Branching ratios of tau lepton decay:
Use your knowledge of the decay of W bosons to justify these rates.
The Attempt at a Solution
The W+ boson can decay to any combination of quarks with +1 charge, but the CKM matrix suppresses many of these heavily, so lets just consider ud, us, cd, cs (where d/s are anti).
BR (electron) = g^2(w) / (3*((2g^2(w) cos^2x + 2g^2(w)sin^2x) + 2g^2(w)
= 1( 6 + 2) = 1/8
where g^2(w) cos^2x is the matrix element squared for ud and and cs
g^2(w)sin^2x is the matrix element squared for us and cd
g^2(w) is the matrix element squared for any lepton.
This doesn't give the right answer. Furthermore shouldn't density of states be very important given the fact that the lepton channel is 3 body, and in real life the tau decays into 3 or 4 particles most commonly?