The Hadrons — Question 3

Question 3

Baryon conservation requires three accompanying protons when an antiproton is made

In $p+p\to\bar p+Xp$, X is an unknown integer number of final protons. No other baryons or charged particles are produced. Use $m_pc^2=.938$ GeV.

1. Find X from baryon number and verify electric charge.

2. For a stationary target proton, calculate incident threshold kinetic energy.

Question 3 - Solution

Baryon conservation requires three accompanying protons when an antiproton is made

(a) Method and calculation

$$B:\ 2=-1+X\Rightarrow\boxed{X=3}.$$$$Q/e:\ 2=-1+3=2,\quad W_{\mathrm{th}}=4m_pc^2.$$

(b) Interpretation and further calculation

$$4m_p^2c^4+2m_pc^2K_{\mathrm{th}}=16m_p^2c^4.$$$$\boxed{K_{\mathrm{th}}=6m_pc^2=5.628\,\mathrm{GeV}}.$$

Physical check

Producing an antibaryon requires compensating positive baryon number. The threshold is greater than the newly created pair rest energy in a fixed-target geometry.