Fig. 1 ( 17 plots ) Plot 1 shows the K+ pi+ missing mass and gamma-gamma mass before and after fitting. Both are equal to the pi0 mass after fitting - as they must be. Note the non-gaussian tails. Plot 2 shows the cda before and after fitting. Plot 3 shows the chi**2 p-distribution together with the chi**2 distribution. There is a long tail to the chi**2 distribution that results in the the low probability peak; the size of the peak suggests that ~ 30% of events are badly measured. The probability distribution outside the low-probabilty peak indicates that the measurement errors are, on average, underestimated. Plots 4,5 : This shows the ratio of the fitted error to the measurement error for the six fitted variables. The 6-constraint fit results in substantial reductions in the error for beam, straw and gamma momenta, and for track angles. Plots 6-17 show the pulls for each fitted parameter. In general, the rms of the pulls are within 50% of unity showing that the estimates of the measurement errors are approximately correct. However the beam and gamma dx/dz show evidence of systematic measurement errors. These features are examined in more detail in the following 4C fits. 4-constraint fits. ------------------ These are fits in which energy and momentum are constrained. There are no constraints on the CDA or gamma-gamma mass; thus the effect of the fit on these parameters can be measured. Fig 2A uses the 'standard' error estimates that were used in the 6C fit. Fig 2B has errors corrected by the standard deviation of the pulls in Fig 2A.
Fig. 2A ( 20 plots ) 4C fit, energy-momentum constrained. See, in particular, plots 1 and 2 for the effect of fitting on the width of the missing mass to the K+ pi+, and on the gamma-gamma mass. The fit reduces the missing mass distribution by about a factor four while the gamma-gamma mass is reduced by about a factor two. Systematic shifts are evident for, in particular, the beam and gamma dx/dz pulls.
Fig. 2B ( 20 plots ) 4C fit, energy-momentum constrained. The meaurement errors have been corrected to get the pulls closer to unity. A comparison of Figs 2 A and B shows that, as a result of the error change: 1) There is little change in the missing mass and gamma-gamma distributions. 2) The probability distribution of the fit has a larger flat component and the low probability peak is reduced from ~20% to ~7%. 3) The systematic shifts in the pulls for the beam and gamma dx/dz remain at about 0.5 sd. Conclusions ----------- In general, the measurement errors are underestimated. There is evidence of systematic errors in the beam and gamma dx/dz at the 0.5 standard deviation level, Non-Gaussian errors are present at the 7% level. ~/aplcon ./clg6C2.sh > clg6C2.out 6C fit ./clg6Ctest2.sh > clg6Ctest2.out 6C fit errors corrected readfile6C2.F readfile6C2.kumac ./clg4C2.sh 4C fit ./clg4Ctest2.sh 4C fit errors corrected