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I have looked up the pdg and found different decay modes in which three of them are the most occurring in nature. They are $\rm\phi\rightarrow K^+K^-$, $\rm\phi\rightarrow K_0\bar K_0$, and $\rm\phi\rightarrow \pi^+\pi^-\pi_0$. How can I calculate each decay width and the total decay with to calculate the branching ratios?

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  • $\begingroup$ The generic dynamical law suppressing the 3 π mode out of the $s\bar s$ comprising the φ led Zweig in 1964 to postulate quarks, and is now called the OZI rule: basically that the strange q's are reluctant to annihilate themselves in favor of gluons, which then produce pions. As @ Chris points out, this is best quantified through nonperturbative techniques. If the rule worked perfectly, all decay modes would consist of Ks. $\endgroup$ – Cosmas Zachos Feb 4 '18 at 22:17
  • $\begingroup$ Related. $\endgroup$ – Cosmas Zachos Feb 4 '18 at 23:52
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You don't, really. At the very least, you need a supercomputer to do the number crunching for you.

Strong decays (i.e. those involving QCD) in general have to be computed non-perturbatively. This means there is no way to get an analytic result, and you can't just compute a few diagrams and get a result that's reasonably close like you can with weak and electromagnetic decays.

QCD quantities can be computed non-perturbatively in some cases using a supercomputer. See lattice QCD, for instance. These computations are very computationally demanding, and the results typically have a large uncertainty at the end.

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