Support final states with equal particles

[redeboer]

This requires keeping track of state IDs in the Particle class.

[redeboer]

@mmikhasenko what is a nice test case for DPD with a final state that has identical particles in the final state? One of the radiative $J/\psi$ decays comes to mind, but $\gamma$ is a bit particular.

[mmikhasenko]

Xib2pK-K-

There is LHCb paper with DPD

https://cds.cern.ch/record/2765808/files/2104.15074.pdf

[redeboer]

Ah then that may even be a nice test case for https://github.com/RUB-EP1/amplitude-serialization, right?

[redeboer]

Xib2pK-K- There is LHCb paper with DPD https://cds.cern.ch/record/2765808/files/2104.15074.pdf

See https://compwa.github.io/ampform-dpd/xib2pkk.html

[mmikhasenko]

Looks great!

• How do you know if symmetrization is done correctly. I remember there are non-trivial permutation properties for helicity couplings due to pK vs Kpi in chains?

• Do you reproduce the fit fractions?

if you can compute this matrix for any arbitrary couplings, it is possible to recover the right couplings by comparing the two tables

[redeboer]

How do you know if symmetrization is done correctly. I remember there are non-trivial permutation properties for helicity couplings due to pK vs Kpi in chains?

Isn't that a matter of setting the correct couplings?

Do you reproduce the fit fractions?

No, none of the parameters are matched yet and the dynamics lineshapes are also not yet the same. For now, the main point of the notebook is to show that a symbolic model can be generated for decay structures with equal particles in the final state. The matching even goes more in the direction of https://github.com/RUB-EP1/amplitude-serialization/discussions/15.

[mmikhasenko]

sounds good

[redeboer]

How do you know if symmetrization is done correctly. I remember there are non-trivial permutation properties for helicity couplings due to pK vs Kpi in chains?

Isn't that a matter of setting the correct couplings?

Actually AmpForm+QRules has a mechanism of doing this. But the implementation is hard to follow (qrules, ampform), so it is hard to port it here.

The question is what is the best way to automate treatment of symmetrization. Should/Can it be encoded into the default values of the couplings or should it be treated mathematically in the amplitude model?

[redeboer]

See Richman 1984, p.35, "Symmetrization of Helicity States for Identical Particles".

[mmikhasenko]

I thought of it down the road.

1. vanila dpd implementation
2. discrete symmetries operations
3. mapping of odd topologies,

   [[1,2],3]

   and

   [[1,3],2]

   Once the code knows what rotations to apply to this configurations, the question on symmetrization is trivial.