TKER Tower

A tracker tower consist of strips of silicon detectors arranged in pairs, with each element of the pair providing a separate measurement in one direction (X or Y) perpendicular to the tower axis. Reconstruction is initally done in separate Z-X and Z-Y projections. Projections are associated with each other whenever possible by matching tracks with respect to length and starting positions.

Multiple Coulomb Scattering (MS). In the absence of interactions, particle trajectories would be straight lines. However, the converter foils needed to produce the interactions (as well as the rest of the material in the detector), cause the particle to under go multiple Coulomb scattering (MS) as they traverse the tracker, complicating both pattern recognition (i.e., finding the particles) and track fitting (determining the particle trajectories), particularly for low-energy electrons and positrons. Pattern recognition must therefore be sensitive to particles whose trajectories depart significantly from straight lines.

The presence of multiple scattering also has implications for the fitting procedure. Without MS, deviations from a straight line are due solely to measurement errors, which occur independently at each measurement plane and are distributed about the true straight track. In the presence of MS, there are real random deviations from a straight line,and these deviations are correlated from one plane to the next. For example, if an individual particle scatters to the right at one plane, it is more likely to end up to the right of the original undeviated path than to the left.

Covariance Matrix. These correlations can be quantified in a covariance matrix of the measurements, which is calculated from the momentum of the particle and the amount of scattering materal between the layers. The dimension of this matrix is the number of measurements. Solving for the track parameters in terms of the measurements involves inverting this matrix. If there is no MS, the matrix is diagonal, and the inversion is trivial; MS introduces off-diagonal elements, which complicates the inversion.

Kalman Filter (KF). The Kalman Filter technique can be useful in both stages of particle reconstruction. First, the initial position, direction, and energy of the particle is estimated. The energy of the particle is based on the response of the calorimeter, and the starting point and direction are derived by looking for three successive hits that line up within some limits.

From this starting point, the track is extrapolated in a straight line to the next layer. Using the estimate of the energy and the amount of material traversed, a decision is made whether the hit in the next layer is within a distance from the extrapolated track allowed by the expected multiple scattering and the uncertainty of the initial estimate. If so, the hit is added to the track, and the position and direction of the track at this plane are modified, incorporating the information from the newly added hit.

The modified track is now extrapolated to the next plane, and the process continues until there are no more planes with hits. All the correlations between layers have been properly taken into account but, at each step, only MS between two successive planes need be considered, and the covariance matrix required is that of the parameters.

The track parameters at the last hit have now been calculated using the information from all the preceding hits. To get the best estimate of the initial direction of the photon, however, it is necessary to know the parameters at the first hit, close to the point where the photon converts to an electron-positron pair.

Smoothing. At this point, smoothing is applied, i.e., the KF is "run backwards" from the last plane to the first, using the appropriate matrices. After smoothing, the track parameters, and their errors have been calculated at each of the measurement planes; in particular, the first plane.

Fig. 3 shows the result of the fitting algorithm applied to a cosmic ray track. "Fit to a cosmic ray track (solid line) in the tracker. Reconstructed energy centroids in the calorimeter (boxes) line up with the track. The track extrapolates to the fired ACD tile."

Calorimeter

A high-energy photon traversing material loses its energy by an initial pair-production process
(λ → e⁺e^-) followed by subsequent bremsstrahlung (e → λ) and pair production, resulting in an electromagnetic cascade, or shower. The scale length for this shower is the radiation length, the mean distance over which a high-energy electron loses all but 1/e of its initial energy.

The calorimeter provides information about the total energy of the shower, as well as the position and direction , and shape of the shower; or of the penetrating nucleus or muon. It consiststs of eight layers of ten CsI(TI) crystals ("logs") in a hodoscopic arrangement, i.e., alternatively oriented in X and Y directions, to provide an image of the electromagnetic shower. It is designed to measure photon energies from 20 MeV to 300 GeV and beyond.

To comfortably contain photons with energies in the 100-GeV range requires a calorimeter at least twenty radiation lengths thick. However, weight constraints forced limiting Fermi's calorimeter to only ten radiation lengths in thickness; thus, it cannot provide good shower containment for high-energy photons.

The mean fraction of the shower contained at 300 GeV is about 30% for photons at normal incidence, at which the energy observed is very different from the incident energy; the shower development fluctuations become larger, and the resolution quickly decreases.

Correcting for Shower Leakage: Method 1 (Shower-profiling) – fit a mean shower profile to observed longitudinal profile. The profile-fitting method proves to be an efficient way to correct for shower leakage, especially at low-incidence angles when the shower maximum is not contained. After the correction is applied, the resolution (as determined from a simulation) is 18% for on-axis TeV photons – an improvement by a factor of two over the result of correcting the energy with a response function based on path length and energy alone.

Correcting for Shower Leakage: Method 2 (Leakage-correction) – use the correlation between the escaping energy and the energy deposited in the last layer of the calorimeter. The last layer carries the most important information concerning the leaking energy: the total number of particles escaping through the back should be nearly proportional to the energy deposited in the last layer.

Both correction methods significantly improve the resolution. The correlation method is more robust, since it does not rely on fitting individual showers; but its validity is limited to relatively well-contained showers, making it difficult to use at more than 70 GeV for low-incidence-angle events.

Event Selection

Background rejection performs the function of particle identification, determining whether the incoming particle was a photon.With the high charged-particle flux in space, shower fluctuations in background interactions can mimic photon showers in non-negligible numbers. Cuts are applied to the events to suppress the background.

First, all events are reconstructed, but only events in which none of the ACD tiles fired are considered. The cut eliminates 90% of triggered events. Most of the rejected events consist of charged particles, but a few legitimate photons are also rejected if, for example, one of the particles in the shower exits the detector through the sides or top, and fires an ACD tile.

Note: This cut could be applied before any reconstruction, but reconstructing all events is useful in comparing the data with simulations.

Next, the reconstructed tracks are tested for track quality, formed from a combination of goodness-of-fit, length of track, and number of gaps on the track. Also, an energy-dependent cut removes events with tracks that undergo an excessive amount of scattering.

Finally, it is required that there be a downward-going vee in both views, and that both tracks in the vee extrapolate to the calorimeter. (This will introduce some inefficiency for high-energy photons, and for highly asymmetric electron-positron pairs. Vees with opening angles that are too large, >60^o, are rejected. Such vees generally come from photons with energies below the range of interest.)

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Other development paths: additional cuts involving extra particles in the event and extra hits not associated with tracks. ======= looking at the spatial distribution of energy in the calorimeter as a way of distinguishing electromagnetic from hadronic showers, and from the showers of photons traveling upward through the instrument.

Fig. 4 shows a photon that converts in the tracker and deposits energy in the calorimeter. "a reconstructed photon. Note the vee in the tracker, the energy deposited in the calorimeter, and the absence of any signals in the ACD.

Event Reconstruction in a Nutshell - Toby (Baseline-Preliminary Design Review, Jan 9, 2002)

• Sequence of operations, each implemented by one or more Algorithms, using TDS for communication.

• Trigger analysis: is there a valid trigger?

• Preliminary CAL to find seed for tracker.

• Tracker recon: pattern recognition and fitting to find tracks and then photons in the tracker  (uses Kalman filter).

• Full CAL recon: finds clusters to estimate energies and directions.

• Must deal with significant energy leakage since only 8.5 X0 thick.

• ACD recon: associate tracks with hit tiles to allow rejection of events in which a tile fired in the vicinity of a track extrapolation.

• Background rejection: consistency of patterns:
  • Hits in tracker.
  • Shower in CAL: alignment with track, consistency with EM shower.

Gleam Output: ROOT Files

Try Googling: LAT +glast +Transient Data Store +Recon +ROOT

see RootIo
calibRootData
reconRootData
mcRootData
overlayRootData

RootConvert
RootDisplay

commonRootData

rootTestData
rootUtil

The role of ROOT files is somewhat confusing until one realizes that ROOT serves as an I/O manager in the GLEAM implementation. All Gleam output is in ROOT format. To read and analyze these files you will need to use an application capable of reading in ROOT files. The easiest path is to use the ROOT analysis environment.

Reconstructed output files are saved in digi ROOT tree format; see digiRootData (detector) and reconRootData (Acd, Tkr, Cal)

Output ntuples are also in ROOT format. (See Gleam Outputs.)

ROOT files as Recon input. Files saved as digiRootData can also serve as inputs to the recon engine(s) should a re-reconstruction be desired.

Note to self: Need sanity check from Heather.