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ComPWA / qrules

Rule-based particle reaction problem solver on a quantum number level
https://qrules.rtfd.io
Apache License 2.0
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Handle CP eigenstates #7

Open redeboer opened 4 years ago

redeboer commented 4 years ago

Original issue: "Handle K0 to K0S transition"

In our current particle_list.yml, we define an isospin projection for $K^0_S$ and 𝐾⁰(L). https://github.com/ComPWA/expertsystem/blob/3f41dce0ba14c3ea120c51baf59e65162d13d20f/expertsystem/particle_list.yml#L368-L375 This is incorrect, because these states are superpositions of the mass eigenstates 𝐾⁰ and 𝐾̅⁰ and do not have a well-defined isospin projection. See also ComPWA/expertsystem#200.

This touches on a larger issue: we should distinguish between Particle instances as the observable states (mass eigenstates) and QuantumState (used internally) as eigenstates of the fundamental forces. That would also allow us to handle 𝐢𝑃-parity conservation (see planned features).

spflueger commented 4 years ago

I'm not sure if such a transition is really needed, since we are just interested in if a transition is possible or not (and why not). K0 are the quark level eigenstates and K0_S/L the CP eigenstates and are just related via K_S ~ K0 + K0_bar or K0 ~ K0_S + K0_L. So this is just some mixing which cannot be broken by definition.

spflueger commented 4 years ago

I'm not sure if such a transition is really needed, since we are just interested in if a transition is possible or not (and why not). K0 are the quark level eigenstates and K0_S/L the CP eigenstates and are just related via K_S ~ K0 + K0_bar or K0 ~ K0_S + K0_L. So this is just some mixing which cannot be broken by definition.

To clarify this comment a bit further. It means that one should only use K0 and K0_bar in the reaction definitions, even if the actual final state would be a K_S or K_L. This is ok, since we don't support CP conservation yet. Regarding ComPWA/expertsystem#200 this would mean we simply drop the particles K_S and K_L.

Regarding CP eigenstates and conservation I have the following suggestions. Since the K_S/L states do not have well defined quark flavors, it is impossible to use such states in the rules of strong interaction. Same counts for K0 and K0_bar, which do not work for weak interactions. Therefore some functionality to do "basis transformations", taking K0 and K0_bar to K_S and K_L and vice versa, is needed.

More generally with the help of the basis transformation functionality we need to allow strong eigenstates to be converted to weak eigenstates if possible (obviously not allowed for elec. charged states). I believe the core of the framework (rules) is designed quite flexible so that this functionality can be added at some later point without major problems. Concretely I can come up with two options on implementing this functionality:

  1. Allow basis transformations on edges/states in order to fullfill conditions of rules at a specific interaction node.
  2. Allow graph edges to be linear combinations of states and dynamically compute quantum numbers in order to fullfill conditions of rules at a specific interaction node.

I have one question to @wgradl : Do we need an extra quantum number CP or do C and P suffice? In my opinion C and P separately suffice. More concretely for the neutral Kaons C(K_S) = -1 and C(K_L) = +1 CP(K_S) = +1 and CP(K_L) = -1. I could not find any concrete confirmation on the defintions of the C parity for K_S/L. Is this correct?

wgradl commented 4 years ago

Hi all,

easy question first:

I have one question to @wgradl : Do we need an extra quantum number CP or do C and P suffice? In my opinion C and P separately suffice. More concretely for the neutral Kaons C(K_S) = -1 and C(K_L) = +1 CP(K_S) = +1 and CP(K_L) = -1. I could not find any concrete confirmation on the defintions of the C parity for K_S/L. Is this correct?

this is correct up to CP violation in the Kaon system, i.e. a 10^-3 effect. I suppose that for most PWA we can safely ignore this.

Cheers,

Wolfgang