K-Long and K-Short pion decay cross sections

[tg85]

In the text-book example of CP violation in the kaon system, the usual statement is that the K_S decays much faster than the K_L 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?

 

[Orodruin]

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.

 

[tg85]

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?

 

[mfb]

Yes, and it is not even clear if that contribution is smaller or larger than one.