Angular Distribution Plots for the PWA Study

We have generated angular distributions for 128,664 polarized and 153,459 unpolarized events for the reaction

a⁺₂(1320) ^{0 + + + -}

Events are genrated using Monte-Carlo code written by Paul Eugenio, and then weighed using our implementation of Adam Szczepaniak's weighting function.

Events are generated polarized in the lab frame. We then rotate to the Gottfried-Jackson frame and define to be the angle between the polarization and the normal to the production plane. We expect these angular distributions for polarized photons to demonstrate the dependence discussed in Curtis Meyer's calculations, namely:

cos(2)-sin(2)

where is the real part and is the imaginary part of the off-diagonal elements in the density matrix of the a⁺₂(1320). In the case where the photon beam is unpolarized, and are both zero so the distributions should be flat. Looking at for = near 0, 180^o corresponds to choosing =0. Looking at for near 90^o corresponds to setting =0.

Polarized Events

Plots of ^++- invariant mass, invariant mass, |t|, and |t| vs.^++- invariant mas are shown without cuts.

In the angular distributions, we first plot vs , then for events having near 0, 180^o and also for near 90^o. The polarized data demonstrates the predicted dependence. The only cuts used in these distributions are those on , as indicated above the last two columns.

To further enhance the depencence, we show these same angular distributions with a 200 MeV wide mass cut (670 MeV to 8709 MeV) on the appropriate two pion invariant mass.

The cos distributions are repeated with the addition of a mass cut.

Distributions of the helicity angles are shown below. No cuts are applied.

Unpolarized Events

Distributions of for events satisfying the indicated cuts on are flat as expected. Again, no cuts are applied, except those stated above the last two columns.

We show these same angular distributions with a 200 MeV wide mass cut (670 MeV to 8709 MeV) on the appropriate two pion invariant mass. No other new cuts are applied.

and cos distributions are shown below. The only applied cuts are on those indicated on .

The cos distributions are repeated with the addition of a mass cut.

Distributions of the helicity angles are shown below. No cuts are applied.