Can Proton and Antiproton Annihilate into Electron, Positron, and Neutrino?

[mateomy]

I'm asked to state whether or not a proton and an antiproton can annihilate into an electron, a positron, and an electron neutrino.

$$p + \overline{p} \rightarrow e + e^+ + \nu_e$$


It doesn't seem allowed to me but I can't fully justify it with any conservation law. I've reasoned that because the electron is a lepton an annihilation of a proton/antiproton pair will not produce such a particle as the former is composed solely of quarks. It seems reasonable to me but which law is broken? I believe its conservation of lepton number. But I can't convince myself for some reason.

Thanks.

 

[Dick]

The quarks have nothing to do with it. The proton and antiproton annihilate. You've got me convinced it violates lepton number. Write down the lepton number for each particle. Not sure why you are harder to convince.

 

[mateomy]

The quarks have nothing to do with it. The proton and antiproton annihilate. You've got me convinced it violates lepton number. Write down the lepton number for each particle. Not sure why you are harder to convince.

Got it. For some reason i was thinking $\nu_e$ had a lepton number of 0.

Thanks.

 

[Vanadium 50]

There is an even more fundamental reason that this doesn't happen. Write down the possible spins of the left and right hand sides.