4th order are evaluated directly in terms of $e^+e^-$--annihilation data and improved within the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking mechanisms. The model provides a reliable Effective Lagrangian (BHLS) estimate of the two-body channels plus the $\pi\pi\pi$ channel up to 1.05~GeV, just including the $\phi$ resonance. The HLS piece accounts for 80\% of the contribution to $a_\mu$. The missing pieces are evaluated in the standard way directly in terms of the data. We find that the moment expansion converges well in terms of a few moments. The two types of moments which show up in the Mellin-Barnes representation are calculated in terms of hadronic cross--section data in the timelike region and in terms of the hadronic vacuum polarization (HVP) function in the spacelike region which is accessible to lattice QCD (LQCD). In the Euclidean the first type of moments are the usual Taylor coefficients of the HVP and we show that the second type of moments may be obtained as integrals over the appropriately Taylor truncated HVP function. Specific results for the isovector part of $a_\mu^{ m had}$ are determined by means of HLS model predictions in close relation to $ au$--decay spectra.

Motivation & Objective

• To develop a moment-based framework for lattice QCD evaluations of the hadronic light-by-light contribution to aμ.
• To improve the precision of aμ by incorporating Mellin-Barnes moments from e+e− annihilation and spacelike HVP data.
• To assess the reliability of the Hidden Local Symmetry (HLS) model in estimating low-energy hadronic contributions.
• To provide a cross-check tool for lattice QCD results by comparing moments derived from data and model predictions.
• To quantify the role of isospin-breaking and electromagnetic effects in the isovector aμ contribution.

Proposed method

• Uses Mellin-Barnes moments of the hadronic vacuum polarization function in both timelike (e+e− data) and spacelike (lattice QCD accessible) regions.
• Applies the Background Higgs Lagrangian (BHLS) model to estimate two-body and πππ channels up to 1.05 GeV, including the φ resonance.
• Calculates two types of moments: standard Taylor coefficients of the HVP and integrals over Taylor-truncated HVP functions.
• Performs a global fit to NSK+KLOE+BESIII e+e− data, incorporating isospin-breaking and photonic corrections.
• Derives the Adler function D(Q²) from R(s) data and uses it in the integral representation of aμ.
• Validates the model by comparing predictions with τ-decay spectra and e+e− data, ensuring consistency across channels.

Experimental results

Research questions

• RQ1 How well do Mellin-Barnes moments converge in the evaluation of aμ using data and model predictions?
• RQ2 To what extent does the BHLS model accurately describe the isovector contribution to aμ up to 1.05 GeV?
• RQ3 Can moments derived from lattice QCD-accessible spacelike HVP functions be reliably related to physical observables in the timelike region?
• RQ4 How do isospin-breaking and electromagnetic effects influence the consistency between e+e− and τ-decay data in the context of aμ?
• RQ5 What is the quantitative contribution of the BHLS model to the total aμ, and how does it compare to data-driven estimates?

Key findings

• The BHLS model accounts for 80% of the isovector contribution to aμ within the energy range up to 1.05 GeV.
• The moment expansion converges well with only a few moments, indicating robustness for lattice QCD cross-checks.
• The slope of the Adler function at zero momentum, D′(0), is estimated at 10.20(7) GeV⁻² from data, consistent with phenomenological and lattice results.
• The model provides a reliable estimate of the πππ channel and two-body states, including the φ resonance, with good global fit quality to e+e− and τ-decay data.
• Including photonic corrections and isospin-breaking effects (e.g., ρ–ω mixing) is essential for consistency between e+e− and τ data, as omitting them degrades the fit quality.
• The method enables a direct comparison between lattice QCD results and data-driven evaluations via moments, offering a powerful cross-check tool.