Revisit of the electromagnetic correction to $\ddot{I}„\to \ddot{I}€\ddot{I}€\hat{I}{½}_{\ddot{I}}„$ and its implication for muon $g-2$ based on $\ddot{I}„$ data

Abstract

In this work we focus on the evaluation of the leading-order hadronic vacuum polarization contribution from the $\ddot{I}€\ddot{I}€$ channel to the muon anomalous magnetic moment $a_{\hat{I}}¼$ by using the experimental $\ddot{I}„\to \ddot{I}€\ddot{I}€\hat{I}{½}_{\ddot{I}}„$ data. The isospin breaking corrections play the decisive role in this approach of computing $a_{\hat{I}}¼$. One of such important isospin breaking sources is the long-distance electromagnetic correction factor $G_{\mathrm{EM}}$ of the $\ddot{I}„\to \ddot{I}€\ddot{I}€\hat{I}{½}_{\ddot{I}}„$ process from the real photon radiation. The latter effect can be calculated from the $\ddot{I}„\to \ddot{I}€\ddot{I}€\hat{I}{½}_{\ddot{I}}„{\hat{I}}^3$ amplitude, which is revised in this work within the resonance chiral theory by simultaneously including the even-intrinsic-parity and odd-intrinsic-parity resonance operators. We update the determination of the only unknown resonance coupling through the $\ddot{I}‰\to \ddot{I}{€}^0\ddot{I}{€}^0{\hat{I}}^3$ decay by including contributions from both the vector and scalar resonances. By taking other remaining contributions from the muon $g-2$ White Paper 2025, we further revise the complete value of $a_{\hat{I}}¼$, which turns out to deviate from the newest world average result after Fermilab's measurement at the level of 2.7 $\ddot{I}ƒ$.

20 pages, 3 figures. To match the published version