Zee.csv Meaning on CERN Webpage - Stats Project Help

In summary: Gaussian distribution.There is quite a bit of information on the statistical properties of Gaussian distributions, but it is beyond the scope of this summary.
  • #1
taper100
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  • #2
It looks like:

RunNo = run number (collider schedule),

EvNo = event number (in terms of recorded events for current run)

E1 (##E_1##) = energy of 1st electron. Units are GeV.

px1 (##p_{x,1}##)= x-component of momentum of 1st e. Units are GeV/c.

py1 = y-component "

pz1 = z-component "
The coordinates are such that the beam axis is identified with the z-axis

pt1 (##p_{T,1}##) = transverse (with respect to the beam direction) momentum of the 1st e. From the choice of axes, ##p_T = \sqrt{p_x^2 + p_y^2}##.

eta1 (##\eta_1##) = pseudorapidity of 1st e. See http://en.wikipedia.org/wiki/Pseudorapidity for a detailed description. It is related to the angle between the electron path and the beam axis.

phi1 (##\phi_1##) = azimuthal angle of 1st e. This is measured in the x-y plane and appears to be in degrees.

Q1 (##q_1##) = charge of the particle, -1 for the electron, +1 for the positron.

The other set of variables are the same for the other particle.

Another link with a pictorial description of the transverse momentum, pseudorapidity, and azimuthal angle is http://www-cdf.fnal.gov/physics/new/qcd/ue_escan/etaphi.html.
 
  • #3
Excellent, that is very helpful. Thanks. In addition, for my statistics project I need to construct a confidence interval in one part of the project. Using the given data, do you have any ideas of a physical quantity I can construct the confidence interval from (such as mass). For example, is there any relation between the given quantities that would yield the mass of the z boson? I'm a math major and I don't know a whole lot about high energy physics although I have some familiarity with quantum mechanics. So any help would be appreciated.
 
  • #4
taper100 said:
Excellent, that is very helpful. Thanks. In addition, for my statistics project I need to construct a confidence interval in one part of the project. Using the given data, do you have any ideas of a physical quantity I can construct the confidence interval from (such as mass). For example, is there any relation between the given quantities that would yield the mass of the z boson? I'm a math major and I don't know a whole lot about high energy physics although I have some familiarity with quantum mechanics. So any help would be appreciated.

This is a great question and the answer is yes. In the center-of-mass frame, the Z-boson is at rest, so its energy is just given by its mass:

$$ E_\mathrm{com} = m_Z c^2.$$

After the decay, the center of mass energy is given by

$$ E_\mathrm{com}^2 = (E_1+E_2)^2 - |\vec{p}_1 + \vec{p}_2|^2 c^2.$$

Since this decay conserves momentum, we can equate these values to derive a formula for the mass of the Z-boson:

$$m_Z = \sqrt{ \left( \frac{E_1+E_2}{c^2}\right)^2 - \left|\frac{\vec{p}_1 + \vec{p}_2}{c}\right|^2 }.$$

In practice, the distribution values computed from the collected energy and momentum data is assumed to be a Gaussian distribution centered on the true Z mass.
 
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  • #5
fzero said:
In practice, the distribution values computed from the collected energy and momentum data is assumed to be a Gaussian distribution centered on the true Z mass.
That is a good assumption for most particles, where the width of the distribution is dominated by the resolution of the detector. The Z boson is different, you can see its natural line shape - a Breit-Wigner distribution, together with some details you probably don't want to care about. This article gives an introduction.

Usual particle physics results here would be the central mass and the width of the distribution, together with confidence intervals. The cross-section is interesting, too, but it cannot be determined with this dataset.By the way: The energy values for the electrons in the .csv are not measured, they are calculated from the momentum and the known electron mass.
 
  • #6
mfb said:
That is a good assumption for most particles, where the width of the distribution is dominated by the resolution of the detector. The Z boson is different, you can see its natural line shape - a Breit-Wigner distribution, together with some details you probably don't want to care about. This article gives an introduction.

Usual particle physics results here would be the central mass and the width of the distribution, together with confidence intervals. The cross-section is interesting, too, but it cannot be determined with this dataset.

Yes, I should not have forgotten that, thanks!. It would be good for taper100 to actually use the Breit-Wigner distribution, since he'd have a chance to discuss the statistical properties of something other than a boring Gaussian.
 
  • #7
Thanks to everyone for the help. I tried to use the equation for mz to calculate the mass. However, I observed a lot of variation and I got a mean around 143 GeV/c^2. I know that the actual mass of the Z boson is around 91 Gev/c^2, so I believe that I must have done something wrong. I used the following equation
sqrt((E1+E2)^2 + (px1+px2)^2+(py1+py2)^2+(pz1+pz2)^2).
Did I do anything wrong which would cause me to not obtain mass in units of Gev/c^2?
 
  • #8
taper100 said:
Thanks to everyone for the help. I tried to use the equation for mz to calculate the mass. However, I observed a lot of variation and I got a mean around 143 GeV/c^2. I know that the actual mass of the Z boson is around 91 Gev/c^2, so I believe that I must have done something wrong. I used the following equation
sqrt((E1+E2)^2 + (px1+px2)^2+(py1+py2)^2+(pz1+pz2)^2).
Did I do anything wrong which would cause me to not obtain mass in units of Gev/c^2?

Sorry, I had a very important minus sign missing:


$$m_Z = \sqrt{ \left( \frac{E_1+E_2}{c^2}\right)^2 - \left|\frac{\vec{p}_1 + \vec{p}_2}{c}\right|^2 },$$

so sqrt((E1+E2)^2 - (px1+px2)^2-(py1+py2)^2-(pz1+pz2)^2) is the right equation to use.

I just noticed that there is a final column that looks very much like the ##m_Z## as computed from the data. If I could get my spreadsheet to work I would check.
 
  • #9
ok, I adjusted for the minus sign and the results do indeed give the mass in the final column. Thanks for the help. The mean of all of the masses is 74.67 Gev/c^2 with a standard deviation of 27.14. Could you explain why the mean isn't closer to the actual boson mass. I figured the mean would be closer to the actual mass due to the large sample size (n=663). Is there a physical phenomenon that I am not taking into account?
 
  • #10
Not all events in the dataset are coming from Z bosons. You have some background events - pairs of electrons from other sources. You have more background events in the lower mass region. Therefore, the average of all events is not useful. You need some fit to the Z-peak, plus (probably optional) some model for the background. I would neglect all events with a very low calculated mass (<40 GeV). If the Breit-Wigner shape does not fit to the remaining events, you can add an exponential function* to account for those background events.

*in a real analysis for a publication, you would have to study the background shape. An exponential distribution should be a good approximation.
 
  • #11
ok that makes sense, thanks again. What I wanted to do with this statistics project was to construct a confidence interval for the mean of the z boson mass. Is there any method to determine which of the events are background events? If i neglect the low masses as you said, will the rest of the masses be majority those of z bosons?
 

1. What is the purpose of the "Zee.csv" file on the CERN webpage?

The "Zee.csv" file on the CERN webpage is a statistical data file that contains information about the Z boson decay process. This data is used by researchers and scientists to study and analyze the properties of the Z boson, which is an elementary particle that is important in understanding the fundamental forces of the universe.

2. How is the data in the "Zee.csv" file collected?

The data in the "Zee.csv" file is collected through experiments conducted at the Large Hadron Collider (LHC) at CERN. The LHC is a particle accelerator that collides protons at high energies, producing a large number of Z bosons. The collisions are recorded by detectors, and the data is then processed and stored in the "Zee.csv" file.

3. What information does the "Zee.csv" file contain?

The "Zee.csv" file contains various statistical data related to the Z boson decay process, such as the energy and momentum of the particles produced in the decay, the angles at which the particles are emitted, and other relevant information. This data is essential in studying the behavior and properties of the Z boson.

4. How is the "Zee.csv" file used in research at CERN?

The "Zee.csv" file is used by researchers and scientists at CERN to analyze the data and make predictions about the Z boson's properties. This data is also used to test and refine theoretical models and to search for new particles or phenomena that may be present in the Z boson decay process.

5. Is the "Zee.csv" file publicly available?

Yes, the "Zee.csv" file is publicly available on the CERN Open Data Portal. This portal provides free and open access to the data collected at CERN, including the "Zee.csv" file. This allows researchers and scientists from all over the world to access and use the data for their own research purposes.

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