Emc Global Alignment (I)

  • These are the current alignment constants. The first line in each block is for the barrel, the second for the endcap. The values in each line are deltaX ,deltaY, and deltaZ in cm, and rotX, rotY, and rotZ in rad.

Related items:

Idea:

When speaking about the alignment of the Electromagnetic Calorimeter (Emc) it is meant to be with respect to the Drift Chamber (Dch) as the system of reference. The idea is to use electrons and positrons from Bhabha-events, and compare their angular track parameters as measured by the Dch with the center of the electromagnetic shower, reconstructed by the Emc. The advantage of electrons and positrons over muons for instance is there large transverse shower dimension, which lead to a better resolution of the cluster position

First Study: As a first study the impact-point of the track with the Emc is compared to the reconstructed cluster position. q and f of the impact-point, and the cluster centroid are accessible in the micro-database. The position of the centroid is derived from the cluster-center, which was than projected onto the front face of the crystal. Note, that the q of the cluster is modified with a small correction. This correction accounts for the fact that the crystal is not pointing towards the IP, thus a plain projection onto the front-face of a crystal would introduce an error.

Alignment without correction for 3-dimensional cluster-center

The plots show the difference between track-impact-point and center-of-gravity of the cluster for (1) the angle q, (2) the angle f, (3) q versus cos(q), and (4) f versus cos(q)

Explanation: So far I have no clear explanation for the behavior of Dq across the calorimeter.

For the Df distribution although, two effects might contribute. Since all events are Bhabha's, the entries on the left side in plot (4) come from positively charged positrons, while the entries on the right are from negative electrons. It seems that the different directions of bending of the track in the magnetic field and the energy deposition happening somewhere inside the crystals explains the shift from the mean into opposite directions. The shift seems to be relatively constant for energies in the range above a couple of MeV. This will be explored next.

The second effect might be a real misalignment, because the two peaks ( for electrons and positrons ) are not equally distant to 0.

Second study: In this I try to remove the effect of the assignment of the cluster-center to the front-face of the crystals.

The longitudinal energy deposition is described by a gamma distribution.

                        

The position of maximum energy deposition and the mean of the shower are then:

                        

Together with the information about the electrons direction of flight at the crystal surface, this allows the calculation of the cluster-center in 3 dimensions. The result shows this correction to be effective.

The difference between positively and negatively charged tracks/clusters disappeared. The leftover shift is due to misalignment between drift chamber and calorimeter.

How big is the Misalignment?

It is now of interest, what sort of shift and/or rotation or even twisting of the calorimeter we have to deal with. First think about the distortion in the x-y-plane. Therefore I look on the Df in different regions of the calorimeter. The detector I divided into 8x8 regions. One region covers 15 crystals in phi and 7 in theta. Endcap and backward barrel are left out in the plot since they had too low statistics.

Plotted is the shift of the azimuthal angle. The scale of the shift is in mrad.

Same as a lego plot.

Entangle the distribution: Different scenarios of the Emc-distortion would show up in the plot above in distinct ways.
  • Rotation of the Calorimeter around the z-axis
    => raise or lower the distribution by a constant value
  • Translation of the Calorimeter into one direction as a whole
    => sinusoidal shape convoluted into the distribution
  • Translation of the Calorimeter into different directions at the forward and backward end
    => transversal patterns

Global alignment has the freedom of adjusting 6 parameters (3 for translation and 3 for rotation). Plan is to model the effect of these parameters on the distribution of the shift and fit them.

First more statistics is needed.