The Muon Finder Algorithm

A traversing muon deposits energy in detector elements along its flight path. The pattern of hit detector elements is usually isolated from the overlap event because of the high granularity of the ZEUS detector and the low occupancy of most events. During visual scan the trained physicist identifies such a pattern easily because it usually forms a straight line.

MUFFIN tries to find all patterns of hit detector elements which form a straight line. It uses tracks from the muon detectors and calorimeter condensates (see section 6.3.1) to find these patterns. For each pattern a set of parameters is calculated and compared to the parameters describing a traversing muon. If MUFFIN were to use a brute force method and just calculate all combinations of tracks and condensates it would take too much time to evaluate an event. Instead MUFFIN uses several tricks to speed up the search for a candidate pattern:

• MUFFIN stops after a single traversing muon has been identified by the trigger conditions.
• MUFFIN temporarily removes all detector hits which belong to a traversing muon candidate from the event. Only if the remaining event fails the trigger conditions for the event (e.g. the CC cut), the candidate pattern is further evaluated. This algorithm is based on the assumption that the event consists of a background event that would normally not pass the trigger and a traversing muon which is responsible for the event passing the trigger.
• MUFFIN uses ray tracing algorithms to speed up the most time consuming part of the processing which is to find the cells which are hit by a muon trajectory. Upon initalization MUFFIN creates 27 evenly distributed volumes ``containers'' (three in each coordinate direction) which contain the entire calorimeter. Each of these volumes contains again 27 volumes, ``boxes''. Each of those boxes contains calorimeter cells. When MUFFIN tries to find the cells hit by a muon it first checks which ``containers'' are hit by the muon and then inside each hit container it checks which ``boxes'' are it. Only then will it check cell by cell.

  In order to test whether a cell is hit MUFFIN has two radii available, the radius of the largest sphere around the cell center that is fully contained in the cell and the radius of the smallest sphere around the cell center that contains the cell . By testing the distance of the cell center to the trajectory MUFFIN can determine quickly whether the trajectory hits the cell ( ) or not ( ). Only for the remaining cases ( ) MUFFIN performs a precise geometric check testing whether the trajectory hits any of the cells surfaces.