28/06/2018
Comparison of 4C fits to K+ -> pi+ pi0 , pi0 -> gamma gamma for DATA Run 6646 and MC.
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Introduction.
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These are energy-momentum constrained least squares fits to the beam and spectrometer tracks
plus two gammas measured in the LKr.
The fits were made using Blobel's APLCON for 12 parameters
subject to 4 constraints. See APLCON
and talk with examples of use .
Giuseppe's K2pi selection code, with small modifications, was used to provide
input for the fits.
The fit parameters were momentum, dx/dz and dy/dz for the four measured particles.
Initially, the covariance matrix was taken to be diagonal with error estimates from
arXiv:1703.0850 and NIM A 574 (2007) 433.
Subsequently for both data and MC, the errors have been adjusted to get the rms of the
pulls within ~10% of unity.
The object was to examine the chi**2 and pulls of the fit to both data and MC
to check consistency with the K2pi channel, check the error estimates, identify systematic errors,
and determine the influence of the fit on the measurement accuracy of the
tracks and missing mass.
RESULTS
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Figs Fig. 1A ( 20 plots ) and Fig. 1B ( 20 plots ) show histograms of the distributions of results of the fits
for data and MC, respectively.
Plot 1 shows that for data and MC the width of missing mass distribution to the K+pi+ system
is reduced by about a factor four as a result of the fit; similarly, Plot 2 shows a
reduction of a factor 2 in the gamma-gamma mass. The widths of the fitted masses
agree within 7% for the data and MC.
The CDA, Plot3, is not significantly influenced by the fit. The data and MC differ
in width by about 10%.
Plot 4 shows the chi**2 and probability of the fits. Both data and MC
show a significant tail to the chi**2 distribution which is also evident
as a peak at low probability in the otherwise flat probability distribution.
Plots 5 and 6 show the reduction in parameter errors as a result of the fit.
The remaining plots show the pulls with plots 19,20 and the Table below summarising the
pulls for the twelve fitted track parameters. The '*' in the Table indicate significant
deviations of the mean pulls from zero.
Mean Pull
Parameter Data MC
Track P -0.175 0.025
dx/dz -0.204 -0.045
dy/dz 0.099 0.089
Beam P 0.200 -0.054
dx/dz 0.543* -0.147
dy/dz -0.135 -0.395*
Gam 1 P 0.001 -0.128
dx/dz -0.586* 0.216
dy/dz 0.152 0.470*
Gam 2 P -0.050 0.039
dx/dz -0.526* 0.203
dy/dz 0.152 0.405*
Fig. 2 ( 6 plots ) shows the pull distributions
for MC events with fit probability less than 1%. These plots suggest that the low
probability fits originate from mismeasurement of the gammas.
Fig. 3 ( 6 plots ) shows the corresponding plots
for data. The lack of statistics make a clear identification of the origin of
the low probability peak difficult although the pulls are consistent with
mismeasurement of the gammas.
Conclusions
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1) After error correction, ~95% of data and MC events give
a 4C fit with the expected flat probability distribution.
2) The fit probability distribution has a peak
at low probability that implies that ~5% of the selected events
are incompatible with the assumed K2pi hypothesis.
For the MC events, the pulls suggest that these low probability
events result from mismeasurement of the gammas in the LKr.
3) There are indications of systematic errors in reconstruction
of about half a standard deviation. For the data, this is for the
beam and gamma dx/dz variables. For the MC, the systematic effects
are in the beam and gamma dy/dz track parameters
(see the variables marked '*' in the above Table).
For reference:
Fig. 2A ( 20 plots ) DATA 4C fit, energy-momentum constrained. Measurement errors uncorrected.
Fig. 2B ( 20 plots ) MC 4C fit, energy-momentum constrained. Measurement errors uncorrected.
~/aplcon
see notes 27-29/06/18