# Traces at pion decay

A negative pion breaks down into a muon and a muon antineutrino.

What do the traces of the pion decay look like in a bubble chamber with a vertical, static homogeneous magnetic field?

My ideas: The B-field deflects the pion on a circular path.

But my question is: How does the radius change after the pion has decayed?

Because of the formation of a neutrino, the muon has less energy than the pion had... But it also has a smaller mass. What does this mean for the radius of the circular orbit? For the radius, the following applies:

$$r=\frac{mv}{qB}$$

The mass is smaller than before, but I'm not sure about the velocity... Or maybe there is another approach?

Could someone please help me? Thanks a lot! :)

## 1 Answer

Have a look at the CERN archive of bubble chamber pictures. You can search for the traces of particles there.

A classic example of a pimue decay

(please read the link for the analysis)

The radius of the muon depends on the momentum of the muon.

The pion decays when it loses its kinetic energy going through the hydrogen and stops and decays into the muon. The mass of the pion is about 139MeV, the mass of the muon about 105MeV. this leaves only about 30Mev to be shared between the muon antineutrino and the muon, so the muon stops in about 1cm losing its kinetic energy in ionisation, into the small fragment seen there. See the calculation here.

The positron with much smaller mass makes a helix in the magnetic field before stopping and annihilating on an electron

• Thanks a lot for the response! Although I have read the explanations on the CERN archive website, I still have difficulties to understand the picture. The great orbit describes the movement of the Pion? As I understand it, the spiral on the left side of the picture is a positron, which results from the decay of the muon. But where exactly in the picture does the decay of the pion into the muon take place and where do you see the movement of the muon? The other link shows that the decay products only receive an impulse of about 30MeV/c. How do we get the radius of the muon from this result?
– Ada
Nov 24, 2020 at 17:18
• Notice where the pion track stops. Notice where the positron track starts. The tiny black line is the muon , there is not much distance (1cm in real space as the link calculates, and that is a two meter bubble chamber picture.) Nov 24, 2020 at 18:47