B meson from proton antiproton collision

[Masafi]

The B+ particle and B- particle are produced by higher energy collisions between protion and anti protons. The B meson has a mass of 5.28 GeV/c^2. The proton has mass 938 MeV/c^2.

Calculate the min KE of the proton neccesary for a B+ B- pair to be produced from a proton anti-proton head on collision.

Not sure of the method to solve this. The answer is 4.3GeV

 

[humanino]

The total 4-momentum in the initial state has zero 3-momentum (head on collision) and twice the energy of one proton. The total 4-momentum in the final state has zero 3-momentum (threshold production) and twice the mass of the B. Let's write down the equality of the squared total 4-momenta

$$4\times E^2=4\times M^2$$

$$E - m=K=M-m$$

$$K=5.28-0.938=4.342$$

 

[Masafi]

The total 4-momentum in the initial state has zero 3-momentum (head on collision) and twice the energy of one proton. The total 4-momentum in the final state has zero 3-momentum (threshold production) and twice the mass of the B. Let's write down the equality of the squared total 4-momenta

$$4\times E^2=4\times M^2$$

$$E - m=K=M-m$$

$$K=5.28-0.938=4.342$$

I haven't studied this method. All I have done is conservation of linear momentum, how to work out KE, and switching from eV/c^2 to kg etc.

Can this be solved using that knowledge?

 

[vela]

The minimum energy to produce the B+ and B- is when they are created at rest, so the total energy is the sum of their rest energies, $2m_Bc^2$. Since both particles are at rest, their total momentum is zero.

Because energy and momentum are conserved, you know the total energy and momentum of the proton and antiproton. From this information, you should be able to calculate the energy of the proton and therefore its kinetic energy.

 

[Masafi]

The minimum energy to produce the B+ and B- is when they are created at rest, so the total energy is the sum of their rest energies, $2m_Bc^2$. Since both particles are at rest, their total momentum is zero.

Because energy and momentum are conserved, you know the total energy and momentum of the proton and antiproton. From this information, you should be able to calculate the energy of the proton and therefore its kinetic energy.

Rest Energy of B mesons produced = 5.28GeV * 2c^2 = 10.56* c^2 GeV

Rest E of proton and anti proton = 1.876 * c^2 GeV

So KE = Rest E of B mesons - Rest E of protons
= 8.684 * c^2 GeV
= 7.82 x 10^17 GeV??

The answer is meant to be 4.3GeV

 

[vela]

An electron-volt is a unit of energy, so the rest energy of a B meson is 5.28 GeV, not 5.28 GeV*c^2. The mass of the B meson could be written as 5.28 GeV/c^2, but you don't generally plug a value in for c. You just leave it as c.

Also, remember that the question asked you for the kinetic energy of the proton, not the proton-antiproton pair.

 

[humanino]

[...] how to work out KE [...]

Can this be solved using that knowledge?

Yes. How do you work out KE ?