Timelike and spacelike kernel functions for the hadronic vacuumpolarization contribution to the muonanomalous magnetic moment (vol 49, 055001, 2022)

This addendum provides results complementary to those obtained in [J.Phys.G49, 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 mu HVP , is obtained. It is shown that the infrared limiting value of the 'spacelike' and 'timelike' kernel functions, which enter the representations for a mu 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 mu HVP(3b) (which includes the leptonic and hadronic insertions) and a mu HVP(3c) (which includes the double hadronic insertion), are studied. The three kernel functions appearing in the representations for a mu HVP(3b) , which involve the hadronic vacuum polarization function, Adler function, and the R-ratio, are presented for the cases of the electron and tau-lepton loop insertions.

Automated summary

This addendum provides results complementary to those obtained in [J.Phys.G49, 055001 (2022)]. Specifically, an equivalent form of the relation between the 'spacelike' kernel functions and the hadronic vacuum polarization contribution to the muon anomalous magnetic moment a_mu HVP is obtained. The infrared limiting value of the 'spacelike' and 'timelike' kernel functions, which enter the representations for a_mu HVP involving the Adler function and the R-ratio, is shown to be identical to the corresponding QED contribution. The next-to-leading order contributions a_mu HVP(3b) and a_mu HVP(3c), which include different types of insertions, are studied.