How Does the Mass of the Bottom Quark Affect Z Boson Decay Calculations?

In summary, the theoretical values of the Z boson decay partial width agreed well with experiment, but there is something that is not quite clear. The mass of the bottom quark is necessary for the calculations to produce accurate results, and without it the partial width would be different for each quark. The phase space factor is also affected by the bottom quark, and is about a percent off from what would be predicted without the quark.
  • #1
Catria
152
4
Hello everyone,

I have read about the theoretical values of the Z boson decay partial width and how well they agreed with experiment. However there is something I do not quite understand: since these theoretical calculations were performed with the hypothesis that the masses of the decay products were negligible with respect to the mass of the Z boson, what changes would have to be effected if one did not neglect the mass of the bottom quark (~4-5 GeV) when computing the partial width of the Z boson into a bottom and anti-bottom quark pair?
 
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  • #2
If the theoretical calculations would not take the mass into account, they would predict the same values for all quarks. They do not, and the predicted difference has been confirmed by experiment.
 
  • #3
Then, what... form would these corrections take? Would those corrections for the bottom quark have the effect of increasing or decreasing the partial width?
 
  • #4
Based on the http://pdg8.lbl.gov/rpp2013v2/pdgLive/Particle.action?node=S044 , it looks like mass is increasing the partial decay width. Hadronization makes it tricky to disentangle the light quarks, but bb gets more than 1/5 of the hadronic decay width.
 
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  • #5
The theoretical effect will be something around 1%. The observational difference is about 1% with an uncertainty of about half a percent.
 
  • #6
How did you get those numbers? Γ(Z → bb¯ )/Γ(Z → hadrons ) is given as 0.21629 ± 0.00066 where bold highlights matching digits. The uncertainty is tiny compared to the difference to 0.2.
 
  • #7
The phase space factor is about a percent. This can be accurately calculated, since its a ratio.

The absolute branching fraction to hadrons has loop effects (color connection) of the order alpha_s/16 pi, or again a good fraction of a percent. So one would need to compare Γ(Z → bb)/[Γ(Z → bb) + Γ(Z → dd) + Γ(Z → ss)] which what I did and is good to half a percent. Your suggestion to lump all the hadrons together is interesting, but it would require taking the weak mixing angle measurement from some other experiment, so one could constrain Γ(Z → uu)/[Γ(Z → dd). I'd have to look more closely to see if you win or not with this.
 

FAQ: How Does the Mass of the Bottom Quark Affect Z Boson Decay Calculations?

What is a Z boson?

The Z boson is a subatomic particle that is responsible for the weak nuclear force, one of the four fundamental forces of nature. It was discovered in 1983 and has a mass of around 91 GeV.

What is decay partial width?

Decay partial width is a measure of how quickly a particle decays into specific final states. It represents the probability of a particle decaying into a particular set of particles, and is expressed in units of energy or mass.

How is the Z boson decay partial width calculated?

The Z boson decay partial width is calculated using the Standard Model of particle physics, which predicts the interactions and decay rates of subatomic particles. It takes into account the mass of the Z boson, the coupling strengths of the weak force, and the masses of the particles it can decay into.

Why is the Z boson decay partial width important?

The Z boson decay partial width is important because it provides valuable information about the properties of the Z boson and the weak nuclear force. By studying its decay patterns, scientists can test and refine the predictions of the Standard Model and search for new physics beyond it.

What are some potential applications of the Z boson decay partial width?

Studying the Z boson decay partial width can help scientists better understand the mechanisms of subatomic particle interactions and possibly lead to new technologies or discoveries. It may also have implications for other fields, such as cosmology, as the weak nuclear force plays a role in the evolution of the universe.

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