# Decay Width's

1. May 4, 2010

### Sonko

i was'nt sure whether to put this here in the homework questions because this is'nt really homework as its for my understanding.... However my particle physics exam is tommoro and i'm having some problems understanding how to calculate decay width's of decays. i have the following from a past paper which i could use some help on (as i'm sure a similar quation will be asked)

A2. A τ− lepton has the following 4 decay channels:
(i) τ− → ν_ e− ¯νe;
(ii) τ− → ν_μ− ¯ ν μ;
(iii) τ− → ν_ ¯u d;
(iv) τ− → ν_ ¯u s.

(a) For each of the 4 decays, draw the lowest order Feynman diagrams, labelling
all external lines, internal lines, and vertices.

(b) Give simplified expressions for the decay width of each decay.
Estimate branching fractions for each decay mode, given that |Vud| = 0.97 and
|Vus| = 0.22.

(c) Estimate the partial width of the decay of the τ− lepton into a muon, given
that its lifetime is τ_ = 3 × 10−13 s [¯h = 6.588 × 10−25 GeV s.]

i can construct the feynman diagrams but i really dont know what is meant by "simplified expressions for the decay width of each decay" or how to estimate the partial width of the τ− lepton into a muon?