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Homework Help: Eta decay -> 3 pion

  1. Aug 19, 2007 #1
    1. The statement, all variables and given/known data
    I am studying the decay of the [tex]\eta[/tex]-particle. Povh et Al, 'Particles and nuclei' say that a decay into 3 pions is not possible via the strong interaction. "For reasons of symmetry 3 pions (isospin equals 1) can not couple to zero isospin." This explains the long lifetime of the eta-particle. I do not understand this.

    2. Relevant equations
    Denote by [tex]D^{(j)}[/tex] the non-reducible representations of a rotation in isospin space, then [tex]D^{(1)}\otimes D^{(1)}=D^{(2)}\oplusD^{(1)}\oplusD^{(0)}[/tex]

    3. The problem
    [tex]D^{(1)}\otimes D^{(1)}\otimes D^{(1)}= ...\oplus D^{(1)}\otimes D^{(1)}\oplus...[/tex], their are [tex]D^{(0)}[/tex] components in the 3 pion system. Am I making a misinterpretation somewhere?
  2. jcsd
  3. Aug 24, 2007 #2
    For the purpose of archiving, here's the answer: the decay violates conservation of G-parity, which is conserved in the strong interaction.
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