As described in Section 3.4.3, the MWPC system determines the position of the electron hit from the delay times, the time it takes the signal to reach both ends of the delay line (see Eq. 3.4). In addition to a hardware discrimination (via pre-amplifier threshold) against noise in the delay signal lines, the following off-line software cut procedure was applied in order to ensure the quality of imaging.
Since the delay lines have a fixed length, the sum of the delay times is expected to be constant, i.e., for the Z-direction, , where ZL and ZH are the delay time measured at beam upstream and downstream ends of the delay lines, respectively, and the sum is multiplied by the dispersion constant, dispZ with a length dimension for convenience. In reality, however, a small but finite amount of time is required between the ionizing electron and the current being induced in the cathode wires, mainly due to the drift time of electrons to the anode, which creates a distribution in SUMZ (and ) reflecting the proximity of the initial hit to the anode. There is a strong correlation between distributions of SUMZ and SUMY, since they are due to the same physical process for both z and y wires, i.e., electron drift to the anode (e.g. if ionization occurs very close to the anode, both SUMZ and SUMY are small due to a small drift time).
Because of this correlation, the plot of SUMZ vs. SUMY for good events occupies only a small area of two dimensional space (a long rectangular box oriented in a diagonal direction), so making independent cuts on each parameter SUMZ and SUMY (corresponding to accepting a large square box on the plane) is rather inefficient in terms of noise elimination. We therefore performed a linear transformation of the coordinate system, introducing new uncorrelated variables, and . With these coordinates, applying the cuts becomes straightforward. DIFSUM, the difference in the sums, typically had a smaller dispersion compared to that of SUMZ or SUMY and SUMSUMlarger. Therefore a small interval for DIFSUM cut ( or mm for this analysis) and a large interval for SUMSUM cut ( mm), cover the entire parameter regions for good events, while efficiently eliminating the noise.
Good hits in each of three MWPCs, thus passing the cut, were fitted to a straight line with the least-squares method. Cuts in the chi-square (<4) and the fit-residual for the second of three chambers (<10 mm) for both z and y variables, were applied to ensure a reasonable fit.
For this analysis, all the above cut values described in this section were taken to be relatively non-restrictive, the largest effect being about 20% rejection due to the chi-square cut, in order to prevent biasing of the data set and to allow for maximum statistics.