In the previous exercise you learned how to calculate the radius out of a particle track. In this part you will learn how you can calculate out of the radius the momentum and then the energy of the particle.
If a particle moves in the kind of circular tracks shown, in which direction must the force acting on it be? What is the name of this force?
Click here for the solution to Exercise 3a
What is the name of the force that makes a charged particle move in a circle when it is in a magnetic field? How do you calculate the size of this force, supposing that the magnetic field (strength B) is perpendicular to the velocity of the particle?
Click here for the solution to Exercise 3b
Combining the two formulas from 3a and 3b and, knowing that the momentum of a particle is the product of its mass and velocity, you should get the following equation for the transverse momentum:
pt = r q B
Use it to calculate the transverse momentum of the particle which was responsible for the orange track. The strength of the magnetic field inside the coil is 1.5 Tesla.
Click here for the solution to Exercise 3c
In the ALEPH experiment, the magnetic field is parallel to the beam axis. We will call this the z-direction. This means that the above radius is perpendicular to z and the momentum related to that radius is the momentum of the particle in the x-y-plane. We will call this momentum the transverse momentum pt. So, we do not know the component along the beam axis or the total momentum of the particle.
Looking at the lower left picture with the cross section, you can see, that the orange track goes upwards, a little bit to the right. The read out electronics gives an angle q of 68 degree. q is defined as the angle between the outgoing track and the z-axis.
Knowing this angle and the transverse momentum pt = 1.047 GeV/c, calculate the component of the momentum of the particle.
Click here for the solution to exercise 3d
Now you have calculated the momentum of one particle and you can imagine how to get the momenta of the other particles.
But, even if you know the charge of the particle (which you get by considering which way it is deflected by the magnetic field), this does not mean that you have identified the particle. The measurements of of the ionisation degree in the chambers and the measurements of the other detectors help to identify the particles.
So let us suppose, that we have identified all the particles. Now comes the really interesting question: what happened before these five particles where created? To answer this we need to calculate the total energy of the five particles. Their masses correspond more ore less to the rest (or invariant) mass of the unseen and very short-lived particle which decayed in the particles that were detected. In the following table you can find the data of all the six particles:
| particle | K- | p- | p+ | p+ | p+ | p- |
| track radius (cm) | 684 | 227 | 708 | 121 | 71 | 117 |
| pt (GeV/c) | 3.071 | 1.047 | 3.182 | 0.547 | 0.321 | 0.525 |
| q | 66 | 68 | 38 | 72 | 65 | 35 |
| p (GeV/c) | 3.362 | 1.129 | 5.168 | 0.575 | 0.354 | 0.925 |
| m (MeV/c2) | 493.7 | 139.6 | 139.6 | 139.6 | 139.6 | 139.6 |
Calculate the energy of all particles.
Click here for solution of exercise 3e