Pion Energy Reconstruction by the Local Hadronic Calibration Method with ATLAS Combined Test Beam 2004 data

The pion energy reconstruction by the local hadronic calibration method on the basis of the 2004 combined test beam data in the energy range 10 -- 350 GeV and $\eta = 0.25$ is performed. In this method energies deposited in each cell are weighted. The weights are determined by the Monte Carlo simulation using Calibration Hits software. We have modified this method by applying cuts in weights. The obtained fractional energy resolution with the conventional method of determination of the energy deposit in the dead material between LAr and Tile calorimeters is $\sigma/E = (67\pm2)\%/\sqrt{E} \oplus (3.9\pm0.2)\% \oplus (95\pm22)\%/E$. This is about 1.5 times better than the results for the hadronic calibration method obtained by the Oxford-Stockholm group and slightly better than the H1 method results for CTB04 obtained by Pisa group. The energy linearity is within $\pm$1\%. We have determined the general normalization constant of 0.91 for which the mean value linearity for the weight cut of 1.05 is about 1. At using this normalization constant the energy resolution has not worsen. We have corrected the cesium miscalibration of the $Tile_1$ and $Tile_2$ longitudinal samplings. The mean value of energy linearity has been increased by about 1\% and becomes equal to 1.002$\pm$0.002. The energy resolution did not change. We have performed weighting without knowing of the beam energies. For this the special procedure has been developed. In this case the energy resolution shows 9\% degradation. Linearities are within $\pm$1\%. We have applied the Neural Networks to the determination of the energy deposit between LAr and Tile calorimeters. The essential improvement of energy resolution is obtained. In this case we have reached the projected energy resolution for hadrons in the ATLAS detector $\sigma/E = 50\%/\sqrt{E} \oplus 3\%$.