Two photons plus jet al LHC: the NNLO contribution from the gg initiated process

The production of the Standard Model Higgs boson of mass ~ 100-140 GeV at the LHC likely gives clear signals in the $\gamma \gamma$ (1) and in the $\gamma \gamma jet$ (2) channels. The quantitative evaluation of the background to channel (1) is very hard since the next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) QCD corrections are large. In particular, the contributions of the NNLO QCD subprocess $gg -> \gamma \gamma$ to inclusive $\gamma\gamma$ production is comparable to the contribution of the leading order subprocess $q\bar{q} -> \gamma \gamma$. The quantitative description of the background to channel (1), therefore, requires to calculate all corrections up to the NNNLO level. In this letter we present results on the contribution of the NNLO QCD subprocess $gg -> g \gamma \gamma$ to the production rate of channel (2). We have found that in this case this NNLO contribution is less than 20% of the Born contribution. Since the NNLO contributions will likely be dominated by this subprocess one can argue that in the case of channel (2) - contrary to the case of channel (1)- a quantitative description of the background can be achieved already at next-to-leading order accuracy.