Performance

Before the final installation, the light output of each crystal was calibrated by using cosmic rays. The crystal by crystal variation of about 10 % was measured. The channel by channel gain variation of electronics was found to be about 5 %. After the installation into the Belle detector in the fall of 1998, the consistency and stability of the calibration constants have been monitored with cosmic rays which penetrated through more than three neighboring counters. The stability of the crystal gains has been observed to be better than 1 % during a period over three months [67].
The absolute energy calibration has been carried out by using Bhabha and events. With a Bhabha sample, the calibration constant of th counter can be obtained by minimizing defined as

(21)

where is the expected energy of the Bhabha electrons. This value is known as a function of $\theta$ in the asymmetric collider. The function is the correction factor due to the shower leakage and the front material effect, which was determined by a Monte Carlo simulation. This function was introduced in the minimization in order to maintain the consistency between real and Monte Carlo events. The minimization was carried out by taking $\sim$ 8000 $\times$ 8000 sparse matrix inversion into account. Approximately 50 events per counter were used for this calibration.
After the KEKB collider was commissioned in June 1999, a large number of Bhabha and events have been accumulated to perform the absolute counter-by-counter calibration. The energy resolution was achieved to be 1.7 % for the barrel ECL, and 1.74 % and 2.85 % for the forward and backward ECL, respectively, as shown in Fig. .

Figure: Energy resolutions measured from Bhabha event samples : overall, barrel, forward end-cap and backward end-cap.

Two-photon invariant mass distributions in hadronic events are shown in Figs.  (a) and (b). The clear peaks of $\pi^0$ and are seen at each nominal mass and the energy resolution has been achieved to be 4.9 MeV for $\pi^0$ and less than 10 MeV for .

Figure: Two photon invariant mass distribution for hadronic events (a) in and (b) in where each photon energy was required to be greater than 30 MeV in the barrel region.

During the operation period of KEKB, ECL received radiation doses associated with the beam background. Thus the light output of each CsI counter has decreased. The instantaneous dose rate is proportional to the total current through the PIN photodiode and the accumulated dose can be calculated by integrating the dose rate over the period of time. An increase of 2.5 nA/crystal for one year ($\sim$10$^7$ s) corresponds to 100 Rad. During the period of June and July 1999, ECL was irradiated with the dose of 4 and 13 Rad/crystal for the barrel and innermost backward end-cap ECL, respectively, as shown in Figs.  (a) and (b). Fig. shows the degradation rate of light output as a function of $\theta$. The light output decreased about 1 % in the barrel region and about 2 % in the end-cap regions.

Figure: Radiation dose at barrel ECL (upper) and end-cap ECL (lower) as a function of time.

Figure: Degradation of the light output of the ECL counters as a function of $\theta$-id.