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

Third QED order hadronic light-by-light (LBL) contributions a(mu)(LBL)(M) to the anomalous magnetic moment of the muon a(mu)(had) from the pole terms of scalar sigma, a(0)(980) and pseudoscalar pi(0), eta, eta' mesons (M) in the framework of the linearized extended Nambu Jona-Lasinio model are evaluated. The off-shell structure of the photon-photon-ineson 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 pi(0), eta, eta' and a(0) 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 sigma-meson coupling constant is taken to be equal to pi(0)-meson coupling constant as it follows from the linearized Nambu-Jona-Lasinio model Lagrangian. Then one obtains a(mu)(LBL)(pi(0)) = (81.83 +/- 16.50) x 10(-11), a(mu)(LBL)(eta) = (5.62 +/- 1.25) x 10(-11,) a(mu)(LBL)(eta') = (8.00 +/- 1.74) x 10(-11), a(mu)(LBL)(sigma) = (11.67 +/- 2.38) x 10(-11) and = (0.62 +/- 0.24) x 10(-11). The total contribution of meson poles in LBL is a(mu)(LBL)(M) = (107.74 +/- 16.81) x 10(-11). (C) 2002 Published by Elsevier Science B.V.