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## Homework Statement

Branching ratios of tau lepton decay:

hadrons 66%

muon 17%

electron 17%

Use your knowledge of the decay of W bosons to justify these rates.

## Homework Equations

## The Attempt at a Solution

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The W+ boson can decay to any combination of quarks with +1 charge, but the CKM matrix suppresses many of these heavily, so let's 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?