# Does the J/$\Psi$ primarily decay into real gluons?

so apparently the this cool looking decay of the $$J/\Psi$$ particle is OZI suppressed, which was confusing to me, because the Particle Data Group (link) says that 64% of its decays are into 3 gluons (as does wikipedia). So my question is, do I misunderstand what the PDG is saying, or does it emit 3 real gluons which don't decay into hadrons? Don't gluons have a finite lifetime because they're not white? Any help would be appreciated, thanks.

• To understand the language, read the branching ratios and make sure you understand what the first line, hadronic BR, is composed of: all BRs have to add up to 100%! There are no real gluons, as they are all virtual, and "decay" to hadrons. But, presumably, you appreciate ggγ is not 3 gluons... – Cosmas Zachos Dec 5 '19 at 1:56
• Hey, I sure am confused about the branching ratio yes. Are you telling me that even though hadronic decays are OZI suppressed, they still acount for 88% of the decays of the $J/\Psi$? – Derian Dec 5 '19 at 2:26
• Linked; further linked. – Cosmas Zachos Dec 7 '19 at 14:26

Hot tip: read the PDG listing mindful that the partial widths given, $$\Gamma_1-\Gamma_6$$ are not mutually exclusive! (Your $$\Gamma_{80}$$ is in $$\Gamma_{3}$$ and $$\Gamma_{1}$$.)

That is, the BRs must sum to 100%.

So, roughly, you either look at real particles in your detector, $$\Gamma_1 + \Gamma_5 + \Gamma _6 \sim \Gamma \\ 87.7+5.94+5.93 \sim 100,$$ or else inferred virtual particles coupling to the charm vertex maintainig symmetries, (C, zero color, etc...), $$\Gamma_2/\Gamma + \Gamma_3/\Gamma + \Gamma_4/\Gamma \sim \Gamma_1/\Gamma \\ 13.50+64.1+8.8 \sim 87.7 ~.$$ All gluons and most photons are virtual.

The striking takeaway, which confused experts to no end when the $$\psi/J$$ was discovered, is that the OZI suppression in, notably, $$\Gamma_3$$ reduces a strong rate to the pitiful status of competing with an EM one, $$\Gamma_2$$; also note the anaemic strong/EM ratio $$\Gamma_3/\Gamma_4$$.

At the time, nobody had seen anything of the sort,$$^*$$ making the narrowness of the $$\psi/J$$ a bewildering scandal.

$$^*$$I was in the corridor when (1975) George Zweig failed to convince Feynman of the logic of his eponymous rule yet again, and had to leave his (RPF's) office dejected with the door angrily slammed behind him... being right is not everything all the time...

• Interesting anecdote of George Zweig. He later departed physics and turned to hedge fund amongst other things. – MadMax Dec 5 '19 at 18:34
• He is still active at MIT, doing exceptionally creative work on the nonlinearities of the cochlea. The OZI rule was actually at the heart of his astounding coinvention/codiscovery of quarks, cf Fig 2 rendering the $\phi$ meson exceptionally stable! Gell-Mann punned on the diagram as "twig diagram". It is a major moment in the intellectual history of the 20th century, to only put it mildly! – Cosmas Zachos Dec 5 '19 at 20:22
• 2016 . – Cosmas Zachos Dec 5 '19 at 20:27
• Too bad the Nobel committee "slammed the door" on George Zweig too. Well, maybe what he made at hedge fund Renaissance is more than the meager \$1M. – MadMax Dec 5 '19 at 20:30