Results

As one of the results of the above described procedure the relative locations of had to be determined. The location of 2C24A beam position monitor and $\gamma$-Profiler were read off the design drawing 28405-E-0034 and related drawings. The $z$ location of the crystal part of HyCal came from survey data. The coordinates of these beam line devices were collected in a table below,

device	x (cm)	y (cm)	z (cm)
$\gamma$-Profiler	-0.8563	0.0322	980.30
HyCAL	0.0	0.0	731.89
Target	-0.063	0.07	0.0
HARP 2H00	0.0	0.012	-65.73
BPM 2C24A	0.0	0.0	-1049.99

In a similar manner as above, the beam position and entrance angles at the face of crystal part of the calorimeter were determined using BPM and $\gamma$-Profiler information. The analysis was done for only a handful of runs shown in a table below.

Table 1: $\pi ^0$ runs used in the study. First 4 rows are high quality data, while the quality of two bottom ones is a little worse.

4979 4980 4981 4982 4984 4985 4987 4988 4989 4998

4999 5001 5002 5003 5004 5012 5013 5016 5018 5030

5032 5033 5034 5035 5037 5039 5041 5042 5043 5044

5047 5050 5051 5054 5055 5056 5057 5058 5059

4977 4983 4986 5000 5005 5006 5007 5014 5015 5017

5024 5025 5036 5038 5040 5053

Inspection of the results shows that the average $x$ position at HyCal was quite stable, but $y$ distribution showed two well defined peaks. Therefore, the results are presented as two separate sets, runs before run 5024 and runs after this run. The run 5024 belongs to the latter.

Figures 7 and 8 show the distributions of beam position in transverse directions at HyCal detector. While $x$ coordinate seems to be well centered, $\sim -0.01$mm with the width of $\sim 0.025$mm, for both sets, $y$ coordinate is off-centered by $\sim -1.4$mm, with the width of $\sim 0.1$mm, for the first set and $\sim -1.2$mm, with the width of $\sim 0.03$mm, for the other. It is worth mentioning that beam position as reported by 2C24A monitor has not changed between the both sets.

Figure 7: Beam position results for runs before run 5024.

Figure 8: Beam position results for runs after run 5024, which is included in this set.

Similarly, the distributions of directional cosines were divided into two sets and Figures 9 and 10 demonstrate the results. Again, in the $y$ direction two distinct average values are observed. In the course of the analysis directional cosines of the beam trajectory relative to HyCal were determined. In Figure 9 the right panel shows the distribution of $\theta_z$, an angle between the beam and $z$-direction. The other two angles are primed to distinguish their different definition. These are the angles that beam makes with its projection on the perpendicular plane. For both $\cos(\theta_x)$ and $\cos(\theta_y)$ the angles are close to 90$^o$ therefore one can write $\cos(\theta_\alpha) = \cos(\pi/2-\theta^\prime_\alpha) = \sin(\theta^\prime_\alpha)$ where $\alpha = x$ or $y$ and $\theta_\alpha + \theta^\prime_\alpha = \pi/2$.

Figure 9: Beam angular stability results for runs before run 5024. See text for angle definitions.

Figure 10: Beam position results for runs after run 5024.

The widths of the $\theta^\prime_y$ and $\theta_z$ distributions for runs prior to run 5024 are comparable with the angular resolutions of the experiment while the angular distributions widths after run 5024, inclusively, tend to be within experimental resolutions.