Corrections of order (Z\alpha)^6 m^2_e/m_\mu in the muonium fine structure, induced by three photon exchange diagrams

Abstract

In the framework of the quasipotential method we calculate the contributions of the kind \alpha^6\ln\alpha, alpha^6 of three-photon exchange diagrams to the energy spectrum of muonium $n^3S_1$ state in the leading order on $m_e/m_\mu$. Analytical expression of obtained correction for arbitrary principal quantum number is equal to (Z\alpha)^6(m_e/m_\mu)m_e(6\ln(2)-35/48)/n^3.