Resummations with renormalon effects for the hadronic vacuum polarization contribution to the muon (g-2)

The hadronic vacuum polarization contribution to the muon (g-2) value is calculated by considering a known dispersion integral which involves the $R_{e^+ e^-}(s)$ ratio. The theoretical part stemming from the region below 1.8 GeV is the largest contribution in our approach, and is calculated by using a contour integral involving the associated Adler function $D(Q^2)$. In the resummations, we account for the renormalon structure of the usual and the modified Borel transform of $D(Q^2)$ via an explicit ansatz and by employing judiciously chosen conformal transformations. This effect increases the predicted value of the hadronic vacuum polarization contribution to the muon (g-2), and therefore diminishes the difference between the recently measured and the SM/QCD-predicted value of (g-2). It is also shown that the total QED correction to the hadronic vacuum polarization is very small, about 0.06 percent.