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The muon g-2 anomaly confronts new physics in $e^\pm$ and $μ^\pm$ final states scattering

The 4.2$σ$ discrepancy between the standard model prediction for the muon anomalous magnetic moment $a_μ$ and the experimental result is accompanied by other anomalies. A crucial input for the prediction is the hadronic vacuum polarization $a_μ^{\rm HVP}$ inferred from $σ_{\rm had} =σ(e^+e^- \to\,$hadrons) data. However, the two most accurate determinations of $σ_{\rm had}$ from KLOE and BaBar disagree by almost 3$\,σ$. Additionally, the combined data-driven result disagrees with the most precise lattice determination of $a_μ^{\rm HVP}$ by $2.1\,σ$. We show that all these discrepancies could be accounted for by a new boson produced resonantly around the KLOE centre of mass energy and decaying promptly yielding $e^+e^-$ and $μ^+μ^-$ pairs in the final states. This gives rise to three different effects: (i) the additional $e^+e^-$ events will affect the KLOE luminosity determination based on measurements of the Bhabha cross section, and in turn the inferred value of $σ_{\rm had}$; (ii) the additional $μ^+μ^-$ events will affect the determination of $σ_{\rm had}$ via the (luminosity independent) measurement of the ratio of $π^+π^-γ$ versus $μ^+μ^-γ$ events; (iii) loops involving the new boson would contribute directly to the prediction for $a_μ$. We discuss in detail this possibility, and we present a simple model that can reconcile the KLOE and BaBar results for $σ_{\rm had}$, the data-driven and the lattice determinations of $a_μ^{\rm HVP}$, the predicted and measured values of $a_μ$, while complying with all phenomenological constraints.