Analysis of W Decays: Counting the quark colours


The W is a very unbiased particle - it decays into any two particles it can with equal probability. This decay is always to a pair of particles, either quarks or leptons, and it must conserve charge. As the W has charge either + or - 1, so must the total of the decay products. Also, the decay products must weigh less than the W they started from, or energy would not be conserved. This excludes the top quark. This means that the following decays are possible:

W-W+
down and anti-up quarks anti-down and up quarks
strange and anti-charm quarks anti-strange and charm quarks
electron and anti-neutrino positron and neutrino
muon and anti-neutrino anti-muon and neutrino
tau lepton and anti-neutrino anti-tau lepton and neutrino
However, this is not the whole story. Because the quarks come in different `colours' the possibilities for making quarks are increased. We will measure the relative abundance of quarks and leptons in W decays and use that to find out how many colours there are.

The reaction e+e- to W+ does not conserve charge, and is not possible. Instead we use e+e- to W+W- . This means that we have a pair of W's in the same event to understand, and the events are more complicated than Z decays.

W+ decayW- decayProbablity IF only 1 colour
Two jets from quarks Two jets from quarks 2/5 * 2/5 = 16%
Two jets from quarks lepton and neutrino 2/5 * 3/5 = 24%
lepton and neutrino Two jets from quarks 3/5 * 2/5 = 24%
lepton and neutrino lepton and neutrino 3/5 * 3/5 = 36%

In general we can see that if there are ncolours colours there are 2ncolours quark modes for each W and 3 leptonic ones. As the W's decay equally to all modes, if we get a large sample of W pairs we will find the relative proprtions of events given in the following table:

leptonicMixedFour jets
lmf
912n4n2

If we take the numbers of events in any two of the categories f,l and m we can solve the equation to obtain ncolours. So we have 3 ratios we can use:

It turns out that the last method is the most accurate, so we will use that. (But the middle one is almost as good - you might like to compare)

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