Understanding the OZI Rule in Particle Physics

aw7879
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HELP! OZI rule

Can anyone give me an explanation of the OZI rule in particle physics which is a bit better than "if you can split a feynman diagram in two by cutting gluon lines then it is suppressed"
 
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Looking at http://demonstrations.wolfram.com/TheOZIRuleInMesonDecay/" it seems that if the decay particles contain the original quarks then it is prefered, ie if the original quarks have to annhilate then the decay is suppressed.
 
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There is a nice qualitative justification in Griffiths's Introduction to Elementary Particles (section 2.5), which I quote below in case you don't have access to the text.

The OZI rule is related to asymptotic freedom, in the following sense: In an OZI-suppressed diagram the gluons must be "hard" (high energy), since they carry the energy necessary to make the hadrons into which they fragment. But asymptotic freedom says that gluons couple weakly at high energies (short ranges). By contrast, in OZI-allowed processes the gluons are typically "soft" (low energy), and in this regime the coupling is strong.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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