arXiv:hep-ph/0106084v3 21 Jan 2002 Scalar and pseudoscalar meson pole terms in the hadronic light–by–light contributions to a had µ E. Bartoˇ s 1 , A.-Z. Dubniˇ ckov´a 1 , S. Dubniˇ cka 2 , E. A. Kuraev 3 and E. Zemlyanaya 4 1 Dept. of Theor. Physics, Comenius Univ., Bratislava, Slovak Republic 2 Inst. of Physics, Slovak Acad. of Sci., Bratislava, Slovak Republic 3 Bogoliubov Lab. of Theor. Physics, JINR Dubna, 141980 Dubna, Russia 4 Lab. of Information Technologies, JINR Dubna, 141980 Dubna, Russia Abstract Third QED order hadronic light–by–light (LBL) contributions a LBL µ (M ) to the anomalous magnetic moment of the muon a had µ from the pole terms of scalar σ, a 0 (980) and pseudoscalar π 0 , 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 m u = m d = m q = (280 ± 20) MeV. The unknown strong coupling constants of π 0 ,η,η ′ and a 0 mesons with quarks are evaluated in a comparison of the corre- sponding theoretical two–photon widths calculated in the framework of our approach with experimental ones. The σ–meson coupling con- stant is taken to be equal to π 0 –meson coupling constant as it follows from the linearized Nambu–Jona–Lasinio model Lagrangian. Then one obtains a LBL µ (π 0 )=(81.83±16.50)×10 −11 , a LBL µ (η)=(5.62±1.25)× 10 −11 , a LBL µ (η ′ )=(8.00 ± 1.74) × 10 −11 , a LBL µ (σ)=(11.67 ± 2.38) × 10 −11 and a LBL µ (a 0 )=(0.62 ± 0.24) × 10 −11 . The total contribution of meson poles in LBL is a LBL µ (M )=(107.74 ± 16.81) × 10 −11 . 1