Identify the correct neutrino (Ve, Vµ, Vτ or their anti-particles)
a) π+ —> p° + e+ + v
b) π+ —> p° + µ+ + v
c) τ+ —> e- + v + v
Please explain why too...I'm really lost. I'd appreciate any help.
To identify the correct neutrino (Ve, Vµ, Vτ, or their anti-particles) for the given reactions, we need to consider the conservation of lepton numbers.
Lepton Number Conservation:
In particle physics, every lepton (such as electrons, muons, and tau particles) and every lepton anti-particle have a lepton number assigned to them. The lepton number (L) is +1 for leptons and -1 for anti-leptons. Lepton number conservation states that the total lepton number before and after a reaction must remain the same.
Looking at each reaction:
a) π+ —> p° + e+ + v
In this reaction, a positive pion (π+) is decaying into a neutral pion (p°), a positron (e+), and a neutrino (v). The positron (e+) has a lepton number of +1, and the neutral pion (p°) and the neutrino (v) have lepton numbers of 0. Therefore, the corresponding neutrino in this reaction is Ve.
b) π+ —> p° + µ+ + v
In this reaction, a positive pion (π+) is decaying into a neutral pion (p°), a muon (µ+), and a neutrino (v). The muon (µ+) has a lepton number of +1, and the neutral pion (p°) and the neutrino (v) have lepton numbers of 0. Therefore, the corresponding neutrino in this reaction is Vµ.
c) τ+ —> e- + v + v
In this reaction, a positive tau particle (τ+) is decaying into an electron (e-), two neutrinos (v). The electron (e-) has a lepton number of +1, and the neutrinos (v) also have lepton numbers of +1 each. Therefore, the corresponding neutrino in this reaction is Vτ.
So, to summarize:
a) corresponds to Ve
b) corresponds to Vµ
c) corresponds to Vτ
Please note that the anti-particles for these neutrinos would have opposite lepton numbers.