Hunting the Higgs Boson. Part 3 Laboratories / Amelia Brennan. August 1, 2017

Transcription

1 Hunting the Higgs Boson Part 3 Laboratories / Amelia Brennan August 1,

2 Contents 1 Introduction 3 2 Background The Standard Model and the Higgs boson Forces of the Standard Model Elementary Particles Higgs decays The Large Hadron Collider and the ATLAS Detector The LHC The ATLAS detector HYPATIA exercise A cut-based analysis 20 4 Main exercise Events Using ROOT Event selection Plotting your histograms Discussion 31 2

3 1 Introduction In 2012, physicists from the ATLAS and CMS experiments announced that, using data produced by the Large Hadron Collider (LHC), they had discovered a new particle that looked very much like the long-proposed Higgs boson, the missing piece of the Standard Model of particle physics. In this lab, you will learn about different ways the Higgs boson can decay, think about observable final-state particles, and understand how these particles are seen and reconstructed by the ATLAS detector. Using real and simulated data from the ATLAS Collaboration, you will develop an analysis to attempt to discover the elusive boson yourself. 2 Background 2.1 The Standard Model and the Higgs boson The Standard Model of particle physics is a self-consistent description of elementary particles and their interactions. It agrees extremely well with experiment, though with some crucial gaps and problems 1 to keep life interesting! It unifies three of the four forces of nature and describes how elementary particles (such as quarks) combine to form composite particles (such as protons and neutrons). 1 See: dark matter, neutrino masses, the hierarchy problem... 3

4 2.1.1 Forces of the Standard Model There are four known forces in nature, the electromagnetic force, the strong force, the weak force and gravity. The electromagnetic force is responsible for electric and magnetic interactions. These are long-range forces which importantly give rise to atomic structure. The strong force is a short-range force responsible for the formation of particles like protons and neutrons and their binding in atomic nuclei. As the name suggests, the strong force is stronger than the other natural forces, and there is much potential energy locked up in nuclei. The weak force can change a particle from one type into another, and is responsible for particle decays and radioactivity. One of the great achievements of the Standard Model is the unification of these three non-gravitational forces within one consistent theory Elementary Particles Many of the particles observed directly are composite, consisting of some combination of elementary particles. Elementary particles have no determinable substructure, and their properties can be thought of as intrinsic. There are 4

5 two main classes of elementary particles, fermions and bosons. By definition, fermions have non-integer spin, while bosons have integer spin. Fermions There are two known types of elementary fermions in nature, quarks and leptons, both with spin All quarks and leptons have anti-particle partners, equal in mass, but with opposite charges. Lepton Mass (MeV/c 2 ) Charge e ν e < µ ν µ < τ ν τ < Table 1: Leptons of the Standard Model. The mass units will be given in MeV from now on, the 1/c 2 is implied. Leptons are fermions with integer electric charge. There are two classes of lepton: charged leptons which have charge 1, and neutrinos which have charge 0. Leptons are subject to the electromagnetic and weak forces, but are blind 5

6 to the strong force. The lightest and arguably most important charged lepton is the electron. Quarks are fermions with fractional electric charges. There are two classes of quarks: up-type quarks which have electric charge + 2 3, and down-type quarks which have charge 1 3. Unlike leptons, quarks are subject to all the forces of nature including the strong force, and have a strong force charge associated with them, known as colour. Quark Mass (MeV) Charge u - up d - down c - charm 1, s - strange t - top 173, b - bottom 4, Table 2: Quarks of the Standard Model. As can be seen in tables 1 and 2 both leptons and quarks have three families. Each family is identical to the last in every respect but the particle masses. For example, muons and tauons can be thought of as heavier versions of the electron, and the charm and top quarks as heavier versions of the up quark. 6

7 Bosons There are two types of elementary boson, spin-1 and spin-0. The spin-1 bosons are known as the force-carrying particles. They are the mediators of the three non-gravitational forces in the Standard Model. Boson Mass (MeV) Charge Force γ (photon) 0 0 electromagnetic W ± 80,385 ±1 weak Z 0 91,188 0 weak gluons (eight) 0 0 strong Table 3: Spin-1 bosons of the Standard Model. The photon mediates the electromagnetic force. As indicated in table 3, it is massless and chargeless. Given that only charged particles feel the electromagnetic force, the photon is not self-interacting. The eight gluons mediate the strong force. While they do not carry electric charge, the gluons do carry colour, and are therefore self-interacting. This has interesting consequences as will be discussed in the next section. Together with quarks, these are referred to as partons. The W ± and Z 0 bosons (often shortened to W and Z) mediate the weak force. The weak force is technically not a conserved force, being broken by the W ± and Z 0 particle 7

8 masses (don t worry about the details of this, but if you are interested see any good particle physics textbook). A W boson can decay to a charged lepton and a neutrino, e.g. W e + ν e, (1) and will do so approximately 11% of the time to each lepton family. (This is known as a branching fraction.) A Z boson can decay to pairs of charged or neutral leptons, e.g. Z e + e Z ν e ν e (2) with branching fractions of 3.4% to each charged lepton family, and 20% to all neutrino families. Both W and Z bosons decay to quarks the rest of the time. The spin-0 boson of the Standard Model is the famous Higgs boson, which was discovered in 2012 at the LHC. The Higgs is responsible for giving mass to the W and Z bosons in a process known as the Higgs Mechanism. In this lab, you will perform a similar analysis to that used by physicists to discover the Higgs boson and its mass. Hadronisation As you will remember from courses in electromagnetism, as charged particles are separated the electric potential between them decreases. The self-interacting nature of gluons 8

9 means the opposite is true for the strong force. As you separate colour-carrying particles they exchange gluons, which in turn create more gluons and the potential between the quarks increases: this leads to quarks being very strongly attracted to each other and bound tightly into composite objects known as hadrons. Quarks can combine into hadrons as either triplets (qqq or q q q), called baryons or doublets (q q), called mesons. Baryons (such as protons and neutrons) consist of three quarks, and are therefore fermionic. Mesons (such as pions or B-mesons) contain two quarks, and are therefore bosonic. Another consequence of the increasing potential as quarks are separated is that, at some point, it increases so much that it becomes energetically favourable to create a new quark/anti-quark pair out of the vacuum, which subsequently join with the existing quarks to create two hadrons. This process is known as hadronisation. High-energy hadrons tend to radiate gluons and quarks, which will themselves hadronise, thereby creating a shower of hadrons of various types, in an approximately cone-shaped region. In the particle collider context, this cone of hadrons is known as a jet, and is how all hadrons appear in a detector. Jets are very important in a hadron collider such as the LHC, as they are produced in extreme abundance. 9

10 Figure 1: The branching fractions of possible Higgs decays, for a range of hypothetical Higgs masses, courtesy of the LHC Higgs Working Group. 2.2 Higgs decays When heavy particles are produced in high-energy interactions, they tend to be very unstable and decay extremely quickly often too quickly to be observed by any kind of detector. Physicists are therefore forced to look for their decay products, which can be difficult to distinguish from other background processes. For example, a Higgs boson may decay to two quarks, which appear as jets to an observer, but this looks extremely similar to a Z boson which may also decay to two quark-jets. Figure 1 shows the branching fractions of Higgs decays to different decay products. At a Higgs mass of 125 GeV, the most likely decay route is H b b. However, these 10

11 events will be extremely hard to find amongst all the other possible physics processes that lead to two jets, which are very common in a hadron collider such as the LHC. Instead, we are going to study the decay chain H ZZ l + l l + l, where l, l [e, µ]. This is because, as we shall see, stable, elementary leptons are much cleaner and easier to study than hadronic jets in the ATLAS detector data. Q. At m H = 125 GeV, what is the branching fraction of decays to ZZ? Given that a Z decays to e + e and µ + µ 3.4% of the time each, what fraction of all Higgs decays have a 4-lepton final state? 2.3 The Large Hadron Collider and the ATLAS Detector The LHC The LHC, situated at CERN in Geneva, Switzerland, is the largest and most powerful particle accelerator in the world. It is a circular collider 27 km around, running as deep as 175m underground under the border between Switzerland and France. It is designed to collide bunches of protons (or sometimes lead ions) at interaction points within the 11

12 four main detectors (ATLAS, CMS, LHCb and ALICE) situated around the ring. You will be using data collected in 2012, when the LHC was colliding protons together at a centre-of-mass energy of 8 TeV. This energy was obtained by accelerating bunches of protons in opposite directions until they had 4 TeV of energy each, then colliding them head-on. Q. What is 8 TeV in units of Joules? How does this compare to, say, the kinetic energy of a tennis ball tossed at 5m/s? Why then is the LHC considered to be such a high-energy machine? Unfortunately, this does not mean than the energy of each parton-parton interaction is exactly 8 TeV! 2 Because there are three quarks in each proton, along with many gluons and additional quarks popping in and out of existence, we can never say exactly how much energy a colliding parton is carrying, or control it. Instead, we have to produce lots of parton-parton collisions, so that at least some of them will have the right energy to produce a Higgs boson. The number of protons in a bunch during 2012 was approximately , and bunches of protons collided 2 If it were, we would just set this centre-of-mass energy to the expected mass of the Higgs boson, and create a Higgs in every collision a so-called Higgs factory! 12

13 with each other every 50 ns. The total amount of useful data collected was 20.3 fb 1, where the units ( inverse femtobarn ) are like an inverse cross-section (1 barn = cm 2 ). This can be multiplied by the cross-section of a particular process, which simply reflects how likely it is to occur, to obtain the expected number of times that process will occur in the data. That is, Number of events (process i) = total amount of data cross-section (process i) Q. Production of a Higgs boson with mass of 125 GeV has a cross-section of roughly 20 pb. How many times do we expect a Higgs boson to appear in the 2012 data? How many of these decay to a 4-lepton final state? The ATLAS detector At 46m long, 25m in diameter and weighing close to 7000 tonnes, the cylindrically-shaped ATLAS detector is the largest detector on the LHC ring. It is a multi-purpose detector, meaning it was designed to detect as many particles, with as broad a range of energies, as possible, and use these to look for evidence of new physics processes, like the Higgs boson. The entire ATLAS detector is shown in fig. 2. It is made 13

14 Figure 2: The ATLAS detector, image courtesy of CERN. up of several different subdetectors, which look for different particles in different ways, described below. (Note that this information is provided only for context, it is not essential that you understand the details!) ATLAS uses a right-handed coordinate system with its origin at the interaction point (where the proton bunches collide) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the interaction point to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The polar angle θ is measured with respect to the LHC 14

15 (a) Figure 3: The coordinate system used at ATLAS (a), and the distribution of pseudorapidity, η (b). Images from M. Schott, M. Dunford and Wikipedia. (b) beam-line. The pseudorapidity η is an approximation for rapidity y in the high-energy limit, and is defined in terms of the polar angle θ by η = ln tan(θ/2). Transverse momentum and energy are defined as p T = p sin(θ) and E T = E sin(θ) respectively; these are the components of the momentum and energy that lie in the transverse place. Q. Why are the transverse components of momentum and energy important? The inner detector The inner detector is 7m long and 2.3m in diameter, and sits within a 2T magnetic field provided by a solenoid surrounding the detector. As particles move through, they 15

16 deposit very small amounts of energy in the detector, from which a particle track can be reconstructed. Charged particles are deflected by the strong magnetic field, and the resulting curvature of the track can be used to calculate the momentum and the charge of the particle. The calorimeters The calorimeter system of ATLAS is designed to measure the energy of particles as they pass into the detector and are stopped. Only neutrinos and muons are able to pass through relatively unaffected. The calorimeter system extends out to η = 4.9, and is separated into the inner EM calorimeter (for EM showers seeded by electrons or photons) and the outer hadronic calorimeter (for showers seeded by hadrons). In both systems, sampling calorimetry is used, in which particles pass through alternate layers of absorbing and active material; the former layers are designed to force an interaction in order to produce a shower, while the latter layers measure the amount of energy in the shower. While some energy is generally lost in the absorbing layers, this can be quantified and calibrated for, meaning we can reasonably accurately measure the energy of the particle. The electromagnetic calorimeter measures the energy of electrons and photons, which cannot be treated independently; electrons can radiate photons, while pho- 16

17 tons can produce electron-positron pairs, undergo Compton scattering with electrons, and be converted to electrons through the photoelectric effect. The low-energy electrons that are ultimately produced in an electron/photon shower will form ions and so are absorbed, ending the showering process. Given a sufficiently deep calorimeter, most of the energy of such a shower can be contained. The hadronic calorimeter is used to measure the decay of hadrons, however a hadronic shower is not strictly contained within the hadronic calorimeter neutral pions, for example, which are produced in 30% of events, are most likely to decay to a pair of photons, which deposit their energy in the EM calorimeter. Hadronic jets in general are quite complicated objects, producing charged and neutral mesons and baryons, as well as invisible processes almost 30% of the time. As a result, a considerable amount of the hadronic energy is undetectable, and, to complicate matters further, the fraction of energy that is observed tends to depend on the energy of the process, requiring a significant calibration effort. The muon spectrometer The muon spectrometer measures the momenta of muons by bending their trajectories through the use of a toroidal magnet system, and measuring the curvature. The magnetic field is produced by the large barrel toroid magnet and 17

18 Figure 4: The signals of various particle-types in the AT- LAS detector, courtesy of ATLAS. smaller endcap magnets in the ends of the barrel toroid. Identifying particles From understanding of how the different subdetectors work, we can work out how to identify particles from the tracks and energy deposits they leave in the detector see fig. 4. For example, an electron will leave a curved track in the inner detector, and an energy deposit in the EM calorimeter, while a positron will look very similar but curve in the opposite way. Q. Look at each of the particles labeled in fig. 4. Make sure you can explain the curvature of the track and the location of the energy 18

19 deposit in each case. Q. Some particles, such as neutrinos (or dark matter!), do not leave any signal in the detector. How can we infer their presence in the interaction? Speak to your demonstrator if you re not sure. This concept is known as missing transverse momentum (MET). 2.4 HYPATIA exercise There are different programs available for visualising single events detected by ATLAS. We will use one of these, HYPATIA, to identify different particle tracks from real data. In your browser of choice, open zpath_teilchenid3.htm and click through the images to read about how to interpret the event displays. Click on Practice!, and test your knowledge. Now work through the Identifying Events section, and see if you can identify the set of 10 events stored in???, using HYPATIA which is accessible from the desktop. (You can also download it for use at home.) 19

20 You may like to read the section Visualization with HYPATIA for information on how to apply cuts on particle transverse momenta. You have now (hopefully) identified by eye a few Higgs candidate events. You may also have applied some basic cuts on particle momenta, and seen how this can be useful in removing background activity. Of course, it is not practical to sort through millions of events like this instead we write code to do it for us. This is the basis of a cut-based analysis. 3 A cut-based analysis A very simple description of the analysis process is as follows: Identify the observable final state of the signal. In our case, this is l + l l + l, i.e. two pairs of sameflavour, opposite-sign leptons. Estimate the contribution of all physical processes that will lead to this signal, by simulating those processes, and selecting events with the desired final state. We make simulations of both the expected signal (in our case, Higgs production), and all other background processes (such as diboson production 20

21 (W W, W Z and ZZ), single-boson production, t t production, and Drell-Yan processes). 3 Apply initial selections ( cuts ), based on our understanding of the detector, to all simulated and real data, with the aim of cleaning it up. For example, the algorithms that turn signals in the ATLAS detector into usable data containing identified particles will sometimes report the same signal as both an electron and a muon. To handle these cases, we might remove events that contain two overlapping particles. Apply further cuts, based on physics reasons, that aim to make the signal stand out more, and also remove background events as much as possible. For example, our H l + l l + l signal does not contain any neutrinos, so the amount of MET will be small, while processes containing a leptonic W boson will contain a larger amount of MET thanks to the neutrino. Therefore we might apply an upper limit on MET in our event selection. Once all cuts have been applied to the simulated signal, the simulated backgrounds and the data, we can finally compare the data with the signal+background. In particular, we compare the numbers of events remaining after cuts, which may be sorted into bins such as m 4l < 50 GeV, 50 GeV < m 4l < 100 GeV, 3 Simulated events are often referred to as Monte Carlo or MC events. 21

22 m 4l > 100 GeV. If the distribution of the number of events remaining in data matches that in background, we haven t found any new physics. If the data shows extra events that match our predicted new physics signal, then we celebrate! 4 Below is a description of some very common cut variables, and the reasons behind them. Particle cuts p T > X, where X commonly lies between 5 and 20 GeV: Interesting events produced by head-on protonproton collisions usually lead to high-energy decay products that travel transversely outward, so they have a lot of transverse momentum. Non-interesting events more commonly produce a spray of low-energy objects, close to the beam line, which we want to reject. η 2.5: See above. z 0 10mm: z 0 is the shortest distance between the particle track and the interaction point (where the main parton-parton interaction is believed to have occured). If z 0 is small, it is likely the particle was produced in that main interaction; if it is large, the 4 Actually, we check, and check again, and get our peers to check our working... and then we celebrate. 22

23 particle may have been produced in a secondary interaction, or its measured track might be unphysical. R(particle 1, particle 2) 1.0: R (φ 1, φ 2 ) 2 + (η 1 is a measure of the angular closeness of two particles. Overlapping particles may be an indication that a single physical particle has been recorded twice, and should be removed. Event cuts Number of leptons/jets < or > X: Some signals will require several leptons or jets, others will require exactly 0. Some analyses will require, say, exactly two leptons with p T > 30 GeV, and no more than one additional lepton with p T > 7 GeV. MET </> X GeV: See above. Invariant mass of several particles </> X GeV: When particles are expected to have come from the decay of a heavier particle (such as a Z boson), we can reconstruct that particle and require that its mass lie in a certain range (say, m Z ± 15 GeV). And so on... Part of the skill of a particle physicist is being able to think of useful points of difference between signal and background processes, and turning these into exploitable variables. 23

24 4 Main exercise Now you will construct your own code to identify H ZZ l + l l + l events. You ll be basing this on an analysis performed by members of the ATLAS Collaboration, and published in Phys. Rev. D (you can find the public version at Events The real data and simulated events you ll be using are provided by the ATLAS Collaboration, made available through ATLAS Open Data, and stored in folder-location. DataEgamma and DataMuon contain 15 million real data events recorded by the ATLAS detector in They are split into streams containing mostly electrons/photons and mostly muons. Files with H125 ZZ4lep in the name are simulated Higgs signal samples. These were simulated assuming a Higgs boson with a mass of 125 GeV that decays via a pair of Z bosons to four leptons. Talk to your demonstrator about what gg and VBF might mean. The remaining files are various background processes, containing 44.3 million events. Have a think about which processes they might be, and discuss with your demonstrator. 24

25 Q. Which background process to you expect to be the main background for this analysis? Why? 4.2 Using ROOT ROOT is an extremely useful software framework used widely in the ATLAS Collaboration. Begin by looking at one of the samples with the ROOT viewer. Open a terminal, and load the root file into ROOT: $ root -l mc_ wz.root root [0] Attaching file mc_ wz.root as _file0... Open the viewer: root [1] TBrowser x Double-click on the root file, and a folder named mini should appear. This is known as the tree, and contains leaves which store all the variables we can use. The information for all events are shown together, but the event structure is preserved underneath. You can ignore the first half of the variables we will only worry about lep n downwards. Hopefully you should be able to guess what a lot of the variables are already! The 25

26 only important variable that is not obvious is lep type, this has value 11 for electrons/positrons, and 13 for (anti- )muons. Also note that mass, momentum and energy variables are given in units of MeV, and that lep z0 has (confusingly) units of 10mm. You can use the command line to see the contents of the root file: root [2].ls TFile** mc_ wz.root TFile* mc_ wz.root KEY: TTree mini;1 4-vectors + variables required or to count the events contained therein: root [3] mini->getentries() (const Long64_t) or to plot a variable: root [4] mini->draw("lep_pt") Info in <TCanvas::MakeDefCanvas>: created default and you can impose basic selections here as well: root [5] mini->draw("lep_pt", "lep_type==13") 26

27 pt of muons mu_pt Entries Mean RMS Figure 5: The muon p T histogram produced with event selection skeleton.c A skeleton code called event selection skeleton.c, written in C++, is provided in location. You should copy this and store in your own folder. You should also copy over HiggsHeader.C and HiggsHeader.h to the same location. The skeleton code loads the input file, and accesses the mini tree. It initialises a histogram (mu pt), and loops over all events. To get you started, code is also included to loop over all leptons in the event, select the muons, enter their p T into the mu pt histogram, and write the histogram to an output file (outfile XX.root). This output file can be opened in the ROOT viewer as described above, and should contain the histogram shown in fig. 5 when first run over the ggh125 ZZ4lep input file. ROOT contains a useful class called TLorentzVector, for use of four-vectors. With this class, you can: 27

28 set the four-vector variables with vec.setptetaphie(p T, η, φ, E), add four-vectors together simply (vec1 = vec2 + vec3), access particular useful variables, such as momentum components (vec1.px()), mass (vec.m()), angular separation (vec1.deltar(vec2)), and others Event selection We ll now step through the particle and event selection, and try to reconstruct the Higgs mass. These selections are based on the original ATLAS H ZZ l + l l + l paper (see section 5 therein). At every step, produce a relevant histogram (say, number of leptons in each event, or their transverse momenta) comparing the signal and the main background (notes on how to do this are below), and justify the location of the cut (say, p T > 15 GeV). If you think the cut should take a different value, by all means, change it and see! Identify electrons (and positrons), and muons (and anti-muons). Select good electrons with p T > 7 GeV, η < 2.47, and z 0 < 10 mm. Select good muons with p T > 6 GeV, η < 2.7, and z 0 < 1 mm. 5 See for further information. 28

29 Remove events where same-flavour leptons overlap within R = 0.1, and different-flavour leptons overlap within R = 0.2. Select events with exactly four good leptons, and where the first-, second- and third-highest-p T leptons satisfy p T > 20, 15, 10 GeV respectively. Sort the leptons into same-flavour, opposite-sign pairs, and sum the TLorentzVectors together to reconstruct two Z boson candidates. If the leptons can be paired in different ways, choose the pair with invariant mass closest to the Z mass as the leading pair. The second pair is referred to as the sub-leading pair. Vector-sum the Z boson candidates together to obtain a Higgs candidate, as you ll need the Higgs candidate mass (which is equivalent to the invariant mass of the four leptons, m 4l ). Require that the leading lepton pair has invariant mass in the range [50, 106] GeV, and the sub-leading pair has mass in the range [m min, 115] GeV, where m min is 12 GeV for m 4l < 140 GeV, 50 GeV for m 4l > 190 GeV, and varies linearly in between. Finally, make sure you create a Higgs mass histogram, and fill it with all remaining Higgs-candidate masses. You should develop your code while working with one of the simulated Higgs samples and a main background sam- 29

30 ple, which you can compare properly following the notes below. Once fully developed, you should run over the two relevant signal samples, the main background sample and, of course, the data. If you have time, you might like to run over the remaining background samples, but be warned this may take many hours! 4.4 Plotting your histograms To compare two histograms, you ll need to make sure that any simulations are scaled appropriately, to the number of events we would realistically expect to see in the 20.3 fb 1 of data. The scale factor for a simulated process (say, ggh125 ZZ4lep) is given by scale factor = σ process L N events in sample (3) where σ is the cross-section of the process at 8 TeV, and L is the total amount of data (i.e fb 1 ). You ll find a list of the samples with their cross-sections (with units of picobarns) in samples info.py (but don t trust the events variable here, better to use mini->getentries()). Note that you should never scale the data! A basic plotting code, mkplots.c, is provided in location, which you should copy and store in your own folder, and edit as necessary. The basic code takes in two output root files, extracts the mu pt histograms, scales these 30

31 and then plots them together and saves the result as a PDF. You may like to add histograms together, such as ggh125 ZZ4lep and VBFH125 ZZ4lep (make sure they have been scaled to data first!); this can be done simply with hist 1->Add(hist 2). You may also like to compare histograms using the ROOT viewer. This should be done with caution, as it will allow you to compare the shape but not the correctly-scaled size of different samples. Simply double-click on a histogram to display it, type same in the Draw Option space, then double-click on a second histogram to display it on top. You can change the colour of one of the histogram lines by rightclicking directly on the blue line, selecting DrawPanel and selecting an alternate colour. 5 Discussion By now, you should have output files for at least the two signal samples, the main background sample and the two data samples, containing histograms of the Higgs candidate mass and other interesting variables. Turn these into useful plots, where inputs have been scaled and added as appropriate, showing the signal, background and data separately. 31

32 Q. What kind of Higgs mass distribution do you expect to see in the Higgs signal output? What do you actually see? Why? Q. How many background events remain? Q. How does the data output compare to your signal and background? Is this useful? Why/why not? Comment on the selections you made, and why you made them. Describe how you would improve on the analysis. 32