Hadronic Shower Shape Comparison

In a similar shower shape study done for EM showers (resulting from normally incident 30 GeV photons), I repeated the shower shape calculation with normally incident 30 GeV charged pions. Figure 1 is the hadronic shower shape for incident pi+'s (red points are edep and blue points are Cherenkov), figures 2 and 3 are the 2-d distributions from which the profiles in figure 1 are computed.

52 positions across the horizontal axis of a cell (denoted "central cell") were selected and 100 30 GeV pions at normal incidence were sent to each position. A point was added to the 2d shower shape for every cell in the same row as the central cell that had a nonzero Edep or number of Cherenkov photons. The Edep shower shape was normalised by the incident energy of the pion. This was done because there is about a 30% fluctuation in the integrated energy deposited from the 30 GeV monoenergetic source, leading to a large spread in the shower shape fraction. The Cherenkov shower shape was normalised to the average number of Cherenkov photons produced for a 30 GeV pion, which is 2.64×105 photons. Again, this was done since there was large variation in the number of Cherenkov photons produced.

Figure 4 is the ratio of the shower profiles, Edep/Cherenkov. Unlike the EM shower, the Cherenkov shower seems to be wider than the Edep shower. The ratio is not as constant within the central cell, as it was in the EM shower. There is, however, a rise in the ratio for the neighbouring cells as one moves away from the central cell which is similar to the EM shower. The rise is steeper in the hadronic shower, however (slope of 0.4 for hadronic, compared to 0.16 for EM).


Figure 1: shower shape for 30 GeV pi+'s (red=edep; blue=cherenkov)

Figure 2 (left): energy depostion shower shape (2d dist);    Figure 3 (right): cherenkov

Figure 4: ratio edep/cherenkov for pi+ shower