ComPWA / compwa.github.io

Source code for the ComPWA Organization website
https://compwa.github.io
Apache License 2.0
5 stars 4 forks source link

DOC: add reports about T-matrix Riemann sheets #261

Closed Zeyna777 closed 5 months ago

Zeyna777 commented 5 months ago

[!TIP] See a temporary preview of the reports here:

  • TR-026: Riemann sheets of a single-channel $T$ matrix
  • TR-027: Riemann sheets of a $T$ matrix for two channels

The report implements and explains the 3D Riemann sheets figures of the PDG by showing exactly which formulas are used. As such the main targets of this report are:

  1. Using MatrixSymbol to derive Breit-Wigner with a phase space factor
  2. Compare the standard phase space factor to Chew-Mandelstam S-wave
  3. Use of the 'new' definition of SignedSqrt as described in Lecture 17 in order to get the correct sub-threshold behavior
  4. How to reach the second sheet from the standard S-wave Chew-Mandelstam

In https://github.com/ComPWA/K-matrix-research/issues/49, this will be extended into two channels, where we need to chose between Riemann sheets in the region between the two thresholds. But in itself these points are already worthy of its own, comprised report to document the sub-threshold behavior for the two Riemann sheets before moving on to the four Riemann sheets in two channels.

### Tasks
- [x] Remove sliders and change to `plotly`
- [ ] https://github.com/ComPWA/compwa-org/issues/206
- [x] Import square root definition (`PosArg` and `SignedSqrt`) from [Lecture 17](https://compwa.github.io/strong2020-salamanca/lecture17.html) for phase between -π and +π
- [x] Derive Breit-Wigner from single-channel K-matrix
- [x] Symbolic expressions for standard phase space factor and Chew-Mandelstam
- [x] Compare the two phase space factors in 1D plot (real part [should be same above threshold](https://ampform.readthedocs.io/en/0.14.x/usage/dynamics/analytic-continuation.html#visualization))
- [ ] Link to [Fig 50.4](https://pdg.lbl.gov/2023/reviews/rpp2022-rev-resonances.pdf#page=12) to compare PDG CM behavior
- [x] Find symbolic expression for second CM Riemann sheet)
- [ ] `assert` that difference above threshold [is 2iρ](https://shenvitor.github.io/strong2020-salamanca/lecture17.html#definition-of-the-g-s-functions)
- [x] Visualize both CM Riemann sheets in 3D with plotly
- [x] Do the plots with pcolormesh
- [x] (?) New visualizations from the PDG (omega and k)
- [ ] Explain how to associate the sheets to physical and unphysical
- [x] Split T-matrix visualization into phys., unphys., and transition plot (see [Fig 50.1](https://pdg.lbl.gov/2023/reviews/rpp2022-rev-resonances.pdf#page=2))
- [ ] Explanation of what we see and why this implementation works (add links to references)
- [x] Finalize: renumber TR notebook
### Tasks from https://github.com/ComPWA/RUB-EP1-AG/issues/102
- [x] Move extra notebooks under `temporary-kmatrix/` to [K-matrix-research](https://github.com/ComPWA/K-matrix-research) repo
- [x] **[TR-026](https://compwa--261.org.readthedocs.build/report/026.html)**: Make yellow line for branch cut start at branch point (3D plot)
- [x] **[TR-027](https://compwa--261.org.readthedocs.build/report/027.html)**: Indicate thresholds on 2D plots in 3D plot
- [x] **[TR-027](https://compwa--261.org.readthedocs.build/report/027.html)**: Zoom in to 3D plots
- [x] **[TR-027](https://compwa--261.org.readthedocs.build/report/027.html)**: Improve 3D labels (put TI before unphysical)
- [x] **[TR-027](https://compwa--261.org.readthedocs.build/report/027.html)**: Add titles to subplots
- [ ] **[TR-027](https://compwa--261.org.readthedocs.build/report/027.html)**: Explain singularities in the plot (which are relevant, which not)
- [ ] **[TR-027](https://compwa--261.org.readthedocs.build/report/027.html)**: Some explanation of final 3D plot
- [ ] **[TR-027](https://compwa--261.org.readthedocs.build/report/027.html)**: Send PDF for feedback
- [x] Switch to g0 instead of gamma0
- [x] Reopen this PR as @Zeyna777

Closes https://github.com/ComPWA/K-matrix-research/issues/46 Closes https://github.com/ComPWA/K-matrix-research/issues/49

review-notebook-app[bot] commented 5 months ago

Check out this pull request on  ReviewNB

See visual diffs & provide feedback on Jupyter Notebooks.


Powered by ReviewNB