How is ##\Phi \rightarrow K^{+}K^{-}## decay possible?

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Discussion Overview

The discussion centers on the decay process of the particle ##\Phi## into a pair of kaons, ##K^{+}K^{-}##. Participants explore the implications of charge conjugation conservation in this interaction, examining the quantum numbers involved and the conditions under which the decay may or may not be allowed.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant notes the charge conjugation values for the particles involved, questioning how total charge conjugation is conserved in the decay process.
  • Another participant challenges the assertion regarding the charge conjugation of the kaons, indicating that ##K^{\pm}## is not an eigenstate of the charge conjugation operator.
  • A subsequent reply raises the concern that this may prevent checking for charge conjugation conservation in the decay process and asks which quantum numbers should be examined to determine if the process is forbidden.
  • It is stated that hadronic interactions are invariant under charge conjugation, suggesting that replacing particles with antiparticles does not invalidate the process.
  • Participants discuss the necessity of checking quark flavors and energy in the decay process, noting that while the process may be possible, it could be unlikely due to considerations of spin and angular momentum.
  • Clarification is provided that while a single charged kaon is not an eigenstate of charge conjugation, the ##K^+K^-## system is, which may allow for charge conjugation conservation checks.

Areas of Agreement / Disagreement

Participants express differing views on the charge conjugation properties of the kaons and the implications for checking conservation in the decay process. The discussion remains unresolved regarding the specifics of charge conjugation conservation in this context.

Contextual Notes

Limitations include the unclear status of charge conjugation conservation for the decay process and the potential dependence on the definitions of the quantum numbers involved. The discussion does not resolve whether the decay is allowed or forbidden based on these considerations.

mPlummers
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I know that, for charge conjugation, ##C_{\Phi} = -1##, ##C_{K^{+}} = 0##, ##C_{K^{-}} = 0##, but ##C_{\Phi} \neq C_{K^{+}}C_{K^{-}}##. How ##C_{tot}## is conserved in this interaction?
 
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What do you mean with ##C_{K^{\pm}}=0##?
##K^{\pm}## is not an eigenstate of the charge conjugation operator.
 
You're right, I've just noticed that. Does it mean i can't check for charge conjugation conservation in this process? If I'm asked to check if this process is forbidden or not, which are the quantum numbers to check? The process is hadronic, and these processes conserve charge conjugation, right?
 
The hadronic interaction is invariant under charge conjugation, yes. If you replace particles with antiparticles in a possible process the process is still possible. If you replace particles with antiparticles here you get the same process again.
Check the quark flavors and the energy. If they work out the process will be possible in general. It can be very unlikely due to spin/angular momentum, something to check as well.
 
Does it mean i can't check for charge conjugation conservation in this process?

A single charged kaon is not an eigenstate of the charge conjugation operator. But a ##K^+K^-## system is.
 
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