Systematic study of the calibration and resolution of drift tubes for Muon tracking in the ATLAS experiment at the LHC

The Muon Spectrometer of the ATLAS experiment consists of three large air core toroidal magnets, one barrel and two end-caps. The bending power is about 3 and 5 Tm respectively. Tracking in the range |¿| < 2 is done with regular arrays of 3 cm diameter high pressure drift tubes, called MDT, arranged in three measurement stations. The aim of the experiment is a relative resolution of 10% at transverse momentum of 1 TeV/c. At this value, the resolution is limited by the detectors alignment and the single point resolution. The second should not exceed 80 ¿m per tube, averaged over the drift distance. The gas composition (93%Ar-7%CO₂) and gain (2·10⁴), chosen in order to limit the aging, makes the drift response function, r(t), highly non linear, thus it depends on temperature, pressure and local value of the magnetic field. An auto-calibration method has been developed to calculate from the data themselves the r(t) function and to extract the resolution function. This method has been extensively tested on a beam of high momentum muons to study systematic effects and the statistics needed to guarantee that the calibration error is indeed much smaller than the single point resolution. We describe the analysis of these data, and present the results on the convergence of the auto-calibration as a function of the track angular range, the number of tracks, the track fit quality requirements, the correlation between angle and position measurement, for both three and four tube layers.