DOCSLIB.ORG

Just a Taste Lectures on Flavor Physics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Just a Taste Lectures on Flavor Physics Just a Taste Lectures on Flavor Physics Lecturer: Yuval Grossman(a) (b) LATEX Notes: Flip Tanedo Institute for High Energy Phenomenology, Newman Laboratory of Elementary Particle Physics, Cornell University, Ithaca, NY 14853, USA E-mail: (a) [email protected], (b) [email protected] This version: December 9, 2010 Abstract This is a set of LATEX'ed notes from Cornell University's Physics 7661 (special topics in theoretical high energy physics) course by Yuval Grossman in Fall 2010. The lectures as given were flawless, all errors contained herein reflect solely the typist's editorial and/or intellectual deficiencies! Contents 1 Introduction 1 2 Model building 2 2.1 Example: the Standard Model . .3 2.2 Global, accidental, and approximate symmetries . .4 2.3 Learning how to count [parameters] . .5 2.4 Counting parameters in low-energy QCD . .6 2.5 Counting parameters in the Standard Model . .8 3 A review of hadrons 10 3.1 What we mean by `stable' . 10 3.2 Hadron quantum numbers . 12 3.3 Binding energy . 14 3.4 Light quarks, heavy quarks, and the heaviest quark . 15 3.5 Masses and mixing in mesons . 16 3.6 The pseudoscalar mesons . 19 3.7 The vector mesons . 20 3.8 Why are the pseudoscalar and vector octets so different? . 25 3.9 Hadron names . 26 4 The flavor structure of the Standard Model 29 4.1 The CKM matrix . 29 4.2 Parameterizations of the CKM matrix . 32 4.3 CP violation . 33 4.4 The Jarlskog Invariant . 35 4.5 Unitarity triangles and the unitarity triangle . 36 5 Charged versus neutral currents 38 6 Why FCNCs are so small in the Standard Model 39 6.1 Diagonal versus universal . 39 6.2 FCNCs versus gauge invariance . 39 6.3 FCNCs versus Yukawa alignment . 40 6.4 FCNCs versus broken gauge symmetry reps . 41 7 Parameterizing QCD 43 7.1 The decay constant . 47 7.2 Remarks on the vector mesons . 50 7.3 Form factors . 52 7.4 Aside: Goldstones, currents, and pions . 53 8 Flavor symmetry and the CKM 57 8.1 Measuring jVudj ..................................... 57 8.2 Measuring jVusj ..................................... 61 8.3 Measuring jVcsj ..................................... 69 8.4 Measuring jVcdj ..................................... 73 9 Intermission: Effective Field Theory 77 9.1 EFT is not a dirty word . 78 9.2 A trivial example: muon decay . 81 9.3 The trivial example at one loop . 83 9.4 Mass-independent schemes . 86 9.5 Operator Mixing . 86 10 Remarks on Lattice QCD 86 10.1 Motivation and errors . 87 10.2 `Solving' QCD . 87 10.3 The Nielsen-Ninomiya No-Go Theorem . 88 10.4 The quenched approximation . 90 11 Heavy quark symmetry and the CKM 90 11.1 The hydrogen atom . 91 11.2 Heavy quark symmetry: heuristics . 92 11.3 Heavy quark symmetry: specifics . 93 11.4 HQET . 95 2 11.5 Measuring jVcbj ..................................... 97 11.6 Measuring Vub ...................................... 101 12 Boxes, Penguins, and the CKM 102 12.1 The trouble with top . 102 12.2 Loops, FCNCs, and the GIM mechanism . 103 12.3 Example: b ! sγ .................................... 103 12.4 History of the GIM mechanism . 104 12.5 Measuring the b ! sγ penguin . 105 12.6 Measuring b ! sγ versus b ! dγ ........................... 106 13 Meson Mixing and Oscillation 108 13.1 Open system Hamiltonian . 109 13.2 Time evolution . 112 13.3 Flavor tagging . 112 13.4 Time scales . 114 13.5 Calculating ∆m and ∆Γ . 116 14 Today's lecture: CP violation 120 14.1 CPV in mesons . 122 15 Lecture 19 124 15.1 CP violation from mixing . 127 16 Lecture 20 130 16.1 B ! ππ and isospin . 130 16.2 CP violation in mixing . 133 17 Kaon Physics 134 17.1 KL ! ππ ........................................ 134 17.2 x and y ......................................... 135 1 17.3 K ! ππ and ∆I = 2 Rule . 136 17.4 CP violation . 137 18 New Physics 139 18.1 Minimal Flavor Violation . 139 19 Supersymmetry 141 20 Monika's lecture: Flavor of little Higgs 142 20.1 Little Higgs . 142 20.2 The Littlest Higgs . 143 20.3 EWP constraints . 144 20.4 Flavor and Little Higgs . 144 3 21 Yuval Again: SUSY 144 21.1 Mass insertion approximation . 145 21.2 What can we say about models . 146 21.3 SUSY and MFV . 147 21.4 Froggat-Nielsen . 147 A Notation and Conventions 148 B Facts that you should memorize 149 C Lie groups, Lie algebras, and representation theory 150 C.1 Groups and representations . 150 C.2 Lie groups . 152 C.3 More formal developments . 155 C.4 SU(3) .......................................... 156 D Homework solutions 158 E Critical reception of these notes 174 F Famous Yuval Quotes 174 4 1 Introduction \What is the most important symbol in physics? Is it this: +? Is it this: ×? Is it this: =? No. I claim that it is this: ∼. Tell me the order of magnitude, the scaling. That is the physics." {Yuval Grossman, 21 August 2008. These notes are transcriptions of the Physics 7661: Flavor Physics lectures given by Professor Yuval Grossman at Cornell University in the fall of 2010. Professor Grossman also gave introduc- tory week-long lecture courses geared towards beginning graduate students at the 2009 European School of High-Energy Physics and the 2009 Flavianet School on Flavor Physics [1] and the 2010 CERN-Fermilab Hadron Collider Physics Summer School [2]. A course webpage with homework assignments and (eventually) solutions is available at: http://lepp.cornell.edu/~yuvalg/P7661/. There is no required textbook, but students should have ready access to the Review of Particle Physics prepared by the Particle Data Group and often referred to as `the PDG.' The lecturer explains that the PDG contains \everything you ever wanted to know about anything." All of the contents are available online at the PDG webpage, http://pdg.lbl.gov/. Physicists may also order a free copy of the large and pocket PDG which is updated every two years. The large version includes several review articles that make very good bed-time reading. The data in the PDG will be necessary for some homework problems. Additional references that were particularly helpful during the preparation of these notes were the following textbooks, • Dynamics of the Standard Model, by Donoghue, Golowich, and Holstein. • Gauge theory of elementary particle physics, by Cheng and Li. Both of these are written from a theorist's point of view but do so in a way that is very closely connected to experiments. (A good litmus test for this is whether or not a textbook teaches chiral perturbation theory.) Finally, much of the flavor structure of the Standard Model first appeared experimentally in the decays of hadrons. The techniques used to describe these decays are referred to as the current algebra or the partially conserved axial current and have fallen out of modern quantum field theory courses. We will not directly make use of these methods but will occasionally refer to them for completeness. While many reviews exist on the subject, including [3] and [4], perhaps the most accessible and insightful for modern students is the chapter in Coleman's Aspects of Symmetry on soft pions [5]. Problem 1.1. Bibhushan missed part of the first lecture because he had to attend the course that he's TA'ing, \Why is the sky blue?" As a sample homework problem, what is the color of the sky on Mars? (Solutions problems in these notes appear in Appendix D.) Finally, an apology. There are several important topics in flavor physics that we have been unable to cover. Among the more glaring omissions are lepton flavor (neutrino physics), soft collinear effective theory for b decays, non-relativistic QCD, chiral symmetries, and current algebra techniques. 1 2 Model building In this lecture we will briefly review aspects of the Standard Model to frame our study of its flavor structure. Readers looking for more background material can peruse the first few sections of [1]. The overall goal of high-energy physics can be expressed succinctly in the following form: L = ? (2.1) That is, our job is to determine the Lagrangian of nature and experimentally determine its pa- rameters. In order to answer this question we would like to build models. In fact, it is perhaps more accurate to describe a theorist's job not as model building, but rather model designing. In order to design our Lagrangian, we need to provide three ingredients: 1. The gauge group of the model, 2. The representations of the fields under this gauge group, 3. The pattern of spontaneous symmetry breaking. The last point is typically represented by a sign, for example the sign of the Higgs mass-squared parameter at the unstable vacuum (µ2 < 0). Once we have specified these ingredients, the next step is to write the most general renormaliz- able Lagrangian that is invariant under the gauge symmetry and provides the required spontaneous symmetry breaking pattern. This is far from a trivial statement. The `most general' statement tells us that all terms that satisfy the above conditions must be present in the Lagrangian, even the terms that may be phenomenologically problematic. For example, even though we might not want to include a term that induces proton decay, we cannot simply omit it from our model without some symmetry principle that forbids it. On the other hand, renormalizability strongly constrains the form of a Lagrangian and, in fact, limits us to only a finite number of terms. This condition comes to us from the principles of effective field theory and Wilsonian renormalization group. We assume that the UV (more fundamental) theory may generate all possible operators|including non-renormalizable terms| at the UV scale..
Load more

Recommended publications
  • The Five Common Particles
    The Five Common Particles The world around you consists of only three particles: protons, neutrons, and electrons. Protons and neutrons form the nuclei of atoms, and electrons glue everything together and create chemicals and materials. Along with the photon and the neutrino, these particles are essentially the only ones that exist in our solar system, because all the other subatomic particles have half-lives of typically 10-9 second or less, and vanish almost the instant they are created by nuclear reactions in the Sun, etc. Particles interact via the four fundamental forces of nature. Some basic properties of these forces are summarized below. (Other aspects of the fundamental forces are also discussed in the Summary of Particle Physics document on this web site.) Force Range Common Particles It Affects Conserved Quantity gravity infinite neutron, proton, electron, neutrino, photon mass-energy electromagnetic infinite proton, electron, photon charge -14 strong nuclear force ≈ 10 m neutron, proton baryon number -15 weak nuclear force ≈ 10 m neutron, proton, electron, neutrino lepton number Every particle in nature has specific values of all four of the conserved quantities associated with each force. The values for the five common particles are: Particle Rest Mass1 Charge2 Baryon # Lepton # proton 938.3 MeV/c2 +1 e +1 0 neutron 939.6 MeV/c2 0 +1 0 electron 0.511 MeV/c2 -1 e 0 +1 neutrino ≈ 1 eV/c2 0 0 +1 photon 0 eV/c2 0 0 0 1) MeV = mega-electron-volt = 106 eV. It is customary in particle physics to measure the mass of a particle in terms of how much energy it would represent if it were converted via E = mc2.
    [Show full text]
  • Positronium and Positronium Ions from T
    674 Nature Vol. 292 20 August 1981 antigens, complement allotyping and Theoretically the reasons for expecting of HLA and immunoglobulin allotyping additional enzyme markers would clarify HLA and immunoglobulin-gene linked data together with other genetic markers the point. associations with immune response in and environmental factors should allow Although in the face of the evidence general and autoimmune disease in autoimmune diseases to be predicted presented one tends to think of tissue particular are overwhelming: HLA-DR exactly. However, there is still a typing at birth (to predict the occurrence of antigens (or antigens in the same considerable amount of analysis of both autoimmune disease) or perhaps even chromosome area) are necessary for H LA-region genes and lgG-region genes to before one goes to the computer dating antigen handling and presentation by a be done in order to achieve this goal in the service, there are practical scientific lymphoid cell subset; markers in this region general population. reasons for being cautious. For example, (by analogy with the mouse) are important In Japanese families, the occurrence of Uno et a/. selected only 15 of the 30 for interaction ofT cells during a response; Graves' disease can be exactly predicted on families studied for inclusion without immunoglobulin genes are also involved in the basis of HLA and immunoglobulin saying how or why this selection was made. T-cell recognition and control; HLA-A,-B allotypes, but it is too early to start wearing Second, lgG allotype frequencies are very and -C antigens are important at the "Are you my H LA type?" badges outside different in Caucasoid and Japanese effector arm of the cellular response; and Japan.
    [Show full text]
  • Design of Low-Altitude Martian Orbits Using Frequency Analysis A
    Design of Low-Altitude Martian Orbits using Frequency Analysis A. Noullez, K. Tsiganis To cite this version: A. Noullez, K. Tsiganis. Design of Low-Altitude Martian Orbits using Frequency Analysis. Advances in Space Research, Elsevier, 2021, 67, pp.477-495. 10.1016/j.asr.2020.10.032. hal-03007909 HAL Id: hal-03007909 https://hal.archives-ouvertes.fr/hal-03007909 Submitted on 16 Nov 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Design of Low-Altitude Martian Orbits using Frequency Analysis A. Noulleza,∗, K. Tsiganisb aUniversit´eC^oted'Azur, Observatoire de la C^oted'Azur, CNRS, Laboratoire Lagrange, bd. de l'Observatoire, C.S. 34229, 06304 Nice Cedex 4, France bSection of Astrophysics Astronomy & Mechanics, Department of Physics, Aristotle University of Thessaloniki, GR 541 24 Thessaloniki, Greece Abstract Nearly-circular Frozen Orbits (FOs) around axisymmetric bodies | or, quasi-circular Periodic Orbits (POs) around non-axisymmetric bodies | are of primary concern in the design of low-altitude survey missions. Here, we study very low-altitude orbits (down to 50 km) in a high-degree and order model of the Martian gravity field. We apply Prony's Frequency Analysis (FA) to characterize the time variation of their orbital elements by computing accurate quasi-periodic decompositions of the eccentricity and inclination vectors.
    [Show full text]
  • First Search for Invisible Decays of Ortho-Positronium Confined in A
    First search for invisible decays of ortho-positronium confined in a vacuum cavity C. Vigo,1 L. Gerchow,1 L. Liszkay,2 A. Rubbia,1 and P. Crivelli1, ∗ 1Institute for Particle Physics and Astrophysics, ETH Zurich, 8093 Zurich, Switzerland 2IRFU, CEA, University Paris-Saclay F-91191 Gif-sur-Yvette Cedex, France (Dated: March 20, 2018) The experimental setup and results of the first search for invisible decays of ortho-positronium (o-Ps) confined in a vacuum cavity are reported. No evidence of invisible decays at a level Br (o-Ps ! invisible) < 5:9 × 10−4 (90 % C. L.) was found. This decay channel is predicted in Hidden Sector models such as the Mirror Matter (MM), which could be a candidate for Dark Mat- ter. Analyzed within the MM context, this result provides an upper limit on the kinetic mixing strength between ordinary and mirror photons of " < 3:1 × 10−7 (90 % C. L.). This limit was obtained for the first time in vacuum free of systematic effects due to collisions with matter. I. INTRODUCTION A. Mirror Matter The origin of Dark Matter is a question of great im- Mirror matter was originally discussed by Lee and portance for both cosmology and particle physics. The Yang [12] in 1956 as an attempt to preserve parity as existence of Dark Matter has very strong evidence from an unbroken symmetry of Nature after their discovery cosmological observations [1] at many different scales, of parity violation in the weak interaction. They sug- e.g. rotational curves of galaxies [2], gravitational lens- gested that the transformation in the particle space cor- ing [3] and the cosmic microwave background CMB spec- responding to the space inversion x! −x was not the trum.
    [Show full text]
  • Qcd in Heavy Quark Production and Decay
    QCD IN HEAVY QUARK PRODUCTION AND DECAY Jim Wiss* University of Illinois Urbana, IL 61801 ABSTRACT I discuss how QCD is used to understand the physics of heavy quark production and decay dynamics. My discussion of production dynam- ics primarily concentrates on charm photoproduction data which is compared to perturbative QCD calculations which incorporate frag- mentation effects. We begin our discussion of heavy quark decay by reviewing data on charm and beauty lifetimes. Present data on fully leptonic and semileptonic charm decay is then reviewed. Mea- surements of the hadronic weak current form factors are compared to the nonperturbative QCD-based predictions of Lattice Gauge The- ories. We next discuss polarization phenomena present in charmed baryon decay. Heavy Quark Effective Theory predicts that the daugh- ter baryon will recoil from the charmed parent with nearly 100% left- handed polarization, which is in excellent agreement with present data. We conclude by discussing nonleptonic charm decay which are tradi- tionally analyzed in a factorization framework applicable to two-body and quasi-two-body nonleptonic decays. This discussion emphasizes the important role of final state interactions in influencing both the observed decay width of various two-body final states as well as mod- ifying the interference between Interfering resonance channels which contribute to specific multibody decays. "Supported by DOE Contract DE-FG0201ER40677. © 1996 by Jim Wiss. -251- 1 Introduction the direction of fixed-target experiments. Perhaps they serve as a sort of swan song since the future of fixed-target charm experiments in the United States is A vast amount of important data on heavy quark production and decay exists for very short.
    [Show full text]
  • Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 12: Hadron Decays
    Particle Physics Dr Victoria Martin, Spring Semester 2012 Lecture 12: Hadron Decays !Resonances !Heavy Meson and Baryons !Decays and Quantum numbers !CKM matrix 1 Announcements •No lecture on Friday. •Remaining lectures: •Tuesday 13 March •Friday 16 March •Tuesday 20 March •Friday 23 March •Tuesday 27 March •Friday 30 March •Tuesday 3 April •Remaining Tutorials: •Monday 26 March •Monday 2 April 2 From Friday: Mesons and Baryons Summary • Quarks are confined to colourless bound states, collectively known as hadrons: " mesons: quark and anti-quark. Bosons (s=0, 1) with a symmetric colour wavefunction. " baryons: three quarks. Fermions (s=1/2, 3/2) with antisymmetric colour wavefunction. " anti-baryons: three anti-quarks. • Lightest mesons & baryons described by isospin (I, I3), strangeness (S) and hypercharge Y " isospin I=! for u and d quarks; (isospin combined as for spin) " I3=+! (isospin up) for up quarks; I3="! (isospin down) for down quarks " S=+1 for strange quarks (additive quantum number) " hypercharge Y = S + B • Hadrons display SU(3) flavour symmetry between u d and s quarks. Used to predict the allowed meson and baryon states. • As baryons are fermions, the overall wavefunction must be anti-symmetric. The wavefunction is product of colour, flavour, spin and spatial parts: ! = "c "f "S "L an odd number of these must be anti-symmetric. • consequences: no uuu, ddd or sss baryons with total spin J=# (S=#, L=0) • Residual strong force interactions between colourless hadrons propagated by mesons. 3 Resonances • Hadrons which decay due to the strong force have very short lifetime # ~ 10"24 s • Evidence for the existence of these states are resonances in the experimental data Γ2/4 σ = σ • Shape is Breit-Wigner distribution: max (E M)2 + Γ2/4 14 41.
    [Show full text]
  • 1 Standard Model: Successes and Problems
    Searching for new particles at the Large Hadron Collider James Hirschauer (Fermi National Accelerator Laboratory) Sambamurti Memorial Lecture : August 7, 2017 Our current theory of the most fundamental laws of physics, known as the standard model (SM), works very well to explain many aspects of nature. Most recently, the Higgs boson, predicted to exist in the late 1960s, was discovered by the CMS and ATLAS collaborations at the Large Hadron Collider at CERN in 2012 [1] marking the first observation of the full spectrum of predicted SM particles. Despite the great success of this theory, there are several aspects of nature for which the SM description is completely lacking or unsatisfactory, including the identity of the astronomically observed dark matter and the mass of newly discovered Higgs boson. These and other apparent limitations of the SM motivate the search for new phenomena beyond the SM either directly at the LHC or indirectly with lower energy, high precision experiments. In these proceedings, the successes and some of the shortcomings of the SM are described, followed by a description of the methods and status of the search for new phenomena at the LHC, with some focus on supersymmetry (SUSY) [2], a specific theory of physics beyond the standard model (BSM). 1 Standard model: successes and problems The standard model of particle physics describes the interactions of fundamental matter particles (quarks and leptons) via the fundamental forces (mediated by the force carrying particles: the photon, gluon, and weak bosons). The Higgs boson, also a fundamental SM particle, plays a central role in the mechanism that determines the masses of the photon and weak bosons, as well as the rest of the standard model particles.
    [Show full text]
  • Pion and Kaon Structure at 12 Gev Jlab and EIC
    Pion and Kaon Structure at 12 GeV JLab and EIC Tanja Horn Collaboration with Ian Cloet, Rolf Ent, Roy Holt, Thia Keppel, Kijun Park, Paul Reimer, Craig Roberts, Richard Trotta, Andres Vargas Thanks to: Yulia Furletova, Elke Aschenauer and Steve Wood INT 17-3: Spatial and Momentum Tomography 28 August - 29 September 2017, of Hadrons and Nuclei INT - University of Washington Emergence of Mass in the Standard Model LHC has NOT found the “God Particle” Slide adapted from Craig Roberts (EICUGM 2017) because the Higgs boson is NOT the origin of mass – Higgs-boson only produces a little bit of mass – Higgs-generated mass-scales explain neither the proton’s mass nor the pion’s (near-)masslessness Proton is massive, i.e. the mass-scale for strong interactions is vastly different to that of electromagnetism Pion is unnaturally light (but not massless), despite being a strongly interacting composite object built from a valence-quark and valence antiquark Kaon is also light (but not massless), heavier than the pion constituted of a light valence quark and a heavier strange antiquark The strong interaction sector of the Standard Model, i.e. QCD, is the key to understanding the origin, existence and properties of (almost) all known matter Origin of Mass of QCD’s Pseudoscalar Goldstone Modes Exact statements from QCD in terms of current quark masses due to PCAC: [Phys. Rep. 87 (1982) 77; Phys. Rev. C 56 (1997) 3369; Phys. Lett. B420 (1998) 267] 2 Pseudoscalar masses are generated dynamically – If rp ≠ 0, mp ~ √mq The mass of bound states increases as √m with the mass of the constituents In contrast, in quantum mechanical models, e.g., constituent quark models, the mass of bound states rises linearly with the mass of the constituents E.g., in models with constituent quarks Q: in the nucleon mQ ~ ⅓mN ~ 310 MeV, in the pion mQ ~ ½mp ~ 70 MeV, in the kaon (with s quark) mQ ~ 200 MeV – This is not real.
    [Show full text]
  • Selfconsistent Description of Vector-Mesons in Matter 1
    Selfconsistent description of vector-mesons in matter 1 Felix Riek 2 and J¨orn Knoll 3 Gesellschaft f¨ur Schwerionenforschung Planckstr. 1 64291 Darmstadt Abstract We study the influence of the virtual pion cloud in nuclear matter at finite den- sities and temperatures on the structure of the ρ- and ω-mesons. The in-matter spectral function of the pion is obtained within a selfconsistent scheme of coupled Dyson equations where the coupling to the nucleon and the ∆(1232)-isobar reso- nance is taken into account. The selfenergies are determined using a two-particle irreducible (2PI) truncation scheme (Φ-derivable approximation) supplemented by Migdal’s short range correlations for the particle-hole excitations. The so obtained spectral function of the pion is then used to calculate the in-medium changes of the vector-meson spectral functions. With increasing density and temperature a strong interplay of both vector-meson modes is observed. The four-transversality of the polarisation tensors of the vector-mesons is achieved by a projector technique. The resulting spectral functions of both vector-mesons and, through vector domi- nance, the implications of our results on the dilepton spectra are studied in their dependence on density and temperature. Key words: rho–meson, omega–meson, medium modifications, dilepton production, self-consistent approximation schemes. PACS: 14.40.-n 1 Supported in part by the Helmholz Association under Grant No. VH-VI-041 2 e-mail:[email protected] 3 e-mail:[email protected] Preprint submitted to Elsevier Preprint Feb. 2004 1 Introduction It is an interesting question how the behaviour of hadrons changes in a dense hadronic medium.
    [Show full text]
  • Mean Lifetime Part 3: Cosmic Muons
    MEAN LIFETIME PART 3: MINERVA TEACHER NOTES DESCRIPTION Physics students often have experience with the concept of half-life from lessons on nuclear decay. Teachers may introduce the concept using M&M candies as the decaying object. Therefore, when students begin their study of decaying fundamental particles, their understanding of half-life may be at the novice level. The introduction of mean lifetime as used by particle physicists can cause confusion over the difference between half-life and mean lifetime. Students using this activity will develop an understanding of the difference between half-life and mean lifetime and the reason particle physicists prefer mean lifetime. Mean Lifetime Part 3: MINERvA builds on the Mean Lifetime Part 1: Dice which uses dice as a model for decaying particles, and Mean Lifetime Part 2: Cosmic Muons which uses muon data collected with a QuarkNet cosmic ray muon detector (detector); however, these activities are not required prerequisites. In this activity, students access authentic muon data collected by the Fermilab MINERvA detector in order to determine the half-life and mean lifetime of these fundamental particles. This activity is based on the Particle Decay activity from Neutrinos in the Classroom (http://neutrino-classroom.org/particle_decay.html). STANDARDS ADDRESSED Next Generation Science Standards Science and Engineering Practices 4. Analyzing and interpreting data 5. Using mathematics and computational thinking Crosscutting Concepts 1. Patterns 2. Cause and Effect: Mechanism and Explanation 3. Scale, Proportion, and Quantity 4. Systems and System Models 7. Stability and Change Common Core Literacy Standards Reading 9-12.7 Translate quantitative or technical information .
    [Show full text]
  • Pion, Kaon, and (Anti-) Proton Production in Au+Au Collisions at NN
    Pion, Kaon, and (Anti-) Proton Production in Au+Au Collisions at sNN = 62.4 GeV Ming Shao1,2 for the STAR Collaboration 1University of Science & Technology of China, Anhui 230027, China 2Brookhaven National Laboratory, Upton, New York 11973, USA PACS: 25.75.Dw, 12.38.Mh Abstract. We report on preliminary results of pion, kaon, and (anti-) proton trans- verse momentum spectra (−0.5 < y < 0) in Au+Au collisions at sNN = 62.4 GeV us- ing the STAR detector at RHIC. The particle identification (PID) is achieved by a combination of the STAR TPC and the new TOF detectors, which allow a PID cover- age in transverse momentum (pT) up to 7 GeV/c for pions, 3 GeV/c for kaons, and 5 GeV/c for (anti-) protons. 1. Introduction In 2004, a short run of Au+Au collisions at sNN = 62.4 GeV was accomplished, allowing to further study the many interesting topics in the field of relativistic heavy- ion physics. The measurements of the nuclear modification factors RAA and RCP [1][2] at 130 and 200 GeV Au+Au collisions at RHIC have shown strong hadron suppression at high pT for central collisions, suggesting strong final state interactions (in-medium) [3][4][5]. At 62.4 GeV, the initial system parameters, such as energy and parton den- sity, are quite different. The measurements of RAA and RCP up to intermediate pT and the azimuthal anisotropy dependence of identified particles at intermediate and high pT for different system sizes (or densities) may provide further understanding of the in-medium effects and further insight to the strongly interacting dense matter formed in such collisions [6][7][8][9].
    [Show full text]
  • The Skyrme Model for Baryons
    SU–4240–707 MIT–CTP–2880 # The Skyrme Model for Baryons ∗ a , b J. Schechter and H. Weigel† a)Department of Physics, Syracuse University Syracuse, NY 13244–1130 b)Center for Theoretical Physics Laboratory of Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, Ma 02139 ABSTRACT We review the Skyrme model approach which treats baryons as solitons of an ef- fective meson theory. We start out with a historical introduction and a concise discussion of the original two flavor Skyrme model and its interpretation. Then we develop the theme, motivated by the large NC approximation of QCD, that the effective Lagrangian of QCD is in fact one which contains just mesons of all spins. When this Lagrangian is (at least approximately) determined from the meson sector arXiv:hep-ph/9907554v1 29 Jul 1999 it should then yield a zero parameter description of the baryons. We next discuss the concept of chiral symmetry and the technology involved in handling the three flavor extension of the model at the collective level. This material is used to discuss properties of the light baryons based on three flavor meson Lagrangians containing just pseudoscalars and also pseudoscalars plus vectors. The improvements obtained by including vectors are exemplified in the treatment of the proton spin puzzle. ————– #Invited review article for INSA–Book–2000. ∗This work is supported in parts by funds provided by the U.S. Department of Energy (D.O.E.) under cooper- ative research agreements #DR–FG–02–92ER420231 & #DF–FC02–94ER40818 and the Deutsche Forschungs- gemeinschaft (DFG) under contracts We 1254/3-1 & 1254/4-1.
    [Show full text]