Method Description

The approach adopted in this study relied on double arm Compton scattering data and Hall B BPM readout to determine the position of the $\gamma$-Profiler with respect to HyCal. This procedure is detailed below.

• Initially, double-arm Compton scattering data (runs 4868, 4871, 4873, 4875, 4877 on Beryllium and runs 4943, 4944, 4945, 4946, 4965, 4966, 4967, 4970, 4971, 4973 on Carbon) were used to find the intersection points for the lines connecting both clusters. These values were used to bring the calorimeter to (0,0) position in transverse directions, $x$ and $y$.

  Figure 1: Distributions of intersection points for lines connecting coordinates of two clusters.

  

  A typical intersection point distributions are shown in Figure 1 for run 4965 taken on a Carbon target.

• This information was then combined with Hall B 2C24A BPM readouts that were fed into the data stream as a part of EPICS events during the experiment. For each run distributions of BPM $x$ and $y$ values were fitted to a Gaussian to determine the mean value. Typical fits, for run 4944, are shown in Figure 2.

  Figure 2: Gaussian fits to 2C24A BPM readouts.

  

• Assuming that there are no magnetic field induced deflections of the electron beam past 2C24A BPM, parametric equations for a straight line,

  
  

  $$x_{\gamma} = x_{BPM} + (x_{HyCal} - x_{BPM})*t$$ (1)

  $$y_{\gamma} = y_{BPM} + (y_{HyCal} - y_{BPM})*t$$ (2)

  $$z_{\gamma} = z_{BPM} + (z_{HyCal} - z_{BPM})*t$$ (3)

  
  

  were employed to project the beam trajectory to the face of $\gamma$-Profiler $x$ scintillators. Its intersection with the $xy$-plane yielded the position of the beam at that detector. Figure 3 shows all the information pertaining to that part of the analysis.

• These calculated values were then compared to the $\gamma$-Profiler scaler readouts that was also part of the EPICS information during the data taking. Before this was possible however, the response of this detector was fitted to a triple Gaussian distribution in order to get the mean position of the beam. This was done on an EPICS-event-by-EPICS-event basis. Typical fits to $\gamma$-Profiler light output are shown in Figure 4. The distributions shown pertain to the run 4943.

  Figure 3: Information needed to determine offsets of the $\gamma$-Profiler.

  

  Figure 4: Triple Gaussian fit to $\gamma$-Profiler light output turned out to be very stable parametrization of that signal through the entire running period.

  

• The weighted average for those position differences in $x$ and $y$ directions were then taken as offsets that needed to be subtracted from the $\gamma$-Profiler measured $x$ and $y$ values. In Figure 5 the differences are plotted as a function of run number. Distributions in Figure 6 test this alignment for one of the $\pi ^0$ runs, namely run 5018.

Figure 5: The results of $\gamma$-Profiler offset determination

Figure 6: The result of application of the found offsets to the $\gamma$-Profiler positions.