Proton + Antiproton annihilation

[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.

 

[paranormal]

Your reasoning is correct. The annihilation of a proton and antiproton into an electron, positron, and electron neutrino violates the conservation of lepton number. Lepton number is a fundamental property that is conserved in all particle interactions. It states that the total number of leptons (such as electrons, neutrinos, and their antiparticles) must remain constant.

In this annihilation process, one lepton (the electron) is produced, but there is no corresponding antilepton produced to balance out the lepton number. Therefore, this process is not allowed according to the conservation of lepton number.

Additionally, the conservation of baryon number is also violated in this process. Baryon number is another fundamental property that states that the total number of baryons (such as protons and neutrons) must remain constant. In this case, two baryons (the proton and antiproton) are annihilated, but no new baryons are produced to balance out the baryon number.

Overall, the annihilation of a proton and antiproton into an electron, positron, and electron neutrino is not allowed due to violations of both lepton number and baryon number conservation laws.