The Carnegie Mellon Partial Wave Analysis Project
Status Report on July 27, 2000

The first successful fit of the blind weight has been performed for the mass bin near the peak of the a2. The fit distributons compared to the blind events are found in the next update. While the fit converges reasonably quickly, and the results look very reasonable for someting in the a2 mass region, we still have some problems.

[1] There is still no way to lock one phase in the pwa-fitter. As such, there are extra ambiguities that confuse the answer.

[2] There is no program to compute the correct errors from the fit. While we will compute them from the diagonals of the covariance matrix, this really throws away a lot of information.

[3] There is no good mechanism to extend the fitter to a whole series of bins in mass and t. The current mechanism relies on the generation of enormous sets of files which is fraught with the potential for making huge errors. This may require the writing of a new fitter to get around this.

 Here are the production amplitudes from the fit:
V_2++1+ = (0.35062,0.28254);
V_2++1- = (0.35982,0.25958);
V_1++1+ = (0.54024,0.66662);
V_1++1- = (0.54106,0.69821);
V_2-+1+ = (-0.057921,0.055808);
V_2-+1- = (-0.067000,0.062874);
V_1-+1+ = (-0.079113,0.091867);
V_1-+1- = (-0.068795,0.087479);
fcn call: 840
nevents: (10724,0)
normalization: (1,0)

The next step will be to repeat this fit near the peak of the 2(1670) to see what is there. At that point, we need to step back and access what we are really going to be able to do in the next month. As noted earlier, we are still not comfortable with what we write down for the unpolarized amplitudes, and without an error calculator and phase locking, most of the results will be very hard to understand and explain. For convenience, we append the weighting function that was used to the end of this message. It looks messy because there is no loop construct to describe the normalization integrals. (NOTE: these weights have been generated by hand. The prolog tool to produce them has not been up to the task; it produces overly complicated, long files that are impossible to verify).

par V_1-+1- ;
par V_2++1- ;
par V_1++1- ;
par V_2-+1- ;

event_loop:

Rpos = V_1-+1+ * 1-+1+.amps + V_1++1+ * 1++1+.amps +
V_2-+1+ * 2-+1+.amps + V_2++1+ * 2++1+.amps ;
Rneg = V_1-+1- * 1-+1-.amps + V_1++1- * 1++1-.amps +
V_2-+1- * 2-+1-.amps + V_2++1- * 2++1-.amps ;

fcn = fcn - log( absSq( Rpos ) * wt3ref_bin1.denmat[0 , 0] +
absSq( Rneg ) * wt3ref_bin1.denmat[1 , 1] );

normalization:
fcn = fcn + nevents * (
absSq(V_1++1+)*wt3ref_bin1.00[1++1+.amps , 1++1+.amps] +
V_1++1+ * conj(V_2++1+)*wt3ref_bin1.00[1++1+.amps , 2++1+.amps] +
V_1++1+ * conj(V_1-+1+)*wt3ref_bin1.00[1++1+.amps , 1-+1+.amps] +
V_1++1+ * conj(V_2-+1+)*wt3ref_bin1.00[1++1+.amps , 2-+1+.amps] +

V_2++1+ * conj(V_1++1+)*wt3ref_bin1.00[2++1+.amps , 1++1+.amps] +
absSq(V_2++1+) *wt3ref_bin1.00[2++1+.amps , 2++1+.amps] +
V_2++1+ * conj(V_1-+1+)*wt3ref_bin1.00[2++1+.amps , 1-+1+.amps] +
V_2++1+ * conj(V_2-+1+)*wt3ref_bin1.00[2++1+.amps , 2-+1+.amps] +

V_1-+1+ * conj(V_1++1+)*wt3ref_bin1.00[1-+1+.amps , 1++1+.amps] +
V_1-+1+ * conj(V_2++1+)*wt3ref_bin1.00[1-+1+.amps , 2++1+.amps] +
absSq(V_1-+1+)*wt3ref_bin1.00[1-+1+.amps , 1-+1+.amps] +
V_1-+1+ * conj(V_2-+1+)*wt3ref_bin1.00[1-+1+.amps , 2-+1+.amps] +

V_2-+1+ * conj(V_1++1+)*wt3ref_bin1.00[2-+1+.amps , 1++1+.amps] +
V_2-+1+ * conj(V_2++1+)*wt3ref_bin1.00[2-+1+.amps , 2++1+.amps] +
V_2-+1+ * conj(V_1-+1+)*wt3ref_bin1.00[2-+1+.amps , 1-+1+.amps] +
AbsSq(V_2-+1+)*wt3ref_bin1.00[2-+1+.amps , 2-+1+.amps]

+

absSq(V_1++1-)*wt3ref_bin1.11[1++1-.amps , 1++1-.amps] +
V_1++1- * conj(V_2++1-)*wt3ref_bin1.11[1++1-.amps , 2++1-.amps] +
V_1++1- * conj(V_1-+1-)*wt3ref_bin1.11[1++1-.amps , 1-+1-.amps] +
V_1++1- * conj(V_2-+1-)*wt3ref_bin1.11[1++1-.amps , 2-+1-.amps] +

V_2++1- * conj(V_1++1-)*wt3ref_bin1.11[2++1-.amps , 1++1-.amps] +
absSq(V_2++1-) *wt3ref_bin1.11[2++1-.amps , 2++1-.amps] +
V_2++1- * conj(V_1-+1-)*wt3ref_bin1.11[2++1-.amps , 1-+1-.amps] +
V_2++1- * conj(V_2-+1-)*wt3ref_bin1.11[2++1-.amps , 2-+1-.amps] +

V_1-+1- * conj(V_1++1-)*wt3ref_bin1.11[1-+1-.amps , 1++1-.amps] +
V_1-+1- * conj(V_2++1-)*wt3ref_bin1.11[1-+1-.amps , 2++1-.amps] +
absSq(V_1-+1-)*wt3ref_bin1.11[1-+1-.amps , 1-+1-.amps] +
V_1-+1- * conj(V_2-+1-)*wt3ref_bin1.11[1-+1-.amps , 2-+1-.amps] +

V_2-+1- * conj(V_1++1-)*wt3ref_bin1.11[2-+1-.amps , 1++1-.amps] +
V_2-+1- * conj(V_2++1-)*wt3ref_bin1.11[2-+1-.amps , 2++1-.amps] +
V_2-+1- * conj(V_1-+1-)*wt3ref_bin1.11[2-+1-.amps , 1-+1-.amps] +
AbsSq(V_2-+1-)*wt3ref_bin1.11[2-+1-.amps , 2-+1-.amps]
)

Last Updated on the 27'th of July, 2000 by Curtis A. Meyer.