CDC

Cosmic ray data were taken with the solenoid operating at its nominal 1.5 T field. A positive high voltage was applied to the sense wires, and the field wires were connected to the end-plates and kept at ground. The sense wire high voltages, typically 2.35 kV, were adjusted layer-by-layer to keep the same gas gain (several $\times 10^4$) for different cell sizes. The chamber was operated at a constant pressure slightly above one atmosphere.
The standard trigger and data acquisition system developed for operation in the Belle experiment was used in the cosmic ray run. Back-to-back cosmic ray events were triggered by the Belle TOF counter system [40]. The event timing was determined with a 0.7 ns resolution using TOF information. The acceptance for cosmic ray tracks was determined by TOF which has a smaller polar angle acceptance than CDC.
We accumulated a sample of $5 \times 10^7$ cosmic ray tracks. After requiring tracks to go through the interaction region ($-2.0$ cm $\le dz \le 3.0$ cm and $\vert dr \vert \le 2$ cm), 56,743 events remain, where $dr$ is the closest distance in the $r$-$\phi$ plane and $dz$ is the closest distance in the $z$ coordinate.
Extensive works on the optimization of the drift-time versus distance function were carried out by minimizing residual distributions for the function iteratively. Separate functions were used for each layer and each incident angle of the track with respect to the radial direction. A correction for the signal propagation time along the wire was applied after the first 3-D track reconstruction. Corrections were also made for the effects of wire sag and distortions of the end-plates caused by the wire tension by using the measured data. The relative alignment of the cathode and inner end-plates with respect to the main end-plates was determined using cosmic ray data. The rotations and translations thus acquired were found to be less than 200 $\mu$m, consistent with the estimated construction accuracy.
Figure shows the $z$ dependence of $B_z$, the axial component of the magnetic field, measured before the installation of CDC. The non-uniformity of the magnetic field is as large as 4 % along the central axis. The Kalman filtering method [41] was used to correct the effects due to the non-uniformity of the measured magnetic field. Fig. shows the spatial resolution as a function of the drift distance. Near the sense wire and near the cell boundary the spatial resolution is significantly poorer. The spatial resolution for tracks passing near the middle of the drift space is approximately 100 $\mu$m.

Figure: Measured axial component of the magnetic field produced by the Belle solenoid. The nominal value of the magnetic field inside CDC is 1.5 T. The difference between the minimum and maximum values along the central axis is about 4 %.

Figure: Spatial resolution as a function of the drift distance.

The $p_t$ resolution as a function of $p_t$ is shown in Fig. . The solid curve indicates the result fitted to the data points, i.e. $(0.201 \pm 0.003) ~p_t \oplus (0.290 \pm 0.006)/\beta)$ in % ($p_t$ in GeV/c). The dashed curve shows the ideal expectation for $\beta = 1$ particles, i.e. $(0.188 ~p_t \oplus 0.195)$ in %. No apparent systematic effects due to the particle charge were observed.

Figure: $p_t$ dependence of $p_t$ resolution for cosmic rays. The solid curve shows the fitted result (0.201 % $p_t \oplus$ 0.290 %/$\beta$) and the dotted curve (0.118 % $p_t \oplus$ 0.195 %) shows the ideal expectation for $\beta$ = 1 particles .