Psi Meson Decay Modes: Spin, Parity, Quark Content & More

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Homework Statement

(a) Explain spin and parity of mesons
(b) State their quark content
(c) Draw a feynman diagram of J/psi decay
(d) Why doesn't $\chi$ undergo leptonic decay?
(e) What is the minimum centre of mass? [/B]

Homework Equations

The Attempt at a Solution

Part(a)[/B]
Spin is either 0 (singlet) or 1 (tripplet) for a pair of fermions. Parity is given by $(-1)^{L+1}$.

Part(b)
Quark content is charm and anti-charm hadron $c\bar c$. For $1^-$ states, $L=0, S=1, J=1$. For $0^+$ states, $L=1, S=1, J=0$ through spin-orbit coupling. For $1^+$ states, $L=1, S=0, J=1$. For $2^+$ states, $L=S=1, J=2$.

Part(c)
EM decay of J\Psi to either $e^+e^-$ or $\mu^+ \mu^-$:

Part (d)
Previously, it was kinematically impossible for strong interactions. Now that the mass of excited $\psi^{''}$ is higher, there is a direct possibility of decay in strong interaction to $D^+D^-$. Strong interactions are preferred over weak interactions.

Part (e)
Why doesn't $\chi$ decay to pairs of charged leptons?
Possible reaction for $\psi^{'} \rightarrow \chi_0 + \mu^{+} + \mu^{-}$ or $\psi^{'} \rightarrow \chi_0 + e^{+} + e^{-}$

For decay to $\chi_1$ and $\chi_2$ only $e^{-}e^{+}$ pairs are allowed.

Part (f)
I suppose minimum mass is $m_{\chi2} + 2m_e = 3557 MeV$.
What are the important elements?

 

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bumpp

 

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Important elements?

 

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What are the important elements in a detector?

 

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bumpppppp

 

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what things that are important make a reactor?

 

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For part (f) : Isn't the minimum centre of mass energy for $\chi$ decays to be observed simply the mass of $m_\chi = 3415 MeV/c^2$?

 

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bumpp part (f)

 

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bump on part (f) Centre of mass energy?

 

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bumpp on part (f)

 

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bump on (f): Centre of Mass Energy

 

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bumpp - Centre of mass energy?

 

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bumpp on part (f)

 

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bumpp - is my centre of mass energy right? Part (f)