# Charmonium: two photon decay

1. Feb 10, 2010

### Derivator

Hi,

one of my books says, that a charmonium $$c\bar c$$ in the sate $$1^1S_0$$ could decay into two phtons: $$c \bar c \rightarrow 2\gamma$$

But I think, conservation of parity is violated (not allowed, since we have electromagnetic interaction)

Parity of a charmonium state is $$(-1)^{L+1}$$, we have L=0, so before the decay we have a parity of -1.
Parity of a photon is -1, we have two photns, so the parity after the decay is +1

So, where have I made an error in reasoning?

--derivator

2. Feb 10, 2010

### clem

The two photons can have mutually parallel polarization, and then the amplitude for their production has E.E, which is a scalar with [positive parity, or they have have mutually perpendicular polarization, corresponding to E.B, which is a psudoscalar with negative parity. In this case of psi decay, they have the perp polarization with negative parity.
This argument is not original with me. It was used by Yang over 50 years ago to propose a test to measure the parity of the pi zero meson. The experiment showed that the pi zero had negative parity.

3. Feb 10, 2010

### blechman

the photons could be in a P-wave, for example.