Addendum: Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (2022 J. Phys. G: Nucl. Part. Phys. 49 055001)

Abstract

Abstract This addendum provides results complementary to those obtained in [J. Phys. G 49, 055001 (2022)]. Specifically, an equivalent form of the relation, which binds together the ‘spacelike’ kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment a μ HVP , is obtained. It is shown that the infrared limiting value of the ‘spacelike’ and ‘timelike’ kernel functions, which enter the representations for a μ HVP involving the Adler function and the R-ratio, is identical to the corresponding QED contribution to the muon anomalous magnetic moment of the preceding order in the electromagnetic coupling. The next-to-leading order contributions a μ HVP ( 3 b ) (which includes the leptonic and hadronic insertions) and a μ HVP ( 3 c ) (which includes the double hadronic insertion), are studied. The three kernel functions appearing in the representations for a μ HVP ( 3 b ) , which involve the hadronic vacuum polarization function, Adler function, and the R-ratio, are presented for the cases of the electron and τ-lepton loop insertions.