Elementary Particles Objective: To learn about the classifications of elementary particles. To reinforce the concept of equivalence of matter and energy. To apply the principle of conservation of momentum on Fermilab data to calculate the mass of the top quark. Apparatus: Computer with internet connection, browser and data analysis software, protractor or angle transparency template. Introduction: You have prior experience with elementary particles in physics lab. Just a few weeks ago in lab, you projected a beam of photons upon a metal, liberating electrons in the process (Photoelectric Effect). In the lab before that, you analyzed the velocities of particles that were created from the beam of protons from the Fermilab accelerator (Special Relativity). In the mid-1930s, physicists believed that these particles, in addition to the neutron, were the basic building blocks of matter. A few years later, accelerator experiments that involved very energetic collisions between known particles revealed the previously undiscovered particles which have very short lifetimes. You have seen this before when you measured the lifetime of the charmed meson in the laboratory frame. Since the 1940s, hundreds of elementary particles have been discovered. In addition, physicists have found out that elementary particles such as the proton and neutron are made up of even smaller particles called quarks. In this lab, we will analyze events from Fermilab data to determine the mass of the top quark, one of several types of quarks..
Theory Fundamental Forces There are four fundamental forces in nature; the two you are familiar with are Gravity and Electromagnetism. Both of these are long-range forces; in fact, their range is infinite. The other two forces, the Nuclear and Weak, act over a short range (<10-15 m). Up to this point, you have considered forces to act at a distance that is, we consider one electron has gravitational and electrical fields around it that extend to infinitity; another electron experiences forces due to these fields but we have neglected exactly how the force is transmitted across the distance. In modern physics, specifically quantum field theory, the force is transmitted via a virtual particles that are exchanged between the two interacting particles. For example, the force between two electrons is due to exchange of virtual photons between them. The photon is then the mediating field particle of the Electromagnetic force. Similarly, the graviton (still undiscovered) is the mediating field particle of the gravitational force. For the remaining two forces, quantum field theory says that the Nuclear force is mediated by the gluon (as in the glue that keeps a nucleus together) while the Weak force is mediated by two particles called the W and Z bosons (named after the physicist Satyendranth Bose). The table below summarizes the forces and their properties: Force Relative Strength Range Field Particle Nuclear 1 10-15 m Gluon Electromagnetic 10-1 Photon Weak 10-5 10-15 m W±,Z 0 bosons Gravitational 10-39 Graviton Taxonomy Except for virtual particles, all elementary particles can be classified into two categories hadrons and leptons. Hadrons are particles that interact through the Nuclear force; leptons are particles that do not. Hadrons are thought to have further structure (composed of quarks); leptons are considered to be truly elementary. Hadrons have two sub-categories of particles: mesons and baryons. Mesons are known to eventually decay into electrons, positrons (the antiparticle of the electron, with similar properties but opposite charge; this is one example of antimatter), photons and neutrinos. Baryons are heavier than hadrons, and eventually decay into particles which include a proton. Leptons, unlike the numerous hadrons, currently number only six the electron, the muon, the tau lepton, and a neutrino associated with each one. Each lepton has an associated antiparticle. Below are some particles properties, in tabular form:
Conservation Laws In addition to the quantities that are conserved during decays or reactions energy, charge, momentum (linear and angular) elementary particles have an additional set of quantities thate need to be conserved: - Baryon Number (B=+1 for baryons, B=-1 for antibaryons, B=0 for all others) - Lepton Number (electron and its neutrino are assigned L e =+1 for leptons, L e =-1 for antileptons, L e =0 for all others; similar quantities L μ and Lτ exist for the muon, tau lepton, and their associated neutrinos). - Strangeness (strange particles are produced in pairs and have unusually long half-lives, they are assigned S=+1 for one particle, S=-1 for the other, S=0 for all non-strange particles). Quarks The original model, as proposed by Gell-Mann and Zweig in 1963, envisioned that hadrons were made up of two or three quarks of different flavors - up, down, and strange. Quarks have fractional electronic charges: up, down and strange have charges of 2/3 e, -1/3 e and -1/3 e, respectively. The three rules of this model required that: - Mesons are composed of quark-antiquark pairs (B=0) - Baryons consist of three quarks - An antibaryon consists of three antiquarks. Due to discrepancies between experiment and this model, physicists added a fourth flavor of quark, charmed, which introduces yet another conservation property charm. The charmed quark has charm C=+1, its antiquark has C=--1 and all other quarks have C=0. Subsequent quark models added still more flavors top and bottom. The additional conservation properties associated with these are topness and bottomness. You must be rolling your eyes at this point, but these quarks have actually all been discovered and the these properties contribute to the Standard Model, the main theory of particle physics which combines all the forces except for Gravity. When Gravity is incorporated into the theory it will be known as the Unified Theory, one that relates all the four fundamental forces to each other. On March 2, 1995, Fermilab announced the discovery of the top quark, the last of the six predicted quarks. The search began in 1977 when physicists found the fifth quark, the bottom, at Fermilab. It took this long because the top quark was much more massive than was originally imagined, so it required a more powerful accelerator to create it. Although the top quark decays too fast to be observed, it does leave behind particles that
give evidence of its existence - a top quark "signature". The top quark can decay in more than one way. Since a top quark appears only once in several billion collisions, it was necessary to perform trillions of collisions. Physicists still do not understand why the top quark is so massive. It is 40 times heavier than the next heaviest quark and about 35,000 times heavier than the up and down quarks that make up most of the matter we see around us. In fact the question still remains why particles have such different masses. Below is a table of the quarks and their properties: Name S y m b o l Mass (Mev/ c 2 ) Spin Charge Baryon Number Strange ness Charm Bottom ness Topness Up u 360 ½ +2/3 e 1/3 0 0 0 0 Down d 360 ½ -1/3 e 1/3 0 0 0 0 Strange s 540 ½ -1/3 e 1/3-1 0 0 0 Charmed c 1500 ½ +2/3 e 1/3 0 1 0 0 Bottom b 5 ½ -1/3 e 1/3 0 0 1 0 Top t? ½ +2/3 e 1/3 0 0 0 1 What you will do in this lab To find the mass of the top quark, you and your lab partner(s) will download from data from a high-energy collision between a proton and antiproton at Fermilab. The proton and antiproton each weigh 0.938 GeV/c 2, more than the Up, Down, and Strange quarks, but less than the Charmed and Bottom quark. The Top Quark far outweighs all of the above combined; in fact it weighs as much as an atom of Gol!. This reinforces the equivalence of matter and energy colliding a proton-antiproton pair is analogous to smashing two ping-pong balls against each other at very high velocity and creating two steel balls, at rest, in the process. Experiment D0 is summarized as follows: 1. A proton and antiproton in the Fermilab's giant Tevatron ring are smashed against each other at very high energies; they are both annihilated in the collision. 2. A top quark and and an antitop quark pair are created in the process.. 3. The top and antitop quarks decay into other particles. 4. These particles are detected by the detector as jets (4 of them), large blasts of particles, and individual particles (3 of them).
While the above 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" 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 can see it in the upper right part of the diagram. This is what the particles detectors see:
The events will be visible in two-dimensional form, viewed from the cross-section (end) of the detector (see circular data plot below). The data consists of momentum and angle:
Note that momentum conservation, as an immutable law of nature, holds throughout the collision and ensuing decays. It will then be possible to calculate the mass of the top quark from the magnitude of the momenta, once you add up their contribution from all the jets and particles as seen above. Be forewarned, though one piece of momentum data (neutrino mass) will be missing from each plot (consisting of 4 jets and 3 particles) you analyzed. You will have to fill that value in using conservation of momentum. The problem is therefore one of vector addition, since the plots you will analyze are in two dimensions. (Recall how you added vectors on the force table in the Forces and Newton's Laws lab last year). The easisest thing to do in two-dimentional conservation of momentum problems is to separate the problem into an X component and a Y component. The equation P total total final = P initial then breaks down to: X Component: Y Component: p final 1 x p final 2 x = p initial 1 x p initial 2 x p final 1 y p final 2 y = p initial 1 y p initial 2 y For more momenta, more terms have to be added - p 3, p 4, p 5, etc. Momentum vectors that lie neither on the X nor Y axis will have to be resolved using trigonometry. For example, in the circular data plot above, the muon with momentum magnitude 61.2 coming out at 18 degrees has these momentum components in the X and Y directions: x :61.2cos18 0 =58.2 x :61.2 sin18 0 =18.9
Making c disappear When you have determined the missing and total momentum, you will need to calculate the masses of both the top quark from it. Remember from the Special Relativity lab that a particle's energy depends on its momentum and mass from the relation: E 2 = p 2 c 2 m 0 c 2 2 (1) In that lab, we used units of MeV/c or GeV/c for momenta and MeV/c 2 or GeV/c 2 for mass so that c or c 2 would conveniently cancel during the calculation. Here we will simplify even further by setting the speed of light c equal to 1 (you have done this before when you plotted velocities 0.9996c to 0.9999c in the Special Relativity lab). At speeds very close to the speed of light (as in Experiment D0), the famous Einstein equation E=mc 2 then becomes E=m. The familiar p=mv becomes p=mc or p=m. Although our scale has changed completely, there is now a simpler relationship (for extremely high velocities) between E, p, and m. Equation (1) then simplifies to: E 2 = p 2 m 0 2 (2) which we rewrite as (dropping the 0 suffix from m): E 2 p 2 =m 2 (3) The masses in question are the two quarks produced right after the proton-antiproton collision. We want an expression for energy and momentum in terms of the mass of the top quark m top so equation (3) becomes: E 2 p 2 = 2 m top 2 (4) The cross-section (end view) plots that you will download represent a plane perpendicular to the colliding proton-antiproton beams. In this plane, net momentum is zero before and after collision, so that equation (4) reduces to this expression: E 2 = 2m top 2 or, E=2m top which gives the mass of the top quark (and antitop quark) in terms of the total energy. In other words, t he total energy (or momenta) from the two top quarks that were formed is equal to the numerical sum of all the momenta discovered after the collision. Procedure A. Study the geometry of Fermilab Experiment D0 1. Go to http://www-ed.fnal.gov/samplers/hsphys/activities/student/event.shtml
2. Click on the plots to examine them in detail and read the description of the plots. 3. Click on the CAL+TKS END VIEW link near the bottom of the page. Read the text to review the identities of the four jets and three particles in the plot. B. Download data from Fermilab Experiment D0 1. Go to http://www-ed.fnal.gov/samplers/hsphys/activities/thumbnails_pdf.html 2. Print out the four circular data plots (not the other two). C. Calculate momenta 1. Note the magnitude and direction (use protractor or estimate using the regulary spaced angular markings on the circular plot) of each jet (4) and particle (3) and record in the back of the data plot. 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 try to choose a line which bisects equal areas of red/blue towers for a given magnitude of momentum. You should have one missing piece of data, the neutrino mass, which you can deduce from momentum conservation show the calculation, and all other calculations, in the back of the printed plots. Remember to write your (and lab partner's) name on the paper. 2. From your calculations, determine the mass of top quark, which should be the same for the antitop quark. Show calculation in back of plot printout. 3. Repeat for the three other plots.