Renormalization and two loop electroweak corrections to lepton anomalous dipole moments in the standard model and beyond (I): heavy fermion contributions

Applying effective Lagrangian method and on-shell scheme, we analyze the electroweak corrections to anomalous dipole moments of lepton from some special two loop diagrams in which a closed heavy fermion loop is attached to the virtual gauge bosons or Higgs fields. As the masses of virtual fermions in inner loop are much heavier than the electroweak scale, we verify the final results satisfying the decoupling theorem explicitly if the interactions among Higgs and heavy fermions do not contain the nondecoupling couplings. At the decoupling limit, we also present the leading corrections to lepton anomalous dipole moments from those two loop diagrams in some popular extensions of the standard model, such as the fourth generation, supersymmetry, universal extra dimension, and the littlest Higgs with T-parity.