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Computing Technical Design Report

3.7.1 Inner Detector

The SemiConductorTracker (SCT) and Pixel detectors each consist of a large number of detector elements, which are the fundamental units for the alignment. (Each detector element has several hundred readout channels.) The alignment strategy for the SCT and Pixels relies basically on two methods, which are being developed in parallel:

• A global chi-squared approach, in which all the correlations among the thousands of individual detector elements are handled simultaneously, and which implies the inversion of a single very large matrix;
• An iterative approach, in which the detector elements are aligned separately and the correlations are fed in indirectly.

The initial conditions for these methods will be extracted from survey data. The precision with which the detector elements have been mounted leads to an expected accuracy of the inter-module distance of 10 to 20 μm for the Pixel layers/disks, and of 50 to 100 μm for the SCT layers/disks.

For the SCT, an online monitoring of the cylinders and disks distortions will be performed by the FSI (Frequency-Scanned Interferometry) system, providing a run-time constraint to the track-based alignment.

The statistics needed to achieve the target precision (a few μm) is of the order of 10 million tracks. It is expected that the alignment will be performed every 24 hours or so, in running mode.

The TRT detector has 350 000 straws whose position and calibration constants need to be determined. Initial survey, together with test-beam and cosmic-ray calibration, will provide a starting point with a spatial precision of about 200 μm.

All further calibration and alignment will have to use the collider data themselves. An iterative procedure is carried out where each iteration performs some of the tasks in the following sequence:

• The position correction and t ₀ for the channel is fitted to the average raw time as a function of track impact position. Internal TRT tracks are used for this.
• The corrections are fitted to rigid transforms of barrel modules or endcap wheel sectors relative to each other. The remaining corrections are fitted to a second degree polynomial in the second coordinate.
• The average track distance from the corrected wire is fitted to a constrained polynomial as a function of drift time.
• Using external or global tracks, the rigid transform of an entire barrel or endcap phi-sector is determined relative to the silicon system.

There are in principle three alignment and six calibration constants per lowest level detector element (the straw), including individual coordinate resolutions and high-threshold hit efficiencies. However, they are stored in structures that may flexibly share calibration values among larger or smaller groups of straws.

The statistics needed for obtaining a 10 μm alignment precision can be extrapolated from test-beam experience (25 000 tracks exposing 230 straws), which yields of the order of 10 million tracks with p _T > 2 GeV. A dedicated stream running before the Tier-0 reconstruction is foreseen to handle the TRT calibration task.

3.7.2 Liquid Argon and Tile Calorimeters

The goals of the ATLAS calorimeters are the accurate measurement of the energy of electrons, photons and jets, the measurement of missing transverse momentum, and particle and jet identification.

A resolution of better than (E in GeV) is required for EM calorimetry to guarantee 1% resolution on a light Higgs mass in the H → γγ or H → 4 e decay channels. Requirements on the energy resolution for the hadronic calorimeter are for |η| < 3 and for 3 < |η| < 5. Earlier studies documented in the ATLAS Physics TDR have indicated that such resolutions are adequate for the tasks of providing jet reconstruction as well as missing p _T measurements for the physical process of interest.

An energy-scale precision of about 0.1% is desirable for EM calorimetry for, for example, W mass measurement, Higgs and various SUSY searches. For heavy vector boson searches the dynamic range up to 5-6 TeV with 2% non-linearity is required, while below 300 GeV a linearity in the response of better than 0.5% is vital for the precision measurement of a light Higgs or top mass.

In order to meet these physics requirements a careful calibration of the calorimeter is performed in three steps:

• Electronic calibration.
• Electromagnetic scale calibration.
• Calibration of the reconstructed objects (clusters, particles, jets).

In ATLAS the energy deposited in the calorimeter is calculated using Optimal Filter (OF) method as:

where A _i are measurements1 of the calorimeter response with 40 MHz frequency, f _i are OF coefficients, C is the overall scale factor to convert ADC counts to energy, and P is the electronic pedestal. A similar formula is used to calculate signal time.

During special electronic calibration runs the scale factors to convert from ADC counts to nanoamperes (or picocoulombs in case of TileCal) as well as all OF coefficients are obtained for all 2 x 10 ⁵ channels. OF coefficients depend on the signal peaking time and usually 25 different sets are calculated in 1 ns steps. Various correlation matrices are also calculated and, in total, approximately 10 ³ parameters per channel need to be stored in the Conditions Database. The complete set of calibration coefficients in the database is expected to be updated every few days at ATLAS start-up and approximately once per month once stable running conditions have been achieved.

The EM scale calibration provides nA/GeV (or pC/GeV) conversion factors for all calorimeter channels. Initial calibration has already been performed over the last 10 years at a variety of beam tests and with detailed Monte Carlo studies. This calibration will be refined in situ during real data-taking. Both the OF coefficients and EM scale factors will be loaded from the Conditions DB to Digital Signal Processors (DSPs) at the start of every data acquisition run, so that the output from the DSP will be the energy calibrated at the EM scale.

The final calibration step, a calibration of final reconstructed objects, tries to compensate as much as possible for various inhomogeneities in the calorimeter and for differences in the electron and pion response. Once again, beam test measurements, Monte Carlo studies and in-situ calibration will be used to obtain the calibration coefficients.

For in situ calibration a large data sample (approximately one month of data taking) needs to be processed in order to achieve good uniformity and resolution. Nevertheless, fast reconstruction of special calibration streams, e.g. , should make it possible to achieve a global constant term of about 0.7% from a few days of data taking and to provide fast feedback to the online system. The expected rate of is about 1 Hz at low luminosity which means that prompt reconstruction should be feasible at the same rate.

3.7.3 Muon Spectrometer

The muon spectrometer is designed for a relative momentum resolution, δp _T /p _T < 1.0 x 10 ^-4 , for p _T > 300 GeV. In order to achieve this resolution by a three-point measurement, with the size and bending power of the ATLAS toroids, each point must be measured with an accuracy better than 50 μm. Monitored Drift Tube (MDT) chambers, built with high mechanical accuracy (30 μm), are used for this purpose over most of the solid angle covered by the spectrometer. However, in order to meet the design accuracy, the chamber deformations and positions must be constantly monitored by means of optical alignment systems (hence the name MDT), and the conversion from measured times to drift radii should be carefully calibrated in order to introduce an additional uncertainty no larger than 30 μm [3-20].

For wire-position monitoring, 7000 optical sensors are mounted in the barrel and 10 000 in the endcap, each sensor providing four measurements. This information is used to fit the geometry parameters describing the position (6 parameters) and the distortions (8 parameters) for each chamber. In total 9100 parameters are fitted in the barrel and 7700 in the endcap. In addition to the optical information, straight muon tracks previously selected by the trigger will be used and integrated into the alignment fit. Alignment information will be updated every 20 minutes.

The MDT calibration provides the time offset (t ₀ ) to better than 1 ns from the drift-time distribution for each of the 370 000 tubes and extracts the strongly non-linear space-time relationship through an auto-calibration procedure, making use of the tracks reconstructed in the MDT chambers. The space-time relationship depends on gas-drift properties and is sensitive to temperature and magnetic field variations: it is then computed for groups of tubes sharing similar working conditions. The total number of space-time relationships needed to describe the whole MDT system at a given time is of the order of a few thousand.

As discussed in detail in See A summary of the ATLAS MDT Calibration Model, ATLAS Internal Note in preparation the t ₀ and space-time relationship computation requires large muon samples. A minimum number of 20 000 hits per tube are needed for a good t ₀ computation. A rough stability check of t ₀ , to be repeated daily, requires at least 5 000 hits/tube. This number corresponds to about 100M muon tracks per day, a sample adequate also for the space-time relationship computation.

The means to collect the required statistics (through dedicated runs or through a continuous calibration stream running at few kHz) are currently under discussion. However, it should be noted that only MDT and trigger detector hits are needed, so the corresponding data size should be limited to about 1 kB/event.

The calibration is an iterative process but the most demanding operations in terms of CPU and data handling (decoding, access to conditions database, access to geometry, and pattern recognition) need only be performed once to obtain and store the drift times for each hit in a track segment. Currently, the best estimate of the time needed for the initial iteration of a muon track is 100 ms on a 2.5 GHz processor. As subsequent iterations just modify the space-time relationship for the hits and refit the track segments, they are much faster. The processing time will at most double after all iterations. Therefore, the processing of a 100M event data set will require approximately 6000 CPU-hours.

Validation of the calibration is needed before releasing the constants to the conditions database and will require additional CPU time. To provide the calibration constants within 24 hours of data collection, a minimum of 300 2.5 GHz processors is needed for all the calibration tasks listed above [3-22]. These processors could be part of Tier-0, or the CERN analysis facility, or could be located remotely. The pro's and con's of the two solutions are under investigation. Remote farms would make additional requirements on both network connections (but the necessary bandwidth is only of the order of 10 MB/s) and on database distribution (up-to-date DCS information is needed to perform the calibration).