Creating Z_0 boson via symmetric beams a. Z0 boson has a rest mass energy of 91.187 GeV. It is produced in collisions of positrons and electrons.
e^- + e^+ to Z_0
How much kinetic energy must the positrons and electrons in symmetric colliding beams have to produce the Z0 boson? The rest mass energy for electrons and positrons is 0.511 MeV.
Creating Z0 boson via positron beam striking electron target
b. Instead, suppose a beam of positrons strike electrons that are at rest. How much energy must the positrons have to produce the Z0 boson?
c. Compare and comment on your answers to part a and b. Hint: The answers should be very different.
To answer both parts a and b, we need to understand the concept of conservation of energy and momentum in particle interactions.
a. In part a, we have symmetric colliding beams of electrons and positrons. To create a Z_0 boson, the total energy before the collision needs to be equal to the total energy after the collision.
The rest mass energy of the Z_0 boson is given as 91.187 GeV. Since the Z_0 boson is created from the annihilation of an electron and a positron, the total energy before the collision would be the sum of rest mass energies of the electrons and positrons.
Each electron and positron has a rest mass energy of 0.511 MeV. Since 1 GeV is equal to 10^6 MeV, the rest mass energy of each electron and positron is 0.511 MeV * 10^(-6) = 0.000511 GeV.
Therefore, the total energy before the collision would be 2 * 0.000511 GeV = 0.001022 GeV.
To find the kinetic energy required for the electrons and positrons, we subtract the rest mass energy from the total energy before the collision:
Kinetic energy = Total energy - Rest mass energy
= 0.001022 GeV - 0.001022 GeV
= 0 GeV
Hence, the positrons and electrons in symmetric colliding beams must have zero kinetic energy to produce the Z_0 boson.
b. In part b, we have a positron beam striking electrons that are at rest. In this case, the positron needs to have enough energy to compensate for the rest mass energy of the electron and produce the Z_0 boson.
The rest mass energy of the electron and positron is still 0.511 MeV, which is 0.000511 GeV. However, to produce the Z_0 boson, additional energy is required.
To find the energy required, we need to subtract the rest mass energy of the electron and positron from the mass energy of the Z_0 boson:
Energy required = Mass energy of Z_0 boson - Rest mass energy of electron/positron
= 91.187 GeV - 2 * 0.000511 GeV
= 91.186978 GeV
Therefore, the positrons need to have an energy of approximately 91.187 GeV to produce the Z_0 boson when striking electrons at rest.
c. The answers to part a and part b are indeed very different.
In part a, where we have symmetric colliding beams, the positrons and electrons need to have zero kinetic energy to produce the Z_0 boson. This is because the rest mass energy of the particles is already sufficient to create the Z_0 boson when they collide.
In part b, where we have a positron beam striking electrons at rest, the positrons need to have an energy of approximately 91.187 GeV. This is because the positron needs to provide enough energy to compensate for the rest mass energy of the electrons and also create the Z_0 boson.
The difference in the required energies stems from the different initial conditions and types of collisions involved in the two scenarios.