The Basic Forces and Messenger Particles — Question 3

Question 3

Charge conservation fixes the sign of an exchanged weak boson

In a charged-current event, $u\to d+W$ and the W then couples to $e^++\nu_e$. Quark charges are +2e/3 and -e/3.

1. Determine the W charge at both vertices.

2. For the conjugate process, write the quark and lepton transitions and verify electron-family number.

Question 3 - Solution

Charge conservation fixes the sign of an exchanged weak boson

(a) Method and calculation

$$Q_W/e=2/3-(-1/3)\Rightarrow\boxed{W^+}.$$$$W^+\to e^++\nu_e:\quad\boxed{+1=+1+0,\quad L_e=-1+1=0}.$$

(b) Interpretation and further calculation

$$\boxed{\bar u\to\bar d+W^-,\quad W^-\to e^-+\bar\nu_e}.$$$$\boxed{-2/3=+1/3-1,\quad L_e=1-1=0}.$$

Physical check

The diagram is charge-flow bookkeeping; whether the W is on shell depends on available invariant energy.