Homework 5: Particle Detectors - Reed...
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Homework 5: Particle Detectors Due March 2 1. Limits of the Tracking System. The tracking system at ATLAS is a cylinder with an outer radius of 1.1 meters which contains a 2 T solenoidal magnetic field (i.e., the magnetic field lines are parallel to the axis of the cylinder). Immediately outside of the tracking system is a region of 0 magnetic field, where the electromagnetic calorimeter is located. (a) The energy of charged particles that do not leave the tracking system is poorly measured because those particles do not reach the calorimetry. Estimate the minimum p T in GeV for an electron to reach the calorimetry. (b) The semiconductor tracker is a subsystem of the tracker that is also a cylinder, but with an outer radius radius of 0.5 meters. It consists of layers of silicon that can measure particle positions accurate to 17 micrometers. Extremely high energy charge particles do not bend enough in the magnetic field to have their charge accurately measured. Estimate the maximum p T in GeV of an electron that the semiconductor tracker can determine bent in the magnetic field. 2. Missing Energy and Neutrinos. The most precise method for measuring the mass of the W boson is in its decays to a lepton l (and electron or muon) and a neutrino ν : W → lν . We’ll discuss the properties of this decay later in this class. Here, we will work to understand this measurement. As discussed in class, neutrinos are not directly observed in collider physics experi- ments, so we aren’t just able to measure the invariant mass of the lepton and neutrino. Also, in protons collisions, a W boson can be produced with a range of momentum along the beam axis, called longitudinal momentum, in the process pp → W → lν . Therefore, we are restricted to measuring the transverse momentum of the visible particle, the lepton. In the following, assume the W boson is on-shell and the leptons are massless. (a) In the process pp → W → lν at the LHC, what is the maximum value of the p T of the lepton? (b) We define the transverse mass m T as the dot product of quantities purely defined from transverse momenta: m 2 T = E T 1 E T 2 - ~ p T 1 · ~ p T 2 , 1
Transcript of Homework 5: Particle Detectors - Reed...
Homework 5: Particle DetectorsDue March 2
1. Limits of the Tracking System. The tracking system at ATLAS is a cylinder with anouter radius of 1.1 meters which contains a 2 T solenoidal magnetic field (i.e., themagnetic field lines are parallel to the axis of the cylinder). Immediately outside of thetracking system is a region of 0 magnetic field, where the electromagnetic calorimeteris located.
(a) The energy of charged particles that do not leave the tracking system is poorlymeasured because those particles do not reach the calorimetry. Estimate theminimum pT in GeV for an electron to reach the calorimetry.
(b) The semiconductor tracker is a subsystem of the tracker that is also a cylinder,but with an outer radius radius of 0.5 meters. It consists of layers of silicon thatcan measure particle positions accurate to 17 micrometers. Extremely high energycharge particles do not bend enough in the magnetic field to have their chargeaccurately measured. Estimate the maximum pT in GeV of an electron that thesemiconductor tracker can determine bent in the magnetic field.
2. Missing Energy and Neutrinos. The most precise method for measuring the mass ofthe W boson is in its decays to a lepton l (and electron or muon) and a neutrino ν:
W → lν .
We’ll discuss the properties of this decay later in this class. Here, we will work tounderstand this measurement.
As discussed in class, neutrinos are not directly observed in collider physics experi-ments, so we aren’t just able to measure the invariant mass of the lepton and neutrino.Also, in protons collisions, a W boson can be produced with a range of momentumalong the beam axis, called longitudinal momentum, in the process
pp→ W → lν .
Therefore, we are restricted to measuring the transverse momentum of the visibleparticle, the lepton. In the following, assume the W boson is on-shell and the leptonsare massless.
(a) In the process pp → W → lν at the LHC, what is the maximum value of the pTof the lepton?
(b) We define the transverse mass mT as the dot product of quantities purely definedfrom transverse momenta:
m2T = ET1ET2 − ~pT1 · ~pT2 ,
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for transverse momentum vectors of particles 1 and 2, and their transverse ener-gies, ET1, ET2. The transverse energy is defined as
ET =√p2T +m2 ,
for a particle of mass m.
What is the maximum value of the transverse mass of the lepton and neutrino?
(c) Below is a recent plot from the ATLAS experiment of the transverse momentumdistribution of electrons in events with electrons and missing energy. This (andother similar) distribution is used for precision measurement of the W boson mass.From this plot and your result in part (a), estimate the W boson mass. (Of courseyou “know” the answer; that’s not what I’m asking! Use features of the plot toestimate the mass.)
This analysis in which this plot was presented produced one of the most precisemeasurements of the W boson mass, accurate to a few parts per 104.
[GeV]lT
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Figure 1: Plot of the transverse momentum of the electron in pp → W− → e−ν̄ events.From M. Aaboud et al. [ATLAS Collaboration], “Measurement of the W -boson mass in ppcollisions at
√s = 7 TeV with the ATLAS detector,” arXiv:1701.07240 [hep-ex].
3. Event Displays. Below is an event display from the ATLAS experiment. The largeimage is a head-on view of the ATLAS experiment, with the tracker, calorimeters,and muon system visible. At the lower right, is a so-called “lego plot”. (Can you tell
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2/8/17, 7:17 AMrun304431-evt2206548301-1GeV.png 2,400×2,400 pixels
Page 1 of 2https://twiki.cern.ch/twiki/pub/AtlasPublic/EventDisplayRun2Physics/run304431-evt2206548301-1GeV.png
Figure 2: Display of a proton collision event from July 25, 2016 in the ATLAS experiment.From ATLAS Experiment c© 2017 CERN.
why it is called that?) This “unrolls” the detector, and displays the distribution of pTdeposited in the (η, φ) plane.
(a) Based on the “hits” in the tracker, EM calorimeter, hadronic calorimeter, andmuon system, identify the particle type of the red and green spike in the legoplot. Both red particles are identical as are both green particles, but red 6= green.
(b) From the lego plot, determine the four-vectors of each of the red and green par-ticles. With these four vectors, answer the following questions:
i. What is the total transverse momentum vector of the four particles?
ii. What is the invariant mass of the four red and green particles together? Thatis, sum their four-momenta and square it. Assume that the particles aremassless. Which particle of the Standard Model does this mass correspondmost closely to?
iii. Approximately what is the speed of this particle along the proton beam di-rection (the z-axis)? To estimate this, approximate the velocity transverse tothe beam as 0.
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4. Analyzing LHC data. From the course website, go to the ATLAS data that is linkedfrom just below this problem set. This links to the Open Data project website byATLAS. We’ll play around with this website and data at various times through therest of this class.
From the main page, go to the “Get Started” page. From there, go to the “ROOTBrowser”. ROOT is software that is ubiquitously used in particles physics for analysisand plotting. From here, you can select different plots of LHC data to play with.
From the drop-down menu below “Read a ROOT file”, select the WtMass.root file,and then click “Load”. You can then select the plot to view below (it’s labeled “Wt-Mass;1”). This shows data (the black dots) on top of simulation (in green, yellow,blue, red, light blue, and orange). Play around with this plot. Note that you can passthe cursor over plot entries (called “bins”) and it will tell you the various values. Howmany data events are in the bin located at MT,W ∈ [70, 75] GeV?
One thing that you can do in ROOT is dynamically change the plotting. As an exampleof this, click and drag the plot from the bin just below 60 GeV to just above 100 GeV.What happens when you release? To go back to the full plot, click the compass rosesymbol in the lower left of the plot.
Continue to play with the ROOT Browser and the Open Data website. You’re actuallymanipulating and analyzing real LHC data!
5. LHC History and pop culture. Watch the “Large Hadron Rap” by Katherine McAlpineand view the first image ever posted on the world wide web at CERN (both linked onthe course website). Who are the back-up dancers in the “Large Hadron Rap”?
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