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

Abstract

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 $a_{\mu }^{\mathrm{HVP}}$ inferred from ${\sigma }_{\mathrm{had}}=\sigma (e^{+}{e}^{-}\to$hadrons) data. However, the two most accurate determinations of ${\sigma }_{\mathrm{had}}$ from KLOE and BaBar disagree by almost 3$\sigma$. Additionally, the combined data-driven result disagrees with the most precise lattice determination of $a_{\mu }^{\mathrm{HVP}}$ 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 ${\sigma }_{\mathrm{had}}$; (ii) the additional ${\mu }^{+}{\mu }^{-}$ events will affect the determination of ${\sigma }_{\mathrm{had}}$ via the (luminosity independent) measurement of the ratio of ${\pi }^{+}{\pi }^{-}\gamma$ 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 ${\sigma }_{\mathrm{had}}$, the data-driven and the lattice determinations of $a_{\mu }^{\mathrm{HVP}}$, the predicted and measured values of $a_{\mu }$, while complying with all phenomenological constraints.

arXiv comment40 pages, 6 figures. Major changes: added a full study of the NP contributions to di-muon events

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