− | where ''a=1'' and ''b=2'' refer to the daughter index. If the two daughter particles belong to the same isospin multiplet, there is a constraint introduced between orbital angular momentum and total isospin that follows from the symmetry of exchanging the two particle identities, because 180 degree rotation is equivalent to the exchange of the daughter identities (''a,b'' becoming ''b,a''). For example, for a two-pion final state in an even-''L'' angular wave, only even ''I'' is allowed, and for an odd-''L'' angular wave, only odd ''I'' is allowed. | + | where ''a=1'' and ''b=2'' refer to the daughter index. If the two daughter particles belong to the same isospin multiplet, there is a constraint introduced between orbital angular momentum and total isospin that follows from the symmetry of exchanging the two particle identities, because 180 degree rotation is equivalent to the exchange of the daughter identities (''a,b'' becoming ''b,a''). For example, for a two-pion final state in an even-''L'' angular wave, only even ''I'' is allowed, and for an odd-''L'' angular wave, only odd ''I'' is allowed. Because of this, it is convenient to define a symmetrized variant of the ''C'' coefficients defined above, |
| C(L)=\frac{1}{\sqrt{2}} \left[ C^{a,b} + (-1)^L C^{b,a} \right] | | C(L)=\frac{1}{\sqrt{2}} \left[ C^{a,b} + (-1)^L C^{b,a} \right] |