Momentum resolved tunneling into the Pfaffian and anti-Pfaffian edges

We calculate the electron spectral functions at the edges of the Moore-Read Pfaffian and anti-Pfaffian fractional quantum Hall states, in the clean limit. We show that their qualitative differences can be probed using momentum resolved tunneling, thus providing a method to unambiguously distinguish which one is realized in the fractional quantum Hall state observed at filling factor $ u=5/2$. We further argue that edge reconstruction, which may be less important in the first excited Landau level (LL) than in the lowest LL, can also be detected this way if present.