We present the first full analytic results of next-to-next-to-leading order (NNLO) QCD corrections to the top-quark decay width by calculating the imaginary part of three-loop top-quark self-energy diagrams.
Combining these contributions with electroweak corrections and the finite $b$-quark mass effect, we determine the most precise top-quark width to be 1.331 GeV for $m_t=172.69$ GeV. In this talk, I will discuss some recent progress on the analytic calculations of top-quark width.