MEASURING PROPERTIES OF W AND Z BOSONS WITH DØ DATA Third Year Laboratory Contributions from Nasim Fatemi-Ghomi, Gavin Hesketh, Peter Walker, Mark Owen, Stefan Söldner-Rembold and David Bailey. © 2009 The University of Manchester 27/08/2009 MEASURING PROPERTIES OF W AND Z BOSONS WITH DØ DATA Third Year Laboratory AIMS 1. To understand the data analysis techniques used in modern particle physics experiments. 2. To use real and simulated data to understand the properties of elec- troweak gauge bosons. 3. To understand the principles of a particle physics detector. OBJECTIVES 1. To write a C++ program to select W and Z events using simulated and real data. 2. To use the data to measure the mass of the W and Z bosons. 3. To use the data to measure the ratio of the W and Z production cross sections and determine the branching ratio BR 푊 ⟶ 휇휐 . 1 27/08/2009 INTRODUCTION DØ is a particle detector at the Tevatron collider at Fermilab near Chicago. The Tevatron collides protons with anti-protons at energies of up to 980 GeV each, giving a collision energy in the centre-of-mass system of 1.96 TeV. The overall aim of the experiment is to test the Standard Model of particle physics and to search for new phenomena – specifically to measure the mass (and other properties) of the top quark and W boson and to search for the Higgs boson. The processes being observed are rare, so statistical analysis is used to sieve information from large quantities of data. During a data-taking period (called a „run‟), millions of interactions (called „events‟) happen every second. Each event produces many kilobytes of information. Ideally we would store all the events for later analysis, but there is simply not enough bandwidth available to record all this information, and a significant amount of it is really of little use. Consequently, “smart” hardware and software triggers are used to make quick decisions about which events should be looked at more closely. These triggers filter out the interesting events, reducing the rate from millions per second to a few hundred per second. This rate is manageable, but still gener- ates many gigabytes of data which require large computing resources to ana- lyse. You have been given a subset of this large dataset which has been preselected (i.e. filtered) to contain at least one muon in every event. CARRIERS OF THE WEAK FORCE: THE W AND Z BOS- ONS Like the other fundamental forces (the strong and electromagnetic interac- tions), the weak interaction is also carried by the exchange of elementary, spin-1 bosons which act as the force carriers between quarks and/or leptons. There are three such bosons – the charged W+ and W- and the neutral Z boson. In contrast to the massless photon of electromagnetism, the weak bos- 2 2 ons have masses of 푀푊 = 80.3 GeV/푐 and 푀푍 = 91.2 GeV/푐 . The W bosons decay into two quarks or into a charged lepton and its corre- sponding neutrino. The Z boson decays into pairs of quarks or leptons of the same flavour. In this experiment you will study the decays of W bosons into a muon and muon-neutrino and the Z boson decays into a pair of muons (휇+휇−). 2 27/08/2009 The branching ratios (i.e. the fraction of all decays of the W/Z that go to this final state) are predicted by the Standard Model. A good introduction can be found in “Particle Physics”, B.R. Martin and G. Shaw, Wiley, Chapter 8. The goal of this analysis is to determine the branching ratio (BR) of W bosons into muons – i.e. the fraction of W bosons decaying into a muon and neutrino. This branching ratio can be calculated in the Standard Model (SM) using other SM parameters as input. Conversely, by measuring SM parameters such as BR 푊 ⟶ 휇휐 or the Z mass, we can constrain as yet unmeasured pa- rameters such as the Higgs mass (assuming the SM is correct). THE DØ DETECTOR AND DATA For an introduction to the DØ detector you can look at http://www- d0.fnal.gov/public/index.html and also read chapter 3 of the MSc thesis by N. Fatemi-Ghomi. A schematic view of the detector is show in Figure 1. You should make sure you understand how muons are identified in the DØ detec- tor before starting your data analysis. Figure 1: Schematic view of the DØ experiment. For this experiment a small subset of the data has been prepared containing events with at least one muon with a momentum component transverse to 3 27/08/2009 the beam (transverse momentum) of more than 15 GeV/푐. The data file, expt.root, contains approximately three million events. It is a slightly sim- plified version of the actual data format used in the experiment. The attrib- utes of the event are stored in a tree-like structure called a „tuple‟. There are four „branches‟: EVT, MET, MU and TRIG. Each branch contains information derived from a different subsystem. Refer to the appendix for details of what each branch contains. To perform the analysis you will need to run over two sets of data. One taken from the experiment and one generated from a Monte Carlo simulation. The Monte Carlo program generates physics processes – in our case the produc- tion of W and Z bosons and their decay into muons. It then takes all the par- ticles produced and tracks them through a full simulation of the detector, producing a data structure equivalent to the experimental data. The Monte Carlo data is then reconstructed by the same programs as real data. The simulated events consist purely of the processes you are looking for, without any background, whereas the real experimental data is a mix of both proc- esses and backgrounds that need to be removed. The experimental data were taken in 2003 over a period of about six months. ANALYSIS As a general rule, always make histograms of the variables you are studying. Especially important are the variables that you use to make event selections with. You should make histograms of these variables before you make a selec- tion so that you can justify your choice later. It‟s also a good idea to either save these histograms in a file or print them to refer to later. When you make histograms, it is always useful to compare real and Monte Carlo (MC) data. Reconstructing and Selecting Z Events In events with two muons, calculate the invariant mass of the two muons. Compare the variables you find in the tuple for the simulated and real Z events and try to find a suitable selection to reduce the background. By plot- ting the invariant mass distribution for selected and rejected events sepa- rately you can study whether your selection rejects mainly background or signal (i.e. real Z events you want to keep). Some questions: What kind of background events are in the data sample? 4 27/08/2009 Why are the Monte Carlo and data invariant mass distributions differ- ent? What is the origin of events where both muons have the same charge? Why are there no events with mass less than 30 GeV/푐2? Which background is rejected by the isolation variables? Do we need to know the muon mass to reconstruct Z events? Cosmics Identify the cosmic events in the data sample using the timing information and the angular separation Δ휃 and Δ휙 between the muons and plot a two- dimensional histogram of 휙 and the pseudorapidity 휂. Some questions: What is the origin of the cosmic ray background in DØ? What scintillator times do you expect for cosmic muons? What is the origin of the structure in the 휂, 휙 histogram? Z Mass Once you have selected a clean sample of Z events, determine the Z mass by fitting a suitable function to the mass histogram. What defines the width of the Z peak? Reconstructing and Selecting W Events Define a selection for W events and reconstruct the transverse mass, defined as: 2 2 2 푀푇 = 퐸/ 푇 + 푝푇 − 퐸/푥 + 푝푥 − 퐸/푦 + 푝푦 where 푝푥 and 푝푦 are the 푥 and 푦 components of the muon momentum and 퐸/푥 and 퐸/푦 are the 푥 and 푦 components of the missing transverse energy 퐸/ 푇. Es- timate the W mass. Why can the longitudinal momentum component of the W boson not be reconstructed? How can you estimate the x and y components of the neutrino‟s mo- mentum? (hint: think about the total transverse momentum before and after the collision). How can you estimate the W mass from the transverse mass distribu- tion? 5 27/08/2009 Can you estimate the number of Z events in your W sample? Why do we have to recalculate 퐸/ 푇 using the momenta of the muon(s) in the event? Why is it relevant that the muon is a “minimum ionising particle” (MIP)? Determination of the Efficiencies The branching ratio BR 푊 ⟶ 휇휐 will be measured from the ratio of the W and Z production cross-sections. Some, but not all, efficiencies will cancel in this ratio if you use the same criteria for selecting the muons. Determine the total efficiencies for reconstructing W and Z events using the Monte Carlo. Calculate the trigger efficiency for MUW_W_L2M3_TRK10 using the inde- pendent trigger method (this assumes that you have selected only events which pass MUW_W_L2M3_TRK10). You must also determine the uncertain- ties on the efficiencies.