The Carnegie Mellon Partial Wave Analysis Project
Status Report on July 12, 2000

We have had a major break through with the polarized a2 today. After staring at algebra for many hours, it became clear that the pwa2000 weight was not written interms of a reflectivity basis, rather it was in some sort of combined refelctivity-helicity basis that reall was not applicable. In order to do this required us also to write the photon density matrix in the reflectivity basis as well. When all of this was done, and the weights written down and tested, the distributions agree extremely well with what was produced by Adam's weight. We will shortly produce a weight-weight plot like for the unpolarized case, but do anticipate it will agree very well.

This also gives us some hope that the a1 amplitudes will be more tractable than the 10 pages of description generated by pwa2000, and that we may be back on track here.

Correct Weight

rmat rawRef.denmat;

damp rawp.amps;
damp rawn.amps;

complex R_-1_1_r+;
complex R_-1_1_r-;
complex R_1_-1_r+;
complex R_1_-1_r-;

complex V_-1_1_r+;
complex V_-1_1_r-;

event_loop:

V_-1_1_r+ = (1,1);
V_-1_1_r- = (1,1);

R_-1_1_r+ = V_-1_1_r+ * rawp.amps;
R_-1_1_r- = V_-1_1_r- * rawn.amps;
R_1_-1_r+ = 1.0 * V_-1_1_r+ * rawp.amps;
R_1_-1_r- = -1.0 * V_-1_1_r- * rawn.amps;

wt = absSq( R_-1_1_r+ ) * rawRef.denmat[1 , 1]
+ absSq( R_-1_1_r- ) * rawRef.denmat[0 , 0]
+ absSq( R_1_-1_r+ ) * rawRef.denmat[1 , 1]
+ absSq( R_1_-1_r- ) * rawRef.denmat[0 , 0];

Original Incorrect Weight from PWA2000

rmat rawP1y.denmat;

damp rawp.amps;
damp rawn.amps;

complex R_1_-1_1_1;
complex R_1_-1_-1_1;
complex R_-1_1_1_1;
complex R_-1_1_-1_1;
complex R_1_-1_1_-1;
complex R_1_-1_-1_-1;
complex R_-1_1_1_-1;
complex R_-1_1_-1_-1;
complex R_rawp.amps_1_-1_1_1;
complex R_rawn.amps_1_-1_1_-1;
complex R_rawp.amps_-1_1_1_1;
complex R_rawn.amps_-1_1_1_-1;

event_loop:
R_rawp.amps_1_-1_1_1 = (-1. , 1.0);
R_rawn.amps_1_-1_1_-1 = (-1., 1.0);
R_rawp.amps_-1_1_1_1 = (1.0 , 1.0);
R_rawn.amps_-1_1_1_-1 = (1.0 , 1.0);

R_1_-1_1_1 = R_rawp.amps_1_-1_1_1 * rawp.amps;
R_1_-1_-1_1 = R_rawp.amps_-1_1_1_1 * rawp.amps;
R_-1_1_1_1 = R_rawp.amps_-1_1_1_1 * rawp.amps;
R_-1_1_-1_1 = R_rawp.amps_1_-1_1_1 * rawp.amps;
R_1_-1_1_-1 = R_rawn.amps_1_-1_1_-1 * rawn.amps;
R_1_-1_-1_-1 = R_rawn.amps_-1_1_1_-1 * rawn.amps;
R_-1_1_1_-1 = R_rawn.amps_-1_1_1_-1 * rawn.amps;
R_-1_1_-1_-1 = R_rawn.amps_1_-1_1_-1 * rawn.amps;

wt = absSq(R_1_-1_1_1) * rawP1y.denmat[0 , 0]
+ absSq(R_1_-1_-1_1) * rawP1y.denmat[1 , 1]
+ R_1_-1_1_1 * conj(R_1_-1_-1_1) * rawP1y.denmat[0 , 1]
+ R_1_-1_-1_1 * conj(R_1_-1_1_1) * rawP1y.denmat[1 , 0]

+ absSq(R_-1_1_1_1) * rawP1y.denmat[0 , 0]
+ absSq(R_-1_1_-1_1) * rawP1y.denmat[1 , 1]
+ R_-1_1_1_1 * conj(R_-1_1_-1_1) * rawP1y.denmat[0 , 1]
+ R_-1_1_-1_1 * conj(R_-1_1_1_1) * rawP1y.denmat[1 , 0]

+ absSq(R_1_-1_1_-1) * rawP1y.denmat[0 , 0]
+ absSq(R_1_-1_-1_-1) * rawP1y.denmat[1 , 1]
+ R_1_-1_1_-1 * conj(R_1_-1_-1_-1) * rawP1y.denmat[0 , 1]
+ R_1_-1_-1_-1 * conj(R_1_-1_1_-1) * rawP1y.denmat[1 , 0]

+ absSq(R_-1_1_1_-1) * rawP1y.denmat[0 , 0]
+ absSq(R_-1_1_-1_-1) * rawP1y.denmat[1 , 1]
+ R_-1_1_1_-1 * conj(R_-1_1_-1_-1) * rawP1y.denmat[0 , 1]
+ R_-1_1_-1_-1 * conj(R_-1_1_1_-1) * rawP1y.denmat[1 , 0];

Last Updated on the 12'th of July, 2000 by Curtis A. Meyer.