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

The 4.2$\sigma$ discrepancy between the standard model prediction for the muon anomalous magnetic moment $a_{\mu }$ and the experimental result is accompanied by other anomalies. A crucial input for the prediction is the hadronic vacuum polarization $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P}}$ inferred from $\sigma_{\rm had} =\sigma(e^+e^- \to,$hadrons) data. However, the two most accurate determinations of ${\sigma }_{\mathrm{h}\mathrm{a}\mathrm{d}}$ from KLOE and BaBar disagree by almost 3$\sigma$. Additionally, the combined data-driven result disagrees with the most precise lattice determination of $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P}}$ by $2.1\sigma$. 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 ${\mu }^{+}{\mu }^{-}$ 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 ${\sigma }_{\mathrm{h}\mathrm{a}\mathrm{d}}$; (ii) the additional ${\mu }^{+}{\mu }^{-}$ events will affect the determination of $\sigma_{\rm had}$viathe(luminosityindependent)measurementoftheratioof$\pi^+\pi^-\gamma$versus$\mu^+\mu^-\gamma$ events; (iii) loops involving the new boson would contribute directly to the prediction for $a_{\mu }$. We discuss in detail this possibility, and we present a simple model that can reconcile the KLOE and BaBar results for ${\sigma }_{\mathrm{h}\mathrm{a}\mathrm{d}}$, the data-driven and the lattice determinations of $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P}}$, the predicted and measured values of $a_{\mu }$, while complying with all phenomenological constraints.