Improved $\hat{I}{\pm }^4$ Term of the Muon Anomalous Magnetic Moment

Abstract

We have completed the evaluation of all mass-dependent $\hat{I}{\pm }^4$ QED contributions to the muon $g-2$, or $a_{\hat{I}}¼$, in two or more different formulations. Their numerical values have been greatly improved by an extensive computer calculation. The new value of the dominant $\hat{I}{\pm }^4$ term $A_2^{(8)}(m_{\hat{I}}¼/m_e)$ is 132.6823 (72), which supersedes the old value 127.50 (41). The new value of the three-mass term $A_3^{(8)}(m_{\hat{I}}¼/m_e,m_{\hat{I}}¼/m_{\ddot{I}}„)$ is 0.0376 (1). The term $A_2^{(8)}(m_{\hat{I}}¼/m_{\ddot{I}}„)$ is crudely estimated to be about 0.005 and may be ignored for now. The total QED contribution to $a_{\hat{I}}¼$ is $116584719.58(0.02)(1.15)(0.85)\times 10^{-11}$, where 0.02 and 1.15 are uncertainties in the $\hat{I}{\pm }^4$ and $\hat{I}{\pm }^5$ terms and 0.85 is from the uncertainty in $\hat{I}\pm$ measured by atom interferometry. This raises the Standard Model prediction by $13.9\times 10^{-11}$, or about 1/5 of the measurement uncertainty of $a_{\hat{I}}¼$. It is within the noise of current uncertainty ($\sim 100\times 10^{-11}$) in the estimated hadronic contributions to $a_{\hat{I}}¼$.

Appendix A has been rewritten extensively. It includes the 4th-order calculation for illustration. Version accepted by PRD