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eendavid
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1. The statement, all variables and given/known data
I am studying the decay of the \eta-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.
Denote by D^{(j)} the non-reducible representations of a rotation in isospin space, then D^{(1)}\otimes D^{(1)}=D^{(2)}\oplusD^{(1)}\oplusD^{(0)}
3. The problem
As
D^{(1)}\otimes D^{(1)}\otimes D^{(1)}= ...\oplus D^{(1)}\otimes D^{(1)}\oplus..., their are D^{(0)} components in the 3 pion system. Am I making a misinterpretation somewhere?
I am studying the decay of the \eta-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.
Homework Equations
Denote by D^{(j)} the non-reducible representations of a rotation in isospin space, then D^{(1)}\otimes D^{(1)}=D^{(2)}\oplusD^{(1)}\oplusD^{(0)}
3. The problem
As
D^{(1)}\otimes D^{(1)}\otimes D^{(1)}= ...\oplus D^{(1)}\otimes D^{(1)}\oplus..., their are D^{(0)} components in the 3 pion system. Am I making a misinterpretation somewhere?