DOC: add manual notebook for lambda-K-Pi

[shenvitor]

Using the exact same model for Eta-Pi-P as a test for Lambda-K-Pi in manual and flexible symbolic sympy way.

Tip

Preview here

[shenvitor]

The Dalitz plot in this PR looks awesome rn 🍡 !
(hopefully, it's correctly formulated, I will double-check later next week)

[redeboer]

I don't see the use of creating an (almost) exact copy of the eta pi p notebook. That one is more for playing around with a super simple amplitude model that has three subsystems and one resonance in each, where you can then see the effect of angular momentum. As we know, that model is not physical.

For $\Lambda K \pi$, we have to step up the game. This is supposed to be a model that formulates the model from the (preferably) ampform-dpd notebook manually, so that it can then be tweaked with a proper treatment of e.g. #58.

What is currently missing are multiple resonances, treatment of spin of the final-state particles, spin alignment, etc. That also makes the UI design not suitable. I would therefore start to try to reproduce the model (symbolic only!) from ampform-dpd.ipynb.

[redeboer]

Why call this manual-symbolic, not manual?

[shenvitor]

I don't see the use of creating an (almost) exact copy of the eta pi p notebook. That one is more for playing around with a super simple amplitude model that has three subsystems and one resonance in each, where you can then see the effect of angular momentum. As we know, that model is not physical.

For $\Lambda K \pi$, we have to step up the game. This is supposed to be a model that formulates the model from the (preferably) ampform-dpd notebook manually, so that it can then be tweaked with a proper treatment of e.g. #58.

What is currently missing are multiple resonances, treatment of spin of the final-state particles, spin alignment, etc. That also makes the UI design not suitable. I would therefore start to try to reproduce the model (symbolic only!) from ampform-dpd.ipynb.

I think the idea here is to have multiple notebooks for symbolic manually in different levels of complications, from simplest to some more complicated ones later in this reaction section.

[redeboer]

I think the idea here is to have multiple notebooks for symbolic manually in different levels of complications, from simplest to some more complicated ones later in this reaction section.

That's fine, but to have multiple copies of the same idea is just a maintenance burden. The 'manual' eta pi p notebook is just a pedagogical exercise: some spinless initial and final state ("p gamma to eta pi p" is even misleading) with one resonance per subsystem. In fact, the only difference between the two notebooks now are the labels of those three imaginary resonances and the imaginary final state (see #101 (comment)).

In the end, what we want to achieve is a physical description of $p\gamma \to \Lambda K \pi$, that is, with correct description of the production process, all dominating resonances in each subsystem, and a proper treatment of spin alignment of the final state. There is no generic package that can do that, so we need to go through a process of manually formulating each of these components to gain understanding of its behaviour.

[redeboer]

I'm fine with adding this notebook, but a lot needs to be done to this PR first, for instance:

• rotations for each decay node (see model from ampform.ipynb and ampform-dpd.ipynb)
• a sum over an arbitrary number of resonances

[shenvitor]

Okay, I see your points. Yup we can make it more accurate than now.

[shenvitor]

Rejected by @redeboer, so close this as not planned for now, but we can still see the record if we need it in the future.