Atmospheric Neutrino: Pion Decay to Muon & Muon Neutrino

[Kolahal Bhattacharya]

Why does pions(coming through atmosphere) decays into a muon and a muon neutrino, not directly into electron and lelectron neutrino?I know it's because splin angular momentum conservation...but I need to be more clear about it.

 

[Norman]

Actually some of the pions do decay directly into electron and anti-neutrino (or positron and neutrino). But the branching ratio for this process is very small- only about 1%.

To explain this, please read:http://hyperphysics.phy-astr.gsu.edu/hbase/particles/hadron.html"

And Griffiths' book on particle physics also has a very good discussion.

Cheers.

 

[sir-pinski]

The decay of pions (coming through the atmosphere) into a muon and a muon neutrino, rather than directly into an electron and an electron neutrino, is due to the conservation of spin angular momentum. This concept is based on the principle of conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque.

In the case of pion decay, the initial state of the pion is a spin-0 particle, while the final state is a spin-1/2 particle (muon) and a spin-1/2 particle (muon neutrino). According to the law of conservation of spin, the total spin angular momentum of the system must remain the same before and after the decay.

If the pion were to directly decay into an electron and an electron neutrino, the total spin angular momentum of the system would not be conserved. This is because the electron has a spin of 1/2, while the electron neutrino has a spin of 1/2 as well, resulting in a total spin angular momentum of 1. However, the initial pion only has a spin of 0, which means that the total spin angular momentum would not be conserved.

In order to conserve spin angular momentum, the pion must decay into a spin-1/2 particle (muon) and a spin-1/2 particle (muon neutrino) with opposite spins, resulting in a total spin angular momentum of 0. This is in accordance with the law of conservation of spin and explains why pions decay into a muon and a muon neutrino rather than directly into an electron and an electron neutrino.

In summary, the conservation of spin angular momentum is the reason why pions decay into a muon and a muon neutrino, not directly into an electron and an electron neutrino. This principle plays a crucial role in understanding the behavior of subatomic particles and their interactions.