Performances of the ATLAS Hadronic Tile Calorimeter Modules for Electrons and Pions

With the aim of establishing of an electromagnetic energy scale of the ATLAS Tile calorimeter and understanding of performance of the 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 calibration constants and electron energy resolutions some of these barrel and extended barrel modules at energies E = 10, 20, 50, 100 and 180 GeV for the cell-scan at $\theta = 20^o$, the $\eta$ scan and the tile scan at $90^o$. The average values of these constants are equal to $\langle R_e \rangle =1.157\pm0.002$ pC/GeV for the cell-scan at $\theta = 20^o$, $\langle R_e \rangle =1.143\pm0.005$ pC/GeV for the $\eta$-scan and $\langle R_e\rangle =1.196\pm0.005$ pC/GeV for the tile-scan at $\theta = 90^o$. The RMS values are the following: for the cell-scan is $RMS=2.6\pm0.1$ \%, for the $\eta$-scan is $RMS=4.2\pm0.3$ \% and for the tile-scan is $RMS=5.7\pm0.3$ \%. The energy linearities of modules are within RMS = 1 \% at $\theta = 20^o$ and 2.5 \% at $\theta = 90^o$. Uniformities for the electron response are in the range of 1 -- 2 \% for cells and about 4 \% for tilerows. The calibration constants for the tile-scan at $\theta = 90^o$ are of 4 \% larger the ones for the cell-scan at $\theta = 20^o$. This is the manifestation of the transition effect. This difference in the calibration constants should be taken into account at creating of the transfer function from the Cs calibration data at $90^o$ to the cell-scan at $20^o$ electron calibration constants for modules unexposed in test beam runs. We have studied the electromagnetic energy resolution. We have determined the statistical and constant terms for the electron energy resolution by fitting of the expressions $\sigma/E=a/\sqrt{E}\oplus b$ and $\sigma/E= a/\sqrt{E}+b$ to the obtained parameters for the quadratic fit are equal to $a=29\pm1.6\ \%\ GeV^{1/2}$, $b=3\pm0.4$ at $\theta = 20^o$ and $a=22\pm1\ \%\ GeV^{1/2}$, $b=2.3\pm0.3$ at $\theta = 90^o$. We have compared our results on energy resolution with the Monte Carlo based paramet\-ri\-zation. Good agreement is observed for the linear fit. Non-com\-pen\-sa\-tion of the Tile calorimeter has been studied. We have determined the $e/h$ ratios of the TILECAL for five values of pseudorapidity $\eta$ in the range of $-0.55\le \eta\le -0.15$ for the beam energy range from 10 GeV to 300 GeV. The obtained $e/h$ ratios are compared with the experimental data of TILECAL 1~m prototype modules and agree with them. The mean value is $e/h=1.36\pm 0.01$, which agrees with the Monte Carlo calculations, $e/h_{MC}=1.40\pm 0.013$, within the errors. The method of the pion calibration of a single module, which uses the electron calibration constants and the known $e/h$ ratio, has been suggested and applied. The mean pion energy, deposited in a single module, amounts to 0.89$\pm$0.01 \% for $\eta$ scan. The lateral energy leakage for one module amounts to about 10 \%. The good ($\pm 1$ \%) energy uniformity is observed. The pion energy resolution for one module has been studied. The mean one is equal to $(6.0\pm0.3)\ \% \ GeV^{1/2}$ for 180 GeV and comparable with the value ($4.8\ \%\ GeV^{1/2}$) expected from the required overall physics performance $\sigma/E=50\ \% GeV^{1/2}/\sqrt{E}\oplus 3\ \%$. The fit filter method of the PMT signal reconstruction demonstrates 30 \% improvement of energy resolution for electron events than the flat filter method and no improvement for pion events. We have compared the pion reconstruction at 180 GeV for $\theta = 90^o$ at different tilerows for the flat filter and fit filter methods. The values of the reconstructed energies obtained for these two methods coincide within the errors. So, for the pion reconstruction the fit filter method does not have appreciable advantages.