# Invariant Mass Distribution

The two-photon invariant mass distribution can be roughly broken up into four pieces, seen below*.

Fig. 1 The black histogram is the invariant mass of all pion candidates (photon pairs) with pt in the given range.  I simulate each of the four pieces in a slightly different way.  My goal is to understand each individual piece of the puzzle and then to add all of them together to recreate the mass distribution.  This will ensure that I properly understand the backgrounds and other systematic errors associated with each piece.  To understand how I simulate each piece, click on the links below.

2.  Eta Peak

Once all of the four pieces are properly simulated they are combined to best fit the data.  The individual shapes of are not changed but the overall amplitude of each piece is varied until the chisquared for the fit is minimized.  Below are plots for the individual bins.  Each plot contains four subplots that show, clockwise from upper left, the four individual peices properly normalized but not added; the four pieces added together and compared to data (in black); the ratio of data/simulatio histogramed for the bin; and a data simulation comparison with error bars on both plots.

Bin 1:  5.2 - 6.75 GeV/c Bin 2:  6.75 - 8.25 GeV/c Bin 3:  8.25 - 10.5 Bin 4:  10.5 - 16.0 Below there is a table containing the normalization factors for each of the pieces for each of the bins as well as the total integrated counts from each of the four pieces (rounded to the nearest whole count.)

Table 1: Normalization factors and total counts
 bin low norm. low integral pion norm. pion integral eta norm. eta integral mixed norm. mixed integral 1 121.3 9727 146.4 75103 20.91 5290 0.723 44580 2 77.34 4467 77.81 51783 20.86 6175 0.658 34471 3 40.13 3899 29.41 23687 12.93 6581 1.02 18630 4 5.373 1464 5.225 8532 2.693 3054 0.521 6276

Table 2 below contains, for each source of background, the total number of counts in the mass window and the background fraction [background/(signal+background)].

Table 2: Background counts and Background Fraction
 Bin Low Counts Low B.F (%) Eta Counts Eta B.F (%) Mixed Counts Mixed B.F (%) 1 2899 3.60 1212 1.50 4708 5.84 2 2205 3.96 917 1.65 3318 5.96 3 2661 9.29 633 2.21 1507 5.26 4 858 8.56 170 1.70 591 5.89

* Note:  An astute observer might notice that the histogram in the top figure, for hPtBin2, does not exactly match the hPtBin2 histogram from the middle of the page (Bin 2.)  The histogram from the middle of the page (Bin 2) is the correct one.  Fig. 1 includes eta from [-1,1] and thus there are more total counts; it is shown only for modeling purposes.

Groups: