Hadronic Vacuum Polarization in True Muonium

Abstract

The leading-order hadronic vacuum polarization contribution to the hyperfine splitting of true muonium is reevaluated in two ways. The first considers a more complex pionic form factor and better estimates of the perturbative QCD contributions. The second, more accurate method directly integrates the Drell ratio $R(s)$ to obtain $C_{1,\mathrm{hvp}}=-0.0489(3)$. This corresponds to an energy shift in the hyperfine splitting of $\Delta E_{hfs,\mathrm{hvp}}^{\mu }=276196(51)$ MHz.

Comments: 5 pages, 1 figure