The Carnegie Mellon Partial Wave Analysis Project
Status Report on 30 October, 2000
We have performed a fit to the blind weight function using not only the
known waves, but also additional wave which are known not to be in the
data set. As before, we make a comparison between simply generated events,
and events which have been run through the Hall D Monte Carlo program.
The first two plots show the ln(Liklyhood) and the total intensity from
the fits. This ln(Likelyhood) is not normalized, so the maximum tracks the
number of events in each bin. The important thing to note is that the values
for the events which have been run through the Hall D Monte Carlo are not very
much smaller than the generated events.
The following show the intensities for the two reflectivities of the four
strongest waves. The 1++ corresponds to the a1(1260),
the 2++ corresponds to the a2(1320), the 1-+
corresponds to the  1(1600)
and the 2-+ corresponds to the
2(1670).
In addition to the intensities, we can also show the phase of the positive
reflectivity wave with respect to the 1++ wave. These show nice
stabel structure.
There are also two rather weak waves in this data set. The 1++ D-wave
and the 2-+ F-wave. The intensities for these are shown below, as
well as the phase difference between the D and S wave for the 1++
and the F and P waves for the 2-+ waves. We expect that these phases
should be either 0 or 180o, and at least in the regions where we
have non--zero fits, this seems to be the case.
We also introduced 6 waves into the fit for which no amplitude was generated.
These correspond to the following, an pair of a3 waves,
3++(1+) and 3++(1-), a pair
of a2 waves in the M=2 state, 2++(2+) and
2++(2-) and finally a pair of
2 waves
in the M=2 state, 2-+(2+) and
2-+(2-). These waves all come out zero in the fit,
even with the events that have been run through the Monte Carlo. There
appears to be no leakage from the generated waves into these waves.
Finally, we have examined the phase between the positive and negative
reflectivity waves for the four dominant waves. It can be shown that
in the case of pure one pion exchange, there is a sign differemce between
the two amplitudes, which should appear as a phase of 180o. We
did not impose such a phase on the fit, but one can see that it falls out
naturally as shown below.
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