phys: investigate symbolic Dalitz Plot Decomposition

[mmikhasenko]

Preview can be viewed here.

The notebook is extended from the TR-018 (#129) to provide a different angle to the three-body decay distribution.

The unpolarized matrix element is casted to a bilinear form on dynamic function $R$ for every LS coupling.
Parity conservation is assumed.

To-do list

• generalize to arbitrary spins of the final particles
• generalize to several isobars in subchannel
• add the step from the angles to polynomials in the Mandelstam variables

[redeboer]

there are just some bugs in the code itself

that I can fix quickly. I need to teach myself to run the notebook thought before committing. haha

I'm having a look at the code now, it may be a bit difficult to rewrite the notebook to a generic form. I think ideally you need some data structure that contains all the info you need for each decay, like LS values in the production node and in the decay node and parent spin.

There's some info on developing with notebooks here. Feedback is welcome.
https://compwa-org.readthedocs.io/develop.html#documentation

If you have the installed a virtual environment with dev requirements, you can do:

tox -e nb docs/report/018.ipynb  # run the notebook in terminal
tox -e doc  # fast documentation build
tox -e docnb  # build documentation with cell outputs

For editing metadata in notebooks, it's best to work with Jupyter Lab. That also renders the myst syntax a bit better

jupyter lab

[mmikhasenko]

Okay. It would be better to work this out in a more rigid way in a library (e.g. ComPWA/ampform#277). But a report would be fine for now, to show that it works.

Certaintly.

[mmikhasenko]

I think ideally you need some data structure that contains all the info you need for each decay, like LS values in the production node and in the decay node and parent spin.

yes, that is what I did before with my julia code.
The only thing that the amplitude builder cares about is

• j0,j1,j2,j3
• chain_ind, j, LS, ls.
  Later, for convenience one can compute possible ls, and LS based on the parities.

[mmikhasenko]

If you have the installed a virtual environment with dev requirements

Do you mean

pip install -e .[dev]

not sure I installed the dev

[redeboer]

Do you mean

pip install -e .[dev]

not sure I installed the dev

Yep. Or to be even safer:

pip install -e .[dev] -c .constraints/py3.8.txt  # your python version here

[redeboer]

The only thing that the amplitude builder cares about is

• j0,j1,j2,j3
• chain_ind, j, LS, ls.
  Later, for convenience one can compute possible ls, and LS based on the parities.

88725fb encapsulates that info as a (mutable) class. Could be rewritten by nesting for instance. I didn't push more modifications to avoid merge conflicts.

[redeboer]

This PR has become superseded by https://github.com/ComPWA/ampform-dpd and https://lc2pkpi-polarimetry.docs.cern.ch.