Pseudoscalar pole terms contributions to hadronic light-by-light corrections to the muonium hyperfine splitting

The contribution of pseudoscalar pole diagrams to the hadronic light-by-light corrections of order alpha^3 E_F to the ground state hyperfine splitting in hydrogenic atom is calculated in the pseudoscalar pole terms approximation. The vector dominance model for the form factor of the transition of a pseudoscalar meson into two photons is used. The correction to the muonium hyperfine splitting is equal to 3.7 Hz. With the account of new experimental data on the cross sections sigma (e^+e^-\to rho, omega \to pi^0(eta)gamma) in the SND and CMD-2 experiments some other hadronic corrections to the muonium hyperfine splitting are calculated