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

TL;DR

This paper refines the estimate of the hadronic vacuum polarization contribution to the muon g-2 using new experimental data, compares it with previous estimates and lattice results, and discusses implications for the Standard Model prediction.

Contribution

It provides an updated, comprehensive estimate of the lowest order HVP contribution to muon g-2 incorporating recent experimental data and compares it with lattice results.

Findings

Updated HVP contribution: (7043±37)×10^{-11}

Phenomenological muon g-2 discrepancy: (81±41)×10^{-11}

SM prediction average: (87±33)×10^{-11}

Abstract

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