Sixth-order radiative corrections to the muon magnetic moment

Abstract

It is shown that theα 3 corrections to 1/2(ℊ−ℊe) can be expressed in the form (α/π)3[2/9(ln(m μ/m e))2−1.114 ln (m μ/m e)+1.344+C], where ℊm and ℊe are theg factors of muon and electron, respectively, andC is a constant independent of the electron massm e yet to be calculated. This formula is derived by simple algebraic manipulations from the second- and fourth-order results ofg e andZ 3 (charge renormalization constant). Our result shows that theα 3 corrections to 1/2(ℊ−ℊe) will not be much larger than 2·10−8, and thus will not seriously affect the experimental determination of theα 2 corrections. Furthermore it will provide a consistency check for any future calculation of the completeα 3 corrections to the muon magnetic moment.