A Pause for Reflection — Question 5

Question 5

Efficiency changes the inferred relative weights of decay branches

In a background-free sample, channels A and B yield 180 and 120 events with efficiencies .30 and .80. Assume these are the only decay modes.

1. Correct both yields and infer branching fractions.

2. If the total width is 5 MeV, calculate both partial widths.

Question 5 - Solution

Efficiency changes the inferred relative weights of decay branches

(a) Method and calculation

$$\boxed{n_A=180/.30=600,\quad n_B=120/.80=150}.$$$$\boxed{B_A=600/750=.80,\quad B_B=.20}.$$

(b) Interpretation and further calculation

$$\Gamma_i=B_i\Gamma_{\mathrm{total}}.$$$$\boxed{\Gamma_A=4\ {\mathrm{MeV}},\quad\Gamma_B=1\ {\mathrm{MeV}}}.$$

Physical check

Observed fractions 180/300 and 120/300 are not branching fractions unless efficiencies are equal.