Special H boson with very high cross section?

In summary, the results of the experiment were that there is a new particle at 125 GeV that has a very large cross section for the decay of the heavyest quark-anti-quark pair.
  • #1
unscientific
1,734
13

Homework Statement


(a) Explain the results.
(b) Why is the cross section much higher? Suggest the dominant decay product pair.[/B]

2013_B4_Q2.png


Homework Equations

The Attempt at a Solution


[/B]
Part(a)
For a centre of mass energy of ##170GeV##, you produce pairs of oppositely charged ##W^{\pm},W^{\mp}## bosons. It is kinematically forbidden to produce ##Z,Z## pair and forbidden by charge to produce ##Z,W^{\pm}## pairs.
First group of 4 hadronic jets can be explained by production of 2 pairs of quark/anti-quark stream. Number of combinations = 3x4 = 12 because of 3 colours possible. ~45%
2013_B4_Q2_2.png

Second group can be explained by a quark/anti-quark stream and a lepton/neutrino stream. Number of possibilities = 3x2 + 2x3 = 12. (3 types of leptons, 2 charge types) ~45%
2013_B4_Q2_3.png

Third group can be explained by 2 pairs of lepton/neutrino stream. Number of possibilities = 3 (leptons must be oppositely charged) ~10%
2013_B4_Q2_4.png


Part (b)

This question stumbled me. Is there something special happening at 125 GeV? I suppose the heaviest quark-anti-quark pair it can decay to is the bottom/anti-bottom quark? Why is the cross section so much higher? Why is it that in part (a) only {u,d,c,s} quarks/anti-quarks are produced and not bottom (b) quarks??
 
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  • #2
unscientific said:
It is kinematically forbidden to produce Z,Z pair
The Z has a large width - you will get ZZ events with one Z a bit off-shell, but I guess you can ignore that here.
unscientific said:
Number of combinations = 3x4 = 12 because of 3 colours possible. ~45%
Why 4? And what about the other W?
unscientific said:
Number of possibilities = 3x2 + 2x3 = 12. (3 types of leptons, 2 charge types)
I don't understand what you are adding here.
unscientific said:
Number of possibilities = 3 (leptons must be oppositely charged)
What about the other W?

unscientific said:
Is there something special happening at 125 GeV?
The LHC found a particle at this energy.
unscientific said:
I suppose the heaviest quark-anti-quark pair it can decay to is the bottom/anti-bottom quark?
Right.
unscientific said:
Why is the cross section so much higher?
What does the Higgs couple to?
unscientific said:
Why is it that in part (a) only {u,d,c,s} quarks/anti-quarks are produced and not bottom (b) quarks??
That is a mistake you have to fix in (a).
 
  • #3
mfb said:
The Z has a large width - you will get ZZ events with one Z a bit off-shell, but I guess you can ignore that here.
Why 4? And what about the other W?
Ok, now thinking about it - each W boson can produce 5 possible types of quarks (u,d,s,c,b) so possibilities are 5x5 = 25? But 3 types of colour so 25x3 = 75.

mfb said:
I don't understand what you are adding here.
For the second picture, 5 quark possibilities, 3 types of colour, 3 types of leptons, 2 charges of leptons so 5x3x3x2 = 90? Doesn't match the first one.

mfb said:
What about the other W?
For the third picture, 3 types of leptons but the W bosons must be oppositely charged, so 3 types for the other W boson. So 3x3 = 9

The numbers are all wrong...

mfb said:
The LHC found a particle at this energy.
Right.
What does the Higgs couple to?
That is a mistake you have to fix in (a).
Right, should have noticed they were talking about the Higgs! The Higgs boson couples to mass, so it naturally has an extremely large cross section with the heaviest possible quark, bottom quark. Why is it 40,000 times as large though?
 
  • #4
Sorry, I was thinking of Z decays with my comment about five quarks. No b in W decays as the top is too heavy.

You don't have so many options for the W. Let's consider the W+ boson: it either decays to up+antidown or charm+antistrange. Just two options, multiplied by three for colors => 6.
The W- has 6 options as well.

unscientific said:
The Higgs boson couples to mass, so it naturally has an extremely large cross section with the heaviest possible quark, bottom quark.
That is the dominant decay mode for the 125 GeV Higgs, right.
unscientific said:
Why is it 40,000 times as large though?
What is the electron to muon mass ratio? Do you see how those numbers could be related?
 
  • #5
mfb said:
Sorry, I was thinking of Z decays with my comment about five quarks. No b in W decays as the top is too heavy.

You don't have so many options for the W. Let's consider the W+ boson: it either decays to up+antidown or charm+antistrange. Just two options, multiplied by three for colors => 6.
The W- has 6 options as well.

Why can't the W+ boson decay to charm/antidown? It is calibbo suppressed by ##sin 13^o ## but it is possible? Also why can't W+ boson decay to ##u\bar u, d\bar d, c\bar c## pairs?

First picture
6 options for each W.
Total = 6x6=36 options

Second picture:
Quark producing W can either be W+ or w- = 2x6 = 12 options
For the lepton decay, 3 options.
Total = 12x3=36 options

Third Picture
3 options for each.
Total = 3x3 = 9 options
mfb said:
That is the dominant decay mode for the 125 GeV Higgs, right.
What is the electron to muon mass ratio? Do you see how those numbers could be related?

Mass of muon = 200 times Mass of electrons

I suppose ##\sigma \propto m^2##?
 
  • #6
unscientific said:
Why can't the W+ boson decay to charm/antidown?
It can, but the probability is small. Small enough to neglect it.
Quark + antiquark of the same type would violate charge conservation.

The new numbers look right.
unscientific said:
I suppose ##\sigma \propto m^2##?
Right.
 
  • #7
mfb said:
It can, but the probability is small. Small enough to neglect it.
Quark + antiquark of the same type would violate charge conservation.

The new numbers look right.
Right.
Why is ##\sigma \propto m^2##? I know that ##\Gamma \propto m^5##. Cross section is also (Rate of reactions/Incident Flux) ##\sigma = \frac{\Gamma}{J}##.
 
  • #8
You have two massive particles in the interaction.
For a better description, see the Lagrangian and QFT.
unscientific said:
Cross section is also (Rate of reactions/Incident Flux)
You are mixing unrelated concepts here.
 
  • #9
mfb said:
You have two massive particles in the interaction.
For a better description, see the Lagrangian and QFT.
You are mixing unrelated concepts here.

I thought lifetime ##\tau \propto \frac{1}{\Gamma}## and rate of reactions is decay width ##\Gamma##?
 
  • #10
The decay width is not the reaction rate. They are related if you take the partial width for the right process (here: electron/positron or muon/antimuon).
Also, the total width is not just the mass (the Higgs mass! Not the decay products) to the fifth power, it is a more complicated function as you have to take multiple processes with different thresholds into account.
 
  • #11
mfb said:
The decay width is not the reaction rate. They are related if you take the partial width for the right process (here: electron/positron or muon/antimuon).
Also, the total width is not just the mass (the Higgs mass! Not the decay products) to the fifth power, it is a more complicated function as you have to take multiple processes with different thresholds into account.

True. Upon doing some reading I realized that there is indeed a relation between cross section and rates, using Fermi's golden rule:

[tex]\frac{d\sigma}{d\Omega} = \frac{\Gamma}{\nu} = \frac{1}{\nu}\frac{2\pi}{\hbar} |M_{fi}|^2\frac{dN}{dE}[/tex]

where ##\nu## is incoming flux.

And for EM interactions like ##e^+e^-\rightarrow \mu^+\mu^-## or ##e^+e^-\rightarrow \tau^+\tau^-##, it is ##\sigma = \frac{4 \pi}{3}\left(\frac{\alpha \hbar c}{W} \right)^2## where ##\alpha = \frac{g_{EM}^2}{4\pi}## and ##W## is the centre of mass energy.
 

1. What is the Special H boson with very high cross section?

The Special H boson with very high cross section is a hypothetical particle predicted by some theories of physics. It is a type of Higgs boson that has a much larger probability of being produced in particle collisions compared to the Standard Model Higgs boson.

2. How does the cross section of the Special H boson compare to the Standard Model Higgs boson?

The cross section of the Special H boson is significantly higher than that of the Standard Model Higgs boson, meaning it is more likely to be produced in particle collisions. This is one of the key features that differentiates it from the Standard Model Higgs boson.

3. What is the significance of the Special H boson with very high cross section?

The existence of the Special H boson with very high cross section would challenge the current understanding of the Higgs mechanism and could potentially lead to new discoveries in the field of particle physics. Its discovery would also provide evidence for the validity of certain theories beyond the Standard Model.

4. How is the Special H boson with very high cross section being studied?

The Special H boson with very high cross section is being studied through particle collisions in large-scale experiments, such as the Large Hadron Collider (LHC) at CERN. Scientists are also exploring different theoretical models and analyzing data from these experiments to search for evidence of its existence.

5. What are the potential implications if the Special H boson with very high cross section is discovered?

If the Special H boson with very high cross section is discovered, it could lead to a significant shift in our understanding of the fundamental particles and forces that make up the universe. It could also open up new avenues for research and potentially lead to the development of new technologies based on this new understanding of particle physics.

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