[!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:
Using MatrixSymbol to derive Breit-Wigner with a phase space factor
Compare the standard phase space factor to Chew-Mandelstam S-wave
Use of the 'new' definition of SignedSqrt as described in Lecture 17 in order to get the correct sub-threshold behavior
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
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:
MatrixSymbol
to derive Breit-Wigner with a phase space factorSignedSqrt
as described in Lecture 17 in order to get the correct sub-threshold behaviorIn 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.
Closes https://github.com/ComPWA/K-matrix-research/issues/46 Closes https://github.com/ComPWA/K-matrix-research/issues/49