Understanding alpha distribution: dominant component

[mmikhasenko]

The distribution of alpha_x alpha_y and alpha_z looks intriguing (bizarre).
There are two effects that play important role:

• alignment rotation for the Lambda and Delta subsystems make the angle of the alpha field dependent on the kinematic
• Various chains interfere significantly modifying the alpha

It leads to an impression that the alpha field is ill defined and can change drastically with a small update of the model.
We need to demonstrate that is it not the case.

Some ideas to investigate

• Surely the LHCb fit systematics will give the critical validation telling really how much we know about the alpha field
• There might be other variables one can construct that reflect importance of statistics. Not all regions of the Dalitz are equally important since have different statistic uncertainty as they are differently populated. From the other side, the product of the intensity and alpha gives the polarization-dependent angular part, which however, gives the modulation with respect to the unpolarized intensity.
• Check the regions of high interference. Search on the Dalitz the areas which are 90% determined by 1 decay chains. The alpha in the selected areas should match the alpha for the isolated chain (but aligned in the same way)

[mmikhasenko]

I wrote a paragraph in the paper on this. We will need a few plots demonstrating the effects which I plan to make.

It already looks cool in my head. Imagine coloring the Dalitz based on the highers conributing resonance.
It will be disjoint islands. Surely, not all isobars will be present. Wondering wheather will be uncolored areas, where interference dominates.

Actually, for the paper, I just want to select a few islands and show how isolated map in this island looks like. For L** or D** it makes sence to plot unaligned in addition to show that we have the Wigner Ry rotation that is understood