Testing the Higgs boson gluonic couplings at LHC

We study Higgs + jet production at hadron colliders in order to look for new physics residual effects possibly described by the $dim=6$ operators ${\O}_{GG}$ and ${\widetilde\O}_{GG}$ which induce anomalous $Hgg$ and $Hggg$ couplings. Two ways for constraining these operators at LHC may be ~useful. The first is based on the total Higgs boson production rate induced by gluon-gluon fusion, in which the main cause of limitations are due to theoretical uncertainties leading to sensitivities of $|d_G|\simeq 3.\times 10^{-4}$ and $|\widetilde{d}_G|\simeq 1.4\times 10^{-3}$ for the corresponding anomalous couplings, in the mass range $100 GeV \lsim \mh \lsim 2~00 GeV$. These results imply sensitivity to new physics scales of 51 and 24 TeV respectively. The second way investigated here concerns the shape of the Higgs transverse momentum; for which the theoretical uncertainties are less severe and the limitations are mainly induced by statistics. A simple analysis, based on the ratio of the number of events at large and low $p_T$ at LHC, leads to similar sensitivities, if only the $H\to \gamma \gamma $ decay mode is used. But the sensitivities can now be improved by a factor 2 to 10, depending on the Higgs mass, if the Higgs decay modes to $WW^*$, $ZZ^*$, $WW$, $ZZ$ are also used.