K-Long and K-Short pion decay cross sections

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    Cross Decay Pion
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Discussion Overview

The discussion revolves around the decay cross sections of K-Long (KL) and K-Short (KS) pions, specifically in the context of CP violation in the kaon system. Participants explore the factors influencing the decay rates, including phase space considerations and the impact of additional gluon vertices in Feynman diagrams.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that the conventional explanation for the faster decay of KS compared to KL is based on larger phase space for two-pion decays versus three-pion decays.
  • Another participant suggests that adding gluon vertices in the Feynman diagrams for three-pion decays may not significantly suppress the decay amplitudes, unlike electromagnetic vertices.
  • A later reply questions whether the contribution from additional gluon vertices is indeed smaller than the phase space suppression, indicating uncertainty in the comparison.
  • One participant expresses doubt about whether the contribution from gluon vertices is definitively smaller or larger than one, highlighting the complexity of the interactions involved.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the relative significance of the contributions from gluon vertices versus phase space effects, indicating that multiple competing views remain in the discussion.

Contextual Notes

The discussion reflects limitations in understanding the contributions of strong interactions and the role of phase space in decay processes, with unresolved questions regarding the magnitude of various factors involved.

tg85
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In the text-book example of CP violation in the kaon system, the usual statement is that the KS decays much faster than the KL because the phase space is larger for a decay into two pions, compared to three pions. (See, for example, Griffiths or "Modern Particle Physics" by Thomson.)

I was wondering if that is the only large contribution. Doesn't a third pion add at least two gluon vertices to the highest-order Feynman diagram? Can this be neglected in comparison with the phase space?
 
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The point with strong interactions is that they are ... well ... strong. Adding gluon vertices does not supress the amplitudes by a large amount as adding EM vertices does.
 
Orodruin said:
The point with strong interactions is that they are ... well ... strong. Adding gluon vertices does not supress the amplitudes by a large amount as adding EM vertices does.
OK, thanks. So there is a contribution, but it's much smaller than the phase space suppression?
 
Yes, and it is not even clear if that contribution is smaller or larger than one.
 

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