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

In this talk, I revisit and present a more comprehensive estimate of the lowest order Hadronic Vacuum Polarization (HVP) contribution $a_{\mu }{\mathrm{\mid }}_{hvp}^{lo}$ 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: $a_{\mu }{\mathrm{\mid }}_{lo}^{hvp}=(7043\pm 37)\times {10}^{-11}$.A comparison with previous data driven ($e^{+}{e}^{-}$ and $\tau$-decays) estimates is done.Including the Higher Order $a_{\mu }{\mathrm{\mid }}_{hvp}^{ho}$ corrections, the phenomenological estimate of the Hadronic Light by Light scattering up to NLO and the QED and Electroweak (EW) contributions, one obtains: $\mathrm{\Delta }{a}_{\mu }^{pheno}\equiv a_{\mu }^{exp}-a_{\mu }^{pheno}=(81\pm 41)\times {10}^{-11}$ 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 $\mathrm{\Delta }{a}_{\mu }^{lattice}=(90\pm 56)\times {10}^{-11}$. Then, we deduce the (tentative) SM prediction average : $\mathrm{\Delta }{a}_{\mu }^{SM}=(87\pm 33)\times {10}^{-11}$. 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: $a_{\tau }{\mathrm{\mid }}_{lo}^{hvp}=(3516\pm 25)\times {10}^{-11}$ and $\mathrm{\Delta }{\alpha }_{had}^{(5)}(M_Z^2)=(2770.7\pm 4.5)\times {10}^{-5}$ for 5 flavours.