Higher-order NLO radiative corrections to polarized muon decay spectrum

Higher-order QED radiative corrections to muon decay spectrum are evaluated within the QED structure function approach in the next-to-leading order logarithmic approximation. New analytical results are given in the $\mathcal{O}\left(\alpha^3 \ln^2(m_\mu^2/m_e^2)\right)$ order. Earlier results in $\mathcal{O}\left(\alpha^2 \ln^1(m_\mu^2/m_e^2)\right)$ and $\mathcal{O}\left(\alpha^3 \ln^3(m_\mu^2/m_e^2)\right)$ orders are partially corrected. Numerical estimates of different contributions are presented.