# G- and C-parity of the pi^0

1. Feb 28, 2013

### copernicus1

Since the pi^0 decays to two photons its C-parity is +1, but its isospin ket is $$|1,0\rangle,$$ which makes it a little tricky to understand why its G-parity is -1. Does the rotation around the I_2 axis somehow generate a minus sign? This seems odd since the isospin ket points into the x-y plane, so it seems the rotation by pi wouldn't affect it.

Last edited: Feb 28, 2013
2. Feb 28, 2013

Staff Emeritus
That doesn't look right. It's |1,0>.

3. Feb 28, 2013

### copernicus1

You're right that was just a mistake; I fixed it. This is what makes the rotation in isospin space hard to understand. Initially it's pointing into the x-y plane, and after a 180 degree rotation it's still into the x-y plane, but somehow the G-parity is different from the C-parity.

4. Mar 1, 2013

### Bill_K

Isn't this what you'd expect for an isovector? Under a 180° rotation about the I2 axis, I1 → - I1, I2 → I2, I3 → -I3. And in the spherical basis, π+ and π- are linear combinations of I1 and I2, and π0 is the I3 component, so it changes sign.