Given its branching fractions how many Higgs can be detected

In summary, the ATLAS experiment recorded a total integrated luminosity of ##5.08fb^{-1}## at 7TeV in 2011 and ##21.3fb^{-1}## at 8TeV in 2012. This allowed for the detection of Higgs bosons through various processes, including gluon-gluon fusion with a cross section of ##\sigma_{ggf} = 19.0 \pm 7.5pb## and vector boson fusion with a cross section of ##\sigma_{vbf} = 1.6 \pm 0.3 pb##. The branching ratio of ##H \rightarrow ZZ## was found to be 2.87%, and for ##
  • #1
Kara386
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Homework Statement


In 2011 the ATLAS experiment had a total integrated recorded luminosity of ##5.08fb^{-1}## at 7TeV, and in 2012 of ##21.3fb^{-1}## at 8TeV. Under these conditions Higgs bosons can be produced in several ways including gluon-gluon fusion and vector boson fusion, which have the cross sections ##\sigma_{ggf} = 19.0 \pm 7.5pb## and ##\sigma_{vbf} = 1.6 \pm 0.3 pb## respectively.

The branching ratio of ##H \rightarrow ZZ## is 2.87%, and for ##Z \rightarrow l^{+}l_{-}## is 3.37% where l is a lepton. How many Higgs, produced by the two processes listed above, could have been detected in the decay mode
##H \rightarrow ZZ^* \rightarrow 4l## where l is electrons or muons?

Homework Equations

The Attempt at a Solution


Integrated luminosity 2012 = ##L_{12}## and for 2011 = ##L_{11}##. I calculated the total number of Higgs produced while the detector was recording by multiplying integrated luminosities for every year by the cross sections for the processes, then adding:
##N = \sigma_{ggf}L_{12} + \sigma_{vbf}L_{12} + \sigma_{ggf}L_{11} + \sigma_{vbf}L_{11}##

##=1.9\times 10^4 fb \times 21.3 fb^{-1} +1.6\times 10^3 fb \times 21.3 fb^{-1} +1.9\times 10^4 fb \times 5.08 fb^{-1} +1.6\times 10^3 fb \times 5.08 fb^{-1}##

##= 543,748## Higgs produced in total.
I don't know how to find the number of detections. I don't have the total decay width and the only equation I know involving branching ratios is ##BF(i) = \frac{\Gamma_i}{\Gamma}##. I thought about just multiplying the probabilities but I think that's probably wrong, and anyway I'm given the branching ratio of Z to any leptons where I need specifically Z to electrons or muons, so I assume that has to be calculated somehow. Can anyone give me some pointers?

Thanks for any help!
 
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  • #2
When I say multiplying probabilities I should clarify I mean multiplying the number of Higgs produced by the probability of the two decay modes i.e. ##543,748\times 0.0287 \times 0.0337 = 52.6##. I'm mainly wondering how to account for the fact that the branching ratio ##3.37%## is to any lepton and actually I want it for electrons or muons.
 
  • #3
Multiplying probabilities works, but you have two Z decays instead of just 1, and you have two possible decays to consider for each Z. The branching fraction is nearly identical for leptons, see your other thread for details, so it is 3.37% for Z->ee and 3.37% for Z->µµ.

The cross section should be different for 7 and 8 TeV, but if the problem statement gives you one value for both energies, well...
 
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  • #4
mfb said:
Multiplying probabilities works, but you have two Z decays instead of just 1, and you have two possible decays to consider for each Z. The branching fraction is nearly identical for leptons, see your other thread for details, so it is 3.37% for Z->ee and 3.37% for Z->µµ.

The cross section should be different for 7 and 8 TeV, but if the problem statement gives you one value for both energies, well...
Ok so it has to go ##H \rightarrow ZZ## so that means 15,606 pairs of Zs are produced. Then it can go ##Z \rightarrow e^+e^-\mu^+\mu^-##, ##Z \rightarrow e^+e^-e^+e^-##, ##Z \rightarrow \mu^+\mu^-\mu^+\mu^-##. Do I need to count ##Z \rightarrow \mu^+\mu^-e^+e^-## as a separate case as well?
 
  • #6
mfb said:
Yes.
If so, should the ##Z \rightarrow e^+e^- e^+e^-## decay and the decay to muon pairs be doubled? By the same kind of logic?
 
  • #7
How many permutations have to be considered? I presume ##e^+e^-## is equivalent to ##e^-e^+##? And on reflection I don't think the other decays have to be doubled, they're the same thing...
 
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  • #8
You can assign labels to the Z bosons: "Z number 1" and "Z number 2". One out of four options is "Z number 1 decays to electron+positron and Z number 2 decays to muon+antimuon". The other options are similar, just by changing the decays.

##e^+ e^-## and ##e^- e^+## is the same thing. You are overthinking this problem.
 
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  • #9
mfb said:
You can assign labels to the Z bosons: "Z number 1" and "Z number 2". One out of four options is "Z number 1 decays to electron+positron and Z number 2 decays to muon+antimuon". The other options are similar, just by changing the decays.

##e^+ e^-## and ##e^- e^+## is the same thing. You are overthinking this problem.
Brilliant, thanks for your help!
 

1. How is the branching fraction of the Higgs determined?

The branching fraction of the Higgs is determined through experimental measurements and theoretical calculations. Scientists use large particle accelerators, such as the Large Hadron Collider, to produce and study the Higgs boson and its decay products. The relative frequencies of different decay modes can then be used to calculate the branching fraction.

2. What is the significance of the Higgs branching fraction?

The branching fraction of the Higgs is important because it tells us how often the Higgs will decay into a specific set of particles. This information is crucial in understanding the properties and behavior of the Higgs boson and its role in the Standard Model of particle physics.

3. How many Higgs bosons can be detected with a certain branching fraction?

The number of Higgs bosons that can be detected depends on several factors, including the energy of the particle accelerator and the experimental conditions. In general, the higher the branching fraction, the more Higgs bosons can be detected.

4. Can the branching fraction of the Higgs change over time?

Yes, the branching fraction of the Higgs can change over time. This can occur due to several reasons, such as new particles being discovered or changes in our understanding of the Standard Model. Scientists continue to study the Higgs and its branching fraction to gain a better understanding of its behavior.

5. How do scientists use the branching fraction to search for new physics?

The branching fraction of the Higgs can provide insight into the existence of new particles or interactions that are not predicted by the Standard Model. By comparing experimental measurements of the Higgs branching fraction to theoretical calculations, scientists can search for discrepancies that may indicate the presence of new physics beyond the Standard Model.

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