Stage 1 � Desired Results by tQ7Cr31i

VIEWS: 4 PAGES: 7

									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 =

								
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