What are the quantum numbers of an exchange particle in the t channel? i know that for an s channel reaction, the quantum numbers of the intermediate particle have to be the same as those of the particles coming in, for example in the reaction $\gamma \pi \rightarrow a_2 \rightarrow \eta \pi$ the in- and outgoing particles have to be in a D-wave in order to produce the quantum numbers of the $a_2$: $I^G(J^{PC})=1^- (2^{++})$.
I was asked to also calculate the amplitude for the t-channel process (with the momentum of the mediating particle being the difference of the Pion momenta) and I do not know how to make a connection between the quantum numbers of the final and initial particles and those of the mediating particle. Imagining the pion to "decay" into the mediating particle and another Pion does not really seem like an option. 
I would be grateful for an explanation or a hint where to look this up.
 A: Look at each vertex independently.


*

*The vertex including the photon also involves a hadron, so the exchange is going to be strong mediated.

*The eta carries certain quark flavors. These can-not have come from the photon, so they came from the exchange particle.

*You have to conserve angular momentum between the initial and final states, whic may involve a change or orbital state.

*There is no change in charge at either vertex.
Your exchange particle is therefore strongly interacting, bosonic and uncharged but could have either parity. I believe that at the level of quantum hadrodynamics this is usually envisioned as 
$$\gamma + \pi \overset{\eta^*}{\to} \eta + \pi \,,$$ 
where the star implies that the exchange $\eta$ is off-shell. 
However, you may find various descriptions at the quark-level to be more helpful. In that view the on-shell photon is often the "exchange" particle. Something like 

The photon interacts with one of the valence quarks, hitting it hard enough to pair produce on the flux tube and after hadronization you have the final state particles.

