K-Long and K-Short pion decay cross sections

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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