Revisiting the Muon Anomaly from $e^+ e^-\to$ Hadrons

TL;DR

This work revisits the LO Hadronic Vacuum Polarization (HVP) contribution to the muon anomalous magnetic moment $a_\mu$ using a comprehensive, data-driven approach anchored in $e^+e^-\to$ hadrons data across the full time-like region, incorporating the latest CMD-3, BABAR, and BELLE2 measurements along with PDG22 and QCD continuum refinements. The analysis delivers a refined $a_\mu^{\text{hvp,lo}}=(7037\pm39)\times10^{-11}$ (and $= (7042.5\pm37.2)\times10^{-11}$ in this work), which, when combined with higher-order hadronic and QED/EW effects, yields $a_\mu^{\text{tot,pheno}}=(7112\pm38)\times10^{-11}$ and implies $\Delta a_\mu^{\text{SM}}\approx (87\pm33)\times10^{-11}$. The results are compared with lattice determinations, which give a slightly smaller deviation from experiment, and the paper discusses implications for the SM consistency and future experiments (e.g., MUonE) to sharpen the SM prediction. It also extends the methodology to the tau sector and to the hadronic contribution to $\Delta\alpha^{(5)}(M_Z^2)$, highlighting the central role of low-energy hadronic data in precision tests of the SM.

Abstract

In this talk, I revisit and present a more comprehensive estimate of the lowest order Hadronic Vacuum Polarization (HVP) contribution $a_μ\vert_{hvp}^{lo}$ to the muon anomalous magnetic moment (muon anomaly) from $e^+e^-\to$ Hadrons obtained recently in Ref.[1]. New CMD-3 data on $e^+e^-\to 2π$ [2] and precise BABAR [3] and recent BELLE2 [4] $e^+e^-\to 3π$ data are usedto update the estimate of the $I=0$ isoscalar channel below the $φ$-meson mass. Adding the data compiled by PDG22 [5] above 1 GeV and the QCD improved continuum used in Ref. [1], one deduces: $a_μ\vert^{hvp}_{lo}=(7043\pm 37)\times 10^{-11} $.A comparison with previous data driven ($e^+e^-$ and $τ$-decays) estimates is done.Including the Higher Order $a_μ\vert_{hvp}^{ho}$ corrections, the phenomenological estimate of the Hadronic Light by Light scattering up to NLO and the QED and Electroweak (EW) contributions, one obtains: $Δa_μ^{pheno}\equiv a_μ^{exp}-a_μ^{pheno}= (81\pm 41)\times 10^{-11}$ where the recent experimental value $a_μ^{exp}$ [6] has been used. This result consolidates the previous one in Ref.[1], after adding the $π^0γ,ηγ$ contributions, and can be compared with the one from the most precise Lattice result $Δa_μ^{lattice}= (90\pm 56)\times 10^{-11}$. Then, we deduce the (tentative) SM prediction average : $Δa_μ^{SM} = (87\pm 33)\times 10^{-11}$. We complete the paper by revising our predictions on the LO HVP contributions in adding the $π^0γ,ηγ$ contributions to the ones in Ref.[1]. Then, we obtain: $a_τ\vert^{hvp}_{lo}=(3516\pm 25)\times 10^{-11} $ and $Δα^{(5)}_{had}(M_Z^2)=(2770.7\pm 4.5)\times 10^{-5}$ for 5 flavours.

Figures (18)

• Figure 1: $a_\mu$ from BNL and FNAL
• Figure 2: Lowest order quantum correction to $a_\mu$
• Figure 3: NLO and N2LO QED quantum corrections to $a_\mu$
• Figure 4: LO electroweak corrections to $a_\mu$
• Figure 5: Lowest order hadronic vacuum polarization contribution to $a_\mu$