Parity in the \eta to two photon decay

[fliptomato]

Greetings, I'm curious about parity conservation in the decay\eta \rightarrow \gamma \gamma. The \eta has odd parity, while the product of the two photon parities (each is odd) is even. Now, parity is conserved in the EM interactions, so there must be a factor of (-1) coming in from orbital angular momentum factors--but the two photon final state has no orbital angular momentum. What am I missing here?

 

[marlon]

IN SHORT : PARITY DOES NOT ADD UP LINEARLY...

I mean : in order for the two-photon state to have J = 0 (conservation of J we must write it as a superposition of two states A and B. Each state has the two photons with anti-parallel spins and in state A the photonspin is aligned with the photon-momentum, in B photon spin is opposite wrt photon momentum. You can derive these states by using the Clebsch-Gordan coefficients.

A photon has indeed parity -1 but since we are working with a superposition of TWO photonstates, the parity is relative. If you had just a single two-photon state then parity would be -1 * -1 but because of the superposition, it is the parity from state A with respect to state B that determins the actual parity of the entire wavefunction...

regards
marlon

More to be found here

 

[Meir Achuz]

Greetings, I'm curious about parity conservation in the decay\eta \rightarrow \gamma \gamma. The \eta has odd parity, while the product of the two photon parities (each is odd) is even. Now, parity is conserved in the EM interactions, so there must be a factor of (-1) coming in from orbital angular momentum factors--but the two photon final state has no orbital angular momentum. What am I missing here?

In \eta-->2\gamma, there is orbital angular momentum l=1, which gives the factor (-1)^l. The angular momentum addition for the photon spins must be S=1+1=1, and then l+S=1+1=0.
The eta decay is the same as the pi^0 decay. The parity of the pi^0, and of the eta^0, were determined by the relative plane polarizations of the two photons, which can be found from the spin addition 1+1=1.
This was first done by Yang.