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Lesson Title: Top Quark Lab Discipline Focus: Physics – Quantum Physics Grade level: 11 and 12 Length of lesson: One 47-minute class period Authors: Lindsey Dietz (Feb 2008) and Marian Kramer (Aug 2008) Stage 1 – Desired Results Content Standard(s): Minnesota Academic Standards (2003), Science K-12 Grade 9-12, II. Physical Science, A. Structure of Matter: The student will understand the nature of matter including its forms, properties and interactions Grade 9-12, II. Physical Science, C. Energy Transformations: The student will understand energy forms, transformations and transfers. Understanding (s)/goals Essential Question(s): Students will understand: How do you calculate the mass and The conservation of momentum and direction of the constituents from the top vector addition. and anti-top decay? The nature of a quantum physics event How do you determine the mass of the through observation. neutrino? The basic concept of matter and anti- matter. Quantum physics vocabulary. The E=mc2 formula. Student objectives (outcomes): Students will be able to: 1. The students will understand the addition of vectors. 2. The students will grasp the concept of conservation of momentum. 3. The students will understand the top quark event from the Fermilab data. 4. The students will successfully use math concepts in finding the mass of the top quark. Stage 2 – Assessment Evidence Performance Task(s): Other Evidence: Have students complete the tasks in Ask the class pre-assessment questions on the attached handout. topics in the “understanding/goals” section. Include the essential questions and student objectives in the unit exam. Stage 3 – Learning Plan Learning Activities: 1. Students will first read the background information about the top quark event and look at diagrams of it happening. 2. Next, students will observe a top quark data sheet and learn how the experiment is documented. 3. Then students will draw a vector diagram of the momentums in the event and will need to calculate the missing momentum. 4. Finally, they will use their calculations to determine the mass of the top quark using physics formulas. Materials: 1. Protractor 2. Ruler 3. Calculator 4. Graph paper or scratch paper for vector drawing 5. Lab handout Vocabulary: 1. Quark- generic type of physical particle that forms one of the two basic constituents of matter 2. Muon- elementary particle with negative electric charge and a spin of 1/2 3. Neutrino- elementary particles that travel close to the speed of light, lack an electric charge, are able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect 4. Boson- particles with an integer spin, force carrier particles 5. Momentum- the product of the mass and velocity of an object 6. Vector- an object defined by both magnitude and direction Calculate the Top Quark Mass E mc Used in the Creation of the Most Massive Quark Yet Discovered! 2 Analysis of D-Zero Data From Fermi National Accelerator Laboratory Introduction Today you will make use of Einstein's famous equation and actual experimental data collected in 1995 from a special event that is two-dimensional rather than three-dimensional to determine the mass of the top quark; this is the most massive quark ever discovered. From a computer generated plot of a collision between a proton and an antiproton, you will need to determine the momentum of each bit of debris that comes from the collision. Be sure to remember that momentum has direction! The diagram below shows the collision for the event labeled Run 92704 Event 14022. The other data plots can be represented by diagrams similar to this but may not have exactly the same debris, going in the directions shown here. To view online: http://ed.fnal.gov/samplers/hsphys/activities/emc2/proton_jet2.html and http://ed.fnal.gov/samplers/hsphys/activities/emc2/quarks_event.html While this event looks complex at first, it may be summarized by noting that a proton and antiproton collide to create a top antitop pair that exist for a very short time. Almost immediately the very massive top and antitop decay into the constituents that are known to be their signature. These include four "jets" (large blasts of particles) that are the result of decays of W bosons and some less massive quarks. It is important to note that one of the jets will often contain a low energy or "soft" muon. The soft muon helps identify the jet as a bottom quark jet. In addition, a muon and neutrino come out as debris from the collision. You will notice that there is no information given about the neutrino except the magenta tower indicating its direction on the color plot. While scientists can predict with confidence that it comes out of the collision, it cannot be detected very easily. Still, a careful consideration of the momenta before the collision and after the collision may give you a clue as to how much momentum this particle has! Project 1: Make a momentum vector diagram from experimental data 1. Remember momentum is conserved! The total momentum of the system – the proton and antiproton – before the collision is zero, and it must be zero after the collision. The vectors must add to zero. 2. When you make the vector diagram, measuring the angle is a bit tricky from these plots because the red and blue towers that represent the momentum of the jets are very wide. Pick the angle that you think best represents the direction of the momentum. 3. Vector Review: a. Draw an x- and y-axis. b. Draw your first vector (vector A) the correct direction and length. c. At the tip of the arrow for vector A, assume that there is a new x-axis and y-axis and draw your vector B. d. Repeat for vector C. e. The missing vector has to be drawn from (0,0) on your original xy-axes. In our situation the vector will be pointing to (0,0) since we are looking for the missing one, not the resultant vector. 4. Example of vector diagram Data Sheet There are four "jets" which send out large blasts of particles (red and blue towers). One of the jets will often contain a low energy or "soft" muon (dotted green line). a muon (green tower), and a neutrino. While scientists can predict with confidence that a neutrino comes out of the collision, it cannot be detected very easily. To view in color: http://ed.fnal.gov/samplers/hsphys/activities/graphics/gifs_72/pix_1_26_caltks_end_view.gif Vector Data Table Jet 1 Jet 2 Jet 3 Jet 4 Muon Soft Neutrino Muon Mass (GeV/c) ? Angle (degrees) ? Project 2: Determine the mass of the neutrino Energy, Mass and Momentum Calculations E 2 p 2 m 2 (E=energy, p=momentum, m=mass) When particles are traveling almost the speed of light, c, E mc 2 becomes E m and p mv (p=momentum, m=mass, v=velocity) becomes p mc or p m . In our case, it follows that one should write energy and momentum in terms of the mass of the top quark. E 2 p2 (2mtop )2 When one observes that the net momentum in a plane perpendicular to the beam direction before the collision is the same as the momentum after and that value is zero, we write: E 2 (2mtop )2 or, taking the positive square root of both sides, E 2mtop We can use the values we calculated for momentum (now as energy values) and incorporate their new value for the missing neutrino before adding all the energies. E = Jet 1 + Jet 2 + Jet 3 + Jet 4 + Muon + Soft Muon + Neutrino E = ______+______+______+______+______+______+______=_______= 2m top m top =