Least Squares fits to K+ ->  mu+ nu
-----------------------------------

These are least squares fits subject to the constraint
that the  nu mass is zero.
The fits were made using Blobel's APLCON for 6 parameters
subject to 1 constraint.
The fit parameters were momentum,  dx/dz,dy/dz for the K+ and mu+.

The object was to check the pulls and chi**2 of the fit, and to examine
the influence of the fit on measurement accuracy.

Fig. 1 6 plots Plot 1 shows the unfitted missing mass distribution. Note the non-gaussian tails. Plot2 shows the pull distribution together with a fitted gaussian distribution plus the chi**2 p-value distribution. The pull distribution is approximately gaussian with sd close to unity, but the distribution is slightly leptokurtic. The p-value distribution suggests that errors are, in general, overestimated and that ~40 events are badly measured. Plot 3 shows the chi**2 distribution with mean ~ 1.0 as would be expected for a one-constraint fit. The distribution has the long tail expected for non-gaussian errors. Plots 4,5 explore the effect of cuts on probability, cda and chisq on the missing mass distribution. As would be expected, the probability and chisq cuts remove the non-gaussian tails. Plot 6: This shows the ratio of fitted error to measurement error for the six fitted variables. The one-constraint fit improves the track momentum measurement accuracy by ~ 10%. This needs further study.