Question 2

Two protons collide emitting a $\pi^0$ meson

$$p+p\rightarrow p+p+\pi^0.$$

What is the minimum total energy of one of the protons in the c.m. frame for this reaction to occur?

[5 marks]

[The (rest) mass of a proton is $0.938\ \hbox{\rm GeV}/c^2$ and the mass of a $\pi^0$ meson is $0.135\ \hbox{\rm GeV}/c^2$.]

Now consider a frame in which one of the protons is at rest. Show that the minimum total energy of the other proton in this frame is $1.218\ \hbox{\rm GeV}$ for the reaction to occur.

[16 marks]

In the second case, what is the momentum of the incoming proton?

[4 marks]

[Hints can be found here, but do not follow this link until you have attempted the question on your own.]