Scalar and pseudoscalar meson pole terms in the hadronic light-by-light contributions to aμhad

Third QED order hadronic light-by-light (LBL) contributions aμLBL(M) to the anomalous magnetic moment of the muon aμhad from the pole terms of scalar σ, a0(980) and pseudoscalar π0,η,η' mesons (M) in the framework of the linearized extended Nambu-Jona-Lasinio model are evaluated. The off-shell structure of the photon-photon-meson vertices is taken into account by means of constituent quark triangle loops. The mass of the quark is taken to be mu=md=mq=(280±20) MeV. The unknown strong coupling constants of π0,η,η' and a0 mesons with quarks are evaluated in a comparison of the corresponding theoretical two-photon widths calculated in the framework of our approach with experimental ones. The σ-meson coupling constant is taken to be equal to π0-meson coupling constant as it follows from the linearized Nambu-Jona-Lasinio model Lagrangian. Then one obtains aμLBL(π0)=(81.83±16.50)x10-11, aμLBL(η)=(5.62±1.25)x10-11, aμLBL(η')=(8.00±1.74)x10-11, aμLBL(σ)=(11.67±2.38)x10-11 and aμLBL(a0)=(0.62±0.24)x10-11. The total contribution of meson poles in LBL is aμLBL(M)=(107.74±16.81)x10-11