Refining Hadronic Contributions to g-2 and the Running of the weak mixing angle: Systematics and Theoretical Uncertainties

We reanalyze muonic g-2 by refining the determination of hadronic vacuum polarization data. The data for e+e− → hadrons is carefully combined to derive the optimal form of R(s) with its associated uncertainties. We carefully look at the agreement between different experiments to estimate the systematic uncertainty on the cross section ratio R(s) and ahad,LO. We also conduct a μ comprehensive analysis of the hadronic contributions to the running of the weak mixing angle, particularly evaluating the uncertainty due to the experimental determination of R(s) and the singlet contributions. We evaluate the expected theoretical uncertainty for the low-energy value of the weak mixing angle, and compare it to the expected uncertainty of the MOLLER experiment at Jefferson Lab.