Indirect new physics effects on ${\sigma }_{\mathrm{had}}$ confront the $(g-2{)}_{\mu }$ window discrepancies and the CMD-3 result

Abstract

Recent lattice determinations of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment $a_{\mu }^{\mathrm{HVP}}$ have confirmed the discrepancy with the data-driven dispersive method. In the meanwhile the CMD-3 collaboration has reported a result for the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ cross section considerably larger than previous experimental results (and close to the lattice determinations) exacerbating the discordance between different $e^{+}{e}^{-}$ datasets. We explore to what extent these disagreements can be accounted for by some new physics effect altering selectively the individual experimental determinations of $\sigma (e^{+}{e}^{-}\to$hadrons). We find that specific effects of GeV-scale new particles are able to shift upwards the KLOE and BaBar results in the low and intermediate energy windows, while leaving unaffected the CMD-3 energy scan. Although these new physics effects cannot fully explain all the discrepancies among the different $\sigma (e^{+}{e}^{-}\to$hadrons) datasets, they succeed in mitigating the overall tension between data-driven and lattice estimates of $a_{\mu }^{\mathrm{HVP}}$. Remarkably, the additional loop corrections involving the new particles concur to solve the residual discrepancy with the experimental value of $(g-2{)}_{\mu }$.

Comments: 13 pages, 5 figures and 2 tables. Version published in Physical Review D, including lattice, CMD-3 and the latest FNAL Muon g-2 experimental results