Alignment to Magnetic Field

Since the magnetic field in the muon tracking region is non-uniform, the tracking stations must be aligned to the field in order to accurately determine the momentum of tracks from their trajectory through the field. To determine what the exact alignment requirements are, the GEANT simulation code was used again. Muons from upsilon decay were tracked through the magnetic field and their hits in the tracking stations were recorded. The hits were then fit to a trajectory using the same magnetic field map that produced the hits, but displacing it by a fixed amount in (x,y), and z. The resulting mass resolutions versus the amount of displacement in the z direction are shown in Figure 4. For the (x,y) displacement, the input map was shifted from (x,y) to (x+offset,y+offset). The resolution versus 'offset' is shown in Figure 5.

 
Figure 4: The upsilon mass resolution in the North arm versus a z displacement of the magnetic field map.  

 
Figure 5: The upsilon mass resolution in the North arm versus a (x,y) displacement of the magnetic field map. The offset in the figure was applied as (x,y)(x+offset,y+offset).  

As can be seen, the spectrometer as a whole can actually be displaced a fair amount before the mass resolution begins to suffer. The z displacement is the least sensitive since the magnetic field integral does not change quickly if the map is just displaced in the z direction. The magnetic field integral does change rather quickly with as shown in table 1 so the mass resolution depends more strongly on a displacement in the x and y directions. No change in the mass resolution was seen for displacements up to 1 cm, a small increase in the resolution was seen for a displacement of 2.5 cm, and at 5 cm displacement the mass resolution increased by 20% to 256 . Given these studies, we require that the spectrometer as a whole be aligned to the magnetic field to at least 2.5/4=0.6 cm in x and y, and only has to be aligned to within several centimeters in the z direction.

  
Table 1: The integrated magnetic field, , in Gaussm for each arm obtained by W. Sondheim.