Electroweak loop corrections to $gg\to gH$ at the LHC

We present the results of the complete electroweak loop corrections to the process $gg \to gH$ at the Large Hadron Collider. The electroweak corrections to the total cross section are found to be approximately $+4\%$. At the differential level, the corrections exceed $+4\%$ in the low Higgs transverse momentum region and fall below $-4\%$ in the high transverse momentum region, leading to a noticeable shape distortion for this distribution. Our results represent a necessary step towards to complete next-to-leading order electroweak correction of the Higgs + jet process.