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### The fit function

The basic peak shape is assumed to be a sum of asymmetric Gaussian with widths depending on the particle type (index ) and track length (number of points ): (1)

The basic parameter setting the width is which is fitted for all bins. The dependence on path-length is assumed to be . The exact dependence on is not a real concern, since the number-of-points distribution is quite strongly peaked in each phase space bin. The dependence of the width on the peak position is parameterised as a power law with power 0.625. This number was extracted from simultaneous fits to from TOF and from the TPC, as illustrated in Figs 1 . Fig 2 shows the result of the two-dimensional fits for the higher beam energies (40, 80 and 158 GeV). The points clearly cluster at values of slightly above 0.5, but significantly below unity. The value 0.625 was takena s a certal value and the sensitivity to this parameter was investigated and found to be small (a few per cent at maximum, for 40 and above).   Figure 1: (upper left) Distribution of the measurement from TOF and the measurement in the MTPCs for positive tracks close to mid-rapidity with transverse momenta close to 0.5 GeV. (lower left) Projection of the two-dimensional histogram on the axis. (upper right) Projection of the two-dimensional histogram ion the axis. In each projected histogram, a projection of the two-dimensional fit is also shown. Indicated are the pion, kaon and proton peaks. The Gaussian peaks are allowed to be asymmetric to reflect the remainder of the tail of the Landau-distribution which is still present in our truncated mean measure of . The total formula for fitting the distribution is then (2)

where are the amplitudes (yields) of each peak. The are numbers of tracks with a certain length, so the second sum is simply the weighted average of the line-shape from the different track-lengths in the sample.

The fit function is evaluated in the T49SumGaus class.   Next: Fit procedure Up: Fitting of histograms Previous: Fitting of histograms
Marco van Leeuwen 2009-01-14