Standard Model radiative corrections in the pion form factor measurements do not explain the $a_{\mu }$ anomaly

Abstract

In this letter, we address the question of whether the almost four standard deviations difference between theory and experiment for the muon anomalous magnetic moment $a_{\mu }$ can be explained as a higher-order Standard Model perturbation effect in the pion form factor measurements. This question has, until now, remained open, obscuring the source of discrepancies between the measurements. We calculate the last radiative corrections for the extraction of the pion form factor, which were believed to be potentially substantial enough to explain the data within the Standard Model. We find that the corrections are too small to diminish existing discrepancies in the determination of the pion form factor for different kinematical configurations of low-energy BABAR, BESS-III and KLOE experiments. Consequently, they cannot noticeably change the previous predictions for $a_{\mu }$ and decrease the deviations between theory and direct measurements. To solve the above issues, new data and better understanding of low-energy experimental setups are needed, especially as new direct $a_{\mu }$ measurements at Fermilab and J-PARC will provide new insights and substantially shrink the experimental error.

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