Complete Electroweak Corrections to Higgs production in a Standard Model with four generations at the LHC

Complete electroweak two-loop corrections to the process $gg\to H$ are presented and discussed in a Standard Model with a fourth generation of heavy fermions. The latter is studied at the LHC to put exclusion limits on a fourth generation of heavy fermions. Therefore also a precise knowledge of the electroweak(EW) next-to-leading-order(NLO) corrections is important. The corrections due to the fourth generation are positive and large for a light Higgs boson, positive but relatively small around the $\bar{t}-t$ threshold and start to become negative for a Higgs boson mass around $M_H=450GeV$. Increasing further the value of the Higgs boson mass, the EW NLO effects tend to become huge and negative, $\mathcal{O}(-100$, around the heavy-fermion threshold, assumed at $1.2TeV$, so that $gg$-fusion becomes non-perturbative. Above that threshold they start to grow again and become positive around $M_H= 1.75 TeV$\mathrm{.}Thebehaviouratevenlargervaluesof$M_H$ shows a positive enhancement, $\mathcal{O}(+100$ at $M_H=3TeV$.