Shower Detector Channels Calibration

  The problem of shower detector channels calibration is to define a coefficients for the amplitude value transformation to the energy deposition for every Preshower and Shower modules.

Magnitudes of amplitudes from each of shower detector blocks has been equalized preliminary by the high voltage using signals from cosmic rays.

As shower detector is intended for electro-magnetic showers registration and $e/\pi$ identification, for the calibration constants definition it necessary to have events, where electron was registered by the shower detector.

Total absorption of electron energy is performed in Preshower and Shower, so for electron energy definition the energy deposition in both of these detectors must be summed up.

Calibration constants are fitted by minimization of functional   $$\begin{eqnarray} \chi^2 = \sum_{i=1}^N \Big[ \sum_{j \in M_{ps}^i} C_j \cdot (A... ...+ \sum_{k \in M_{sh}^i} C_k \cdot (A_k^i-P_k) - P_{kin}^i \Big]^2.\end{eqnarray}$$

Here: $i=1\; ÷N$ -- number of selected calibration event; $j$ -- number of Preshower block, included into the cluster, reconstructed in the $i$-th event; $k$ -- number of Shower block, included into the cluster, reconstructed in the $i$-th event; $M$_psⁱ -- set of Preshower blocks numbers, included into the cluster, reconstructed in the $i$-th event; $M$_shⁱ -- set of Shower blocks numbers, included into the cluster, reconstructed in the $i$-th event; $A$_jⁱ -- amplitude value into the $j$-th Preshower block in the $i$-th event; $A$_kⁱ -- amplitude value into the $k$-th Shower block in the $i$-th event; $P$_j -- mean value of pedestal of the $j$-th Preshower channel; $P$_k -- mean value of pedestal of the $k$-th Shower channel; $P$_kinⁱ -- particle momentum corrected for kinematic broadening in the $i$-th event; $C$_j , $C$_k -- Preshower and Shower blocks calibration constants to be fitted. Total number of these constants is 144 ( 48 of them for Preshower, and 96 for Shower).

Calibration events (i.e. events where the charged particle, detected in spectrometer, is electron with the biggest probability) are selected on the following conditions:

• Data reconstruction in all of spectrometer detectors packages was successful;
• Only one particle has been detected in the electron arm Scintillators S1 and S2;
• Only one track has been reconstructed in the VDC system;
• Sum of amplitudes of Gas Cherenkov signals is greater than a certain threshold (300 channels);
• Only one cluster has been reconstructed in each of Preshower and Shower;
• Each of reconstructed clusters are coincident with the ``golden track''.

Calibration events selection is realized by program shcal_events, calibration constants calculation -- by program shcal_dofit (see sec.3.2).