Angular Distribution from various Waves.

We have started to fit the blind-test data for 100% Polarized photons. However, before starting, we wanted to see what the angular distributons look like. We have examined 4 possible waves, a 1⁺⁺, a 1^-+, a 2⁺⁺ and a 2^-+ wave, all produced via pion exchange. Our plan is to fit 2 to 4 bins from the blind test distributions. The first two will be near the peak of the a₂(1320) and near the peak of the ₂(1670). The following four plots are what the weights would look like for the four waves for a narrow bin near the peak of the a₂(1320). (Note: There is no resonance shape imposed in the fit).

[1⁺⁺ Wave] [2⁺⁺ Wave] [2^-+ Wave] [1^-+ Wave]

In order to generate the above weights, we have used the following camp file, where for the above plots we have only turned on the corresponding production strengths, V_(JPC)(M epsilon). Something rather interesting is how the (770) appears washed out in the 1^+- data set. It is also striking how the distribution can help select out different naturalities of the final state particle, particularly for the ⁺ distributions versus _GJ.

The Dalitz plots for these four are shown below.

1⁺⁺ 2⁺⁺
1^-+ 2^-+

Given below is the simple camp file that produces the distributions.

rmat gen1_bin1.denmat;

damp 2++1+.ramps;
damp 2++1-.ramps;
damp 1++1+.ramps;
damp 1++1-.ramps;
damp 2-+1+.ramps;
damp 2-+1-.ramps;
damp 1-+1+.ramps;
damp 1-+1-.ramps;

damp 1-+1+nsym.amps;
damp 1-+1-nsym.amps;

complex Rpos;
complex Rneg;

complex V_2++1+ ;
complex V_2++1- ;
complex V_1++1+ ;
complex V_1++1- ;
complex V_2-+1+ ;
complex V_2-+1- ;
complex V_1-+1+ ;
complex V_1-+1- ;

event_loop:

V_2++1+ = (1,1);
V_2++1- = (1,1);
V_1++1+ = (2,2);
V_1++1- = (2,2);
V_2-+1+ = (0,0);
V_2-+1- = (0,0);
V_1-+1+ = (0,0);
V_1-+1- = (0,0);

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

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

wt = ( absSq( Rpos ) * gen1_bin1.denmat[0 , 0] +
absSq( Rneg ) * gen1_bin1.denmat[1 , 1] );