Dependence of the sensitivity for a low mass Higgs detection on the pp center of mass energy.

Sensitivity to the detection of the Higgs with a mass of $120~GeV$ is studied as a function of the center of mass of the colliding protons. The analysis is based on the three most sensitive topologies in this mass region: direct production of Higgs followed by the decay $H \rightarrow \gamma \gamma $ and associated production of Higgs with either a W boson or a top quark pair, followed by the decay $H \rightarrow b\bar b$. The analysis in each channel follows the steps discussed either in the TDR or in recent ATLAS notes. The study is performed for $\sqrt s$ ranging from $2~TeV$ to $16~TeV$. While the sensitivity for the $WH$ channel is found to reach a plateau for $\sqrt s \simeq 8~TeV$, the sensitivity for $\Hgg$ and $\ttH$ increases with increasing center of mass energy. For an integrated luminosity of $30~fb^{-1}$ the combined sensitivity of the three channels varies almost linearly from $1.2$ at $\sqrt s = 2~TeV$ to $6.5$ at $\sqrt s = 16~TeV$