Estimate of the $m_H$ shift due to interference between signal and background processes in the $H \rightarrow \gamma\gamma$ channel, for the $\sqrt{s} = 8$ TeV dataset recorded by ATLAS

In the context of precision measurements of the properties of the Higgs boson, one of the most fundamental parameters is the knowledge of its mass. One of the achievements of the first run of the LHC is the precise estimate of the Higgs Boson mass, that has been measured by the ATLAS and CMS collaborations at a precision of 0.2\% using $H \to \gamma \, \gamma$ and $H \to Z \, Z^* \to 4 \ell$ final states. In the analysis of the experimental data, interference effects of non-resonant $gg \to \gamma \gamma$ and other processes with resonant $gg \to H \to \gamma \gamma$ production are not taken into account. The real part of the interference terms change the line-shape of $m_{\gamma \gamma}$ in such a way that an apparent mass shift appears. In this note a study is carried out that quantifies the expected shift of the mass peak position for the SM Higgs boson in the $H \to \gamma \gamma$ channel for the ATLAS measurement. The purpose is to perform this analysis using the correct detector description and event categorization used for this measurement. The expected median mass shift is found to be $\Delta m_H = - 35 \pm 9$ MeV assuming a Standard Model width of 4 MeV for the Higgs boson, which is negligibly small with respect to the current experimental error. In addition the mass shift for non Standard Model widths is discussed.