On the Contribution of Muon Loops to the Anomalous Magnetic Moment of the Muon

Abstract

We consider a contribution to the anomalous magnetic moment of the muon from the specific class of Feynman diagrams involving the lowest order vacuum polarization by muon loops. We have obtained analytical expressions for the corresponding coefficients for 4, 5, 6 and 7 loops. The effect of reducing large terms in the obtained analytical expressions is discussed. We have found that if for a small number of muon pairs the coefficients at the degrees determining the contribution of these diagrams to the anomalous magnetic moment of the muon decrease, then starting with the contribution of 7 muon loops these coefficients begin to grow. The reasons for this behavior change are discussed. Numerical results are given for a large number of muon loops with a high accuracy.