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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 pathlength is assumed to be
. The exact dependence on is not a real concern, since
the numberofpoints 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
[2]. Fig 2 shows the result of
the twodimensional 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 2:
Value of the scaling parameter
for the width of the
peaks as a function of the position, as determined in
different bins of total momentum and . The different panels
show results at the three different beam energies. The dashed lines are at
.

The Gaussian peaks are allowed to be asymmetric to reflect the
remainder of the tail of the Landaudistribution 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 lineshape from the different
tracklengths 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
20090114