Improved evaluation of theα3vacuum-polarization contribution to theα4muon anomalous magnetic moment

The contribution of the eighth-order vertices containing sixth-order one-electron-loop vacuum-polarization subdiagrams to the muon anomalous magnetic moment, which was evaluated previously using the integration routine riwiad on a CDC 7600 computer, is reevaluated using the integration routine vegas on an IBM ES/9000 computer. The previous calculation was found to suffer from a severe underestimation of errors. The new result, -0.241 5(19), is close to the asymptotic analytic result obtained recently by Broadhurst et al. using a renormalization group technique. The difference between the numerical and analytic results may be written as $10.23\left(39\right)\left(\frac{m_e}{m_{\mu }}\right)$.