Decay of Z boson I have following queries regarding the decay width of Z boson.


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*In thisThomson's lectures, page 479, it says that decay of Z to hadrons have a large cross section because of factor 3 from colors. But, I mean why is the color factor not working for quarks individually then?

*Also, when I say decay of Z to hadrons, what do I exactly mean? I guess before hadronisation, at parton level, the Z boson has to decay to parton first (i.e. quarks). Then why do we talk about decay width of Z boson to hadrons? 
 A: Because of the form of the strong force quarks are never free. The basic interactions of quarks with the weak and electromagnetic and strong forces  are successfully calculated in QFT using Feynman diagrams exchanging the appropirate carrier, gluons for strong, photons for electromagnetic and Z and W for weak.

The left is the first order diagram for mu+mu- creation and the right one for qq_bar of a specific color anticolor.
Muons though are free, quarks cannot exist free, they have to grab qq_bar pairs of the appropriate colors so that a color neutral state of at least two hadrons has to be built up. At the energy available from a Z on mass decay this generates quark jets, because of the proliferation of strong interactions.

all the energy of the individual  quark distributed according to quantum chromodynamics to a number of hadrons as the energy of each quark is half the mass of the Z in the center of mass.

it says that decay of Z to hadrons have a large cross section because of factor 3 from colors. But, I mean why is the color factor not working for quarks individually then? 

In the standard model the quarks come in three colors, and each color anticolor pair counts as much as the decay to a mu+mu-, so there are more hadronic decays, whereas the leptons come in single electron and muon and tau ,seperable, for the quarks in the table of elementary particles.

In this sense, when the energy of the incoming electron positron within the mass width of the Z the creation of q q_bar pairs of a given color  is as probable as a neutrino antineutrino . The color factor enters in all QCD calculations. 

Then why do we talk about decay width of Z boson to hadrons? 

It is the sum of all the possible decays to individual quarks times their color numbers. One  does not list, for example, bottom_red, bottom_blue, bottom _green in the elementary particle list, it is understood and a simpler table. The probabilities can be calculated using the standard model of particle physics and are well validated by the measurements.
