Day 2 Measuring the Z boson and determining the luminosity
In this lab, we want to
- see the Z boson
- measure the mass and width; understand the limitations of the approach
- determine the purity (estimate the background)
- determine the luminosity, from the number of Z events observed
- study the jet multiplicity if these events, and compare to MC predictions
Half of the class will work with electrons, the other half with muons. We will then compare.
We have to copy some files to the work area (more precisely, we will create symbolic links to the files available). When this is done, we can start Jupyter, that will be used for the rest of this lab.
conda activate cms-analysis
cd LPHYS2131/analysis
./prepare.sh
jupyter-lab
We have ntuples for data and Monte Carlo events (Drell-Yann events produced with MadGraph). Using these files, one can determine the selection criterias needed to get a pure sample, keeping the efficiency high. Monte Carlo files generated by CMS using a detailed simulation of the detector are provided in addition to the sample that was produced in the first lab.
We are looking for Z bosons decaying into either electrons or muons. How would you select such events based on the content on the ntuples produced on day 1?
In Jupyter, open the visualization.ipynb in labo2. That notebook contains already the skeleton of the analysis selection. Many more possibilities are available (like 2D plots, etc.) but should not be needed for this activity.
A natural selection will consist in asking two leptons of the same flavor. A cut on the isolation and on the Pt of these leptons might also be a good idea. Where should we cut? You can make up your mind by comparing data to Monte Carlo, interactively. Would you suggest additional cuts? What about jets and missing transverse momentum?
When preparing the cuts, keep in mind that the Monte Carlo simulation is imperfect. Don't blindly cut on quantities there without making sure that this makes also sense on data.
Even with a good selection, there may be remaining background events. To estimate this, we will do a fit of the data with two contributions:
- the invariant mass Z events, either from the MadGraph Monte Carlo distribution or from an analytical form
- an ad hoc background distribution
This will give us an estimate of the purity, and depending on the fit a mesure of the Z boson mass and width.
The fit is easily done with MINUIT. The Zlineshape.ipynb notebook will guide you in the fitting procedure.
Things that should be adapted in the script are: the input files, the binning, the cuts, and the analytical form of the background contribution.
Knowing the number of selected events, the purity, the Z cross-section (from MadGraph) and the selection efficiency, it is easy to get the luminosity:
N_Z = sigma * L * efficiency = N_data * Purity
For this, we have of course to assume that the efficiency in data and simulations are the same.
- if you use the sample produced on day 1, the cross-section is given by MadGraph and can be found in the MadGraph folder where you produced the MC sample: file:///home/cms-opendata/MG5_aMC_v2_4_3/ppNeutralCurrents/crossx.html. Remember that we produced 10000 events.
- in case you use the official CMS sample, you must know that it has a cross-section of 2475pb, and contains originally 40'000'000 events.
- the efficiency is given by the number of MC events passing your cuts divided by the number of generated events.
- N_data, Purity, and N_Z (the product of the two) are given by the Jupyter notebook. There are different ways to determine these numbers, and the precision will depend on your selection.
Good to know: we run on a subset of the 2011 data. The total luminosity recorded in 2011 was 5.55/fb, but the sample available for this lab (2011A, corresponding to data up to 21/08/2011) represents 2.676/fb.
One of the fit that you can perform relies on an analytical description of the Z mass peak. A proper function will allow you to determine the Z boson mass and its width. Does it match your expectations?
Does the result depend on the fit function? How would you take that into account when giving the uncertainty?
- Look at events with one jet. What is the angle between the lepton pair and the jet? How does the Pt of the jet and the Pt of the lepton pair compare. Is that expected? What is the origin of that jet?
- Look at the jet multiplicity. Does the MC reproduce the data? What if you generate events at NLO? Try to fit with a power law or an exponential. Why does it work?
- Compare electrons and muons samples. Are the results the same?