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 Re +e-(s) ratio. The theoretical part stemming from the region below 1.8 GeV i s the largest contribution in our approach, and is calculated by using a co ntour integral involving the associated Adler function D(Q(2)) In the resum mations, we explicitly take into account the exactly known renormalon singu larity of the leading infrared renormalon in the usual and in the modified Borel transform of D(Q(2)), and map further away from the origin the other renormalon singularities by employing judiciously chosen conformal transfor mations. The renormalon effect increases the predicted value of the hadroni c vacuum polarization contribution to the muon (g - 2), and therefore dimin ishes 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 ha dronic vacuum polarization is very small, about 0.06%. (C) 2001 Elsevier Sc ience B.V. All rights reserved.