The Hadrons — Question 10

Question 10

A baryon asymmetry differs from the total number of baryonic particles

A collision region contains 120 baryons and 100 antibaryons, each with baryon-number magnitude one. It then creates 50 additional baryon-antibaryon pairs without losses.

1. Find net baryon number before and after pair creation.

2. Find asymmetry $A=(N_B-N_{\bar B})/(N_B+N_{\bar B})$ before and after, and explain the change.

Question 10 - Solution

A baryon asymmetry differs from the total number of baryonic particles

(a) Method and calculation

$$\boxed{B_{\mathrm{net}}=120-100=20}.$$$$\boxed{B_{\mathrm{net}}\prime=(120+50)-(100+50)=20}.$$

(b) Interpretation and further calculation

$$\boxed{A=20/220=.0909091,\quad A\prime=20/320=.0625000}.$$$$\boxed{A\prime/A=220/320=.6875}\quad\text{although net baryon number is unchanged}.$$

Physical check

Pair production changes total abundance without changing the conserved difference. A normalized asymmetry can evolve even when the underlying net charge is conserved.