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We calculate the meson exchange contribution to the interaction operator of muon and proton, which is determined by the meson coupling with two photon state. For the construction of transition form factor  Meson  →  γγ  we use the existing parametrizations based on experimental data including the monopole parametrization over photon four-momenta. For an estimate of the form factor value atzero photon four-momenta squared we use experimental data on the decay width Γ  Meson → γγ  . It is shown that scalar, pseudoscalar, axial vector and tensor mesons exchanges give significant contribution to the Lamb shift (LS) and hyperfine splitting (HFS) in muonic hydrogen which should be taken into account for a comparison with precise experimental data.

Effects of light-by-light scattering in the Lamb shift and hyperfine structure of muonic hydrogen