Electron Energy Resolution of the ATLAS TILECAL Modules with Fit Filter Method (July 2002 test beam)

The constructed ATLAS detector at the LHC will have the great physics discovery potential, in particular in the detection of a heavy Higgs boson. Calorimeters will play a crucial role in it. It is necessary to have confidence that the calorimeters will perform as expected. With the aim of understanding of performance of the ATLAS Tile hadronic calorimeter to electrons 12\% of modules have been exposed in electron beams with various energies by three possible ways: cell-scan at $\theta =20^o$ at the centers of the front face cells, $\eta$-scan and tilerow scan at $\theta = 90^o$ for the module side cells. We have extracted the electron energy resolutions of the $EBM-$ (ANL-44), $EBM+$ (IFA-42) and $BM$ (JINR-55) Modules of the ATLAS Tile Calorimeter at energies E = 10, 20, 50, 100 and 180 GeV and $\theta = 20^o$ and $90^o $ and $\eta$ scan from the July 2002 testbeam run data using the fit filter method of the PMT signal reconstruction. We have determined the statistical and constant terms for the electron energy resolution by fitting of the quadratic $\sigma/E=a_s/\sqrt{E}\oplus b_s$ and linear $\sigma/E= a_l/\sqrt{E}+b_l$ expressions to the obtained data. The parameters of the electron energy resolution for the quadratic fit are equal to $a_s=28.8\pm0.8\ \%\ \sqrt{GeV}$, $b_s=2.8\pm0.2\ \%$ at $\theta = 20^o$ and $a_s=20.5\pm0.2\ \%\ \sqrt{GeV}$, $b_s=2.1\pm0.1\ \%$ at $\theta = 90^o$. For the linear fit the ones are $a_l=25\pm1\ \%\ \sqrt{GeV}$, $b_l= 1.5\pm0.2\ \%$ for $\theta = 20^o$ and $a_l=17.5\pm0.5\ \%\ \sqrt{GeV}$, $b_l=1.2\pm0.1\ \%$ for $\theta = 90^o$. We have compared our results on energy resolution with the Monte Carlo based paramet\-ri\-zation. Good agreement is observed for the linear fit. Comparison of the corresponding values of the electron energy resolution obtained by the flat filter and fit filter methods shows their coincidence within the errors.