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The $c\bar{c}$ meson decays to a lighter meson in the following reactions: $$\psi(3686)\rightarrow J/\psi(3097)+\eta^0$$ $$\psi(3686)\rightarrow J/\psi(3097)+\pi^0.$$

My aim is to find out which conservation law is causing one of these decay channels to be massively suppressed, but my lack of understanding of this notation is making this difficult.

I'm guessing that $\psi$ us a representation of the wave function of a $c\bar{c}$ on the LHS and a lighter meson on the RHS. However, there is added confusion for me with the $J$, which I assume to be the total angular momentum, as a denominator of this fraction.

Can someone help me solve this problem, whilst at the same time explaining the notation? I think that would help me and others best understand it.

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    $\begingroup$ I have the feeling that this is just an error of the compiler or something like that. The particle is called $J/\psi$, see J/psi meson. $\endgroup$ – AccidentalFourierTransform Jan 11 '17 at 14:13
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    $\begingroup$ Is the expression $\frac J\psi$ rather than $J/\psi$ in your original source? If so, could you link? $\endgroup$ – rob Jan 11 '17 at 14:47
  • $\begingroup$ Edited to show that it is J/$\psi$ $\endgroup$ – ODP Jan 11 '17 at 15:42
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    $\begingroup$ It is strange to see the (3097) part. The $J/\psi$ is unambiguously the lightest 1S vector $c\overline{c}$ state. $\endgroup$ – dukwon Jan 11 '17 at 15:51
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This confusing notation arose from the simultaneous discovery of this resonance by two seperarate teams of researchers in 1974. One group named the particle J while the other group called it psi. The accepted name is a combination of the two.

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The notation $J/\psi$ is historical, the particle was simultaneously discovered by two groups and called, respectively, $J$ and $\psi$.

The decay into a $\pi^0$ is suppressed by isospin conservation. The $\psi$ and the $J/\psi$ are iso-singlets, but the $\pi^0$ is th third component of an iso-triplet. The decay requires isospin violation, caused by the small up and down quark mass difference or electromagnetism.

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