Inter-calibration of the CMS Barrel Electromagnetic Calorimeter Using $\pi^0 \rightarrow \gamma\gamma$ Decays

Inter-calibrating the electromagnetic calorimeter of the CMS detector {\it in situ} at the LHC to the design goal of $0.5\% $ precision is going to be important to fully exploit the physics reach of the detector, particularly for the discovery of the Higgs boson in the two-photon decay channel. In this paper we evaluate the potential of a novel calibration technique that makes use of photon pairs produced in neutral pion decays, $\pi^0 \rightarrow \gamma \gamma$. Such photon pairs will be selected from the QCD events accepted by the Level-1 triggers using an online filter farm. Assuming a Level-1 trigger rate of 12.5~kHz, the rate of suitable neutral pions is found to be about 0.9~kHz. We show that 95\% of the barrel electromagnetic calorimeter can be calibrated to at least 1\% (0.5\%) precision after several days (weeks) of data-taking in the low-luminosity scenario of LHC, $\mathcal{L} = 2 \cdot 10^{33} \, \mathrm{cm}^{-2}\,\mathrm{s}^{-1}$. In addition, we show that a 1\% calibration precision is achieved with $\pi^0$ decays produced in the $\pi^-$ test beam runs during November 2006. The obtained calibration constants are successfully used for the reconstruction of $50~GeV$ electrons from the test beam data.