Data-based form factor corrections between the two-pion $\ddot{I}„$ and $e^{+}{e}^{-}$ spectral functions

Abstract

The $\ddot{I}„$ spectral functions are an alternative to $e^{+}{e}^{-}$ cross-sections, where different measurements are not consistent, for computing the hadronic vacuum contribution to the muon magnetic anomaly $a_{\hat{I}}¼$. This requires a control of isospin-breaking effects which have to be corrected for. So far these corrections have been evaluated using theoretical models. In this letter, a new approach based only on data is presented for the determination of the most critical correction relating the $e^{+}{e}^{-}$ and $\ddot{I}„$ pion form factors. An updated evaluation of the total isospin-breaking correction is given and its impact is discussed in the context of $e^{+}{e}^{-}$-based $a_{\hat{I}}¼$ predictions and of the direct measurement.

17 pages, 9 figures, 3 tables