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We present the evaluation of the complete set of NLO corrections to three-jetproduction at the LHC. To this end we consider all contributions of$\mathcal{O}(\alpha_s^n\alpha^m)$ with $n+m=3$ and $n+m=4$. This includes inparticular also subleading Born contributions of electroweak origin, as well aselectroweak virtual and QED real-radiative corrections. As an application wepresent results for the three- over two-jet ratio $R_{32}$. While the impact ofnon-QCD corrections on the total cross section is rather small, they can exceed$-10\%$ for high jet transverse momenta. The $R_{32}$ observable turns out tobe very stable against electroweak corrections, receiving absolute correctionsbelow $5\%$ even in the high-$p_T$ region.

Full NLO corrections to 3-jet production and R32 at the LHC