The 1P1 cannot go via a photon due to it's parity. The tricky part is how much of the rate to attribute to transitions to the other charmonium states. So far there is a lot of qualitative discussions, but few numbers so far. Hitoshi has suggsted that we bring Peter Lepage into the fray, as he is a big expert. If you get a chance to ask him about this, I'd be grateful.
Every decay mode has a comment on where it came from or who made it up.
Of course you have to deannotate it before use, but Dan Riley, god of sed, sent me a little command to deannotate decay.annotated. In any case, the PDG decided not list it in the main table. I think the measurement is a suspect, in fact becuase they did not see the 2 pi mode. I think the C parity is the reason why it is forbidden. I that is the tricky part, and I don't think anybody really know it better than factor of 5 or 10.