Electroweak corrections to Higgs+jet production in gluon fusion

We present the calculation of complete next-to-leading order electroweak corrections to the Higgs boson production in $gg\to g H$ channel. We apply the method of differential equations combined with the selection of optimized master integrals to accomplish the calculation of master integrals. We consider three distinct $α$ schemes. At leading order, the differential distributions and the total cross section differ among them. However, these discrepancies are considerably suppressed once electroweak corrections are taken into account. For $G_μ$ scheme, the electroweak correction amounts to approximately $4.5\%$. Importantly, this correction exhibits non-trivial kinematic dependence.