Nonfactorizable QCD and Electroweak Corrections to the Hadronic $\mathit{Z}$ Boson Decay Rate

We present an analysis of two-loop mixed QCD and electroweak corrections to the decay of the $Z$ boson into light quarks. We find that the naive factorization of QCD and electroweak corrections does not describe correctly the two-loop effects. The nonfactorizable corrections shift the width of the $Z$ boson by approximately $-0.59\mathrm{}\left(3\right)\mathrm{MeV}$ and increase the central value of the strong coupling constant determined at the CERN $e^{+}{e}^{-}$ collider LEP by 0.001.