Hadronic light-by-light scattering contribution to 1S-2S transition in muonium

We study hadronic light-by-light scattering contribution to the energy interval (1S-2S) in muonium. Various amplitudes of interaction of a muon and an electron are constructed, in which the effect of hadronic scattering of light-by-light is determined using the transition form factor of two photons into a meson. Their contributions to the particle interaction operator in the case of S-states are obtained in integral form, and to the energy spectrum in numerical form. The contributions of pseudoscalar, scalar, axial vector mesons are taken into account.