DOCSLIB.ORG

Collision Dynamics and Reactions of Fractional Vortex Molecules in Coherently Coupled Bose-Einstein Condensates

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Collision Dynamics and Reactions of Fractional Vortex Molecules in Coherently Coupled Bose-Einstein Condensates PHYSICAL REVIEW RESEARCH 2, 033373 (2020) Collision dynamics and reactions of fractional vortex molecules in coherently coupled Bose-Einstein condensates Minoru Eto ,1,2 Kazuki Ikeno,3 and Muneto Nitta2,4,* 1Department of Physics, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata, Yamagata 990-8560, Japan 2Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521, Japan 3Adavito Inc., Hongo-cho 4-26-12, Bunkyo-ku, Tokyo, 113-033, Japan 4Department of Physics, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521, Japan (Received 18 December 2019; accepted 30 March 2020; published 8 September 2020) Coherently coupled two-component Bose-Einstein condensates (BEC) exhibit vortex confinement resembling quark confinement in quantum chromodynamics (QCD). Fractionally quantized vortices winding only in one of two components are attached by solitons, and they cannot stably exist alone. Possible stable states are “hadrons” either of mesonic type, i.e., molecules made of a vortex and antivortex in the same component connected by a soliton, or of baryonic type, i.e., molecules made of two vortices winding in two different components connected by a soliton. Mesonic molecules move straight with a constant velocity while baryonic molecules rotate. We numerically simulate collision dynamics of mesonic and baryonic molecules and find that the molecules swap partners in collisions in general like chemical and nuclear reactions, as well as summarizing all collisions as vortex reactions, and describe those by Feynman diagrams. We find a selection rule for final states after collisions of vortex molecules, analogous to that for collisions of hadrons in QCD. DOI: 10.1103/PhysRevResearch.2.033373 I. INTRODUCTION vortex molecule composed of two fractional vortices [14,16], for which a vortex in the first component and that in the Ultracold atomic gases are experimentally controllable sys- second component are confined by a sine-Gordon soliton. tems offering setups to simulate various problems in physics If the two vortices are at an equilibrium distance, then the [1–3]. For instance, Bose-Einstein condensates (BECs) are molecule is static. On the other hand, if they are slightly superfluids admitting quantized vortices, i.e., vortices carrying more separated or instead pulled closer together, then the quantized circulations [4] known as global strings in cosmol- molecule rotates clockwise or counterclockwise, respectively. ogy, and nucleation of vortices and detecting real-time dynam- If they are further pulled to be more separated, then the ics of them were achieved experimentally recently [5]. Among soliton connecting them is broken by creating another pair of various systems, coherently coupled two-component BECs fractional vortices, and therefore fractional vortices can never realized by the JILA group [6,7] are one interesting system for be liberated (unless the Rabi coupling is turned off). This situ- understanding high-energy physics; when each component is ation resembles the confinement of quarks in QCD; the QCD a different hyperfine state of the same atom, one can introduce vacuum is considered to be a dual superconductor [29–31], a Rabi (Josephson) coupling between them. Then they allow where chromoelectric fluxes are confined to color electric flux vortex molecules, fractionally quantized vortices confined by tubes due to the condensation of magnetic monopoles. Then solitons (linearly extended objects) [8], which are suggested quarks are confined by color electric flux tubes with energy to share several properties with confinement phenomena of linearly dependent on the distance between them. quantum chromodynamics (QCD), a theory of the strong In Ref. [16], we previously indentified fractionally quan- interaction consisting of quarks and gluons. Such fractional tized vortices winding in the first and second components as vortex molecules have been extensively studied theoretically an up-type vortex (or u-vortex for short) and a down-type [9–17], including sine-Gordon like solitons [18–21]. More- vortex (or d-vortex), respectively, borrowing the terminology over, such studies have been extended to three or more com- from quarks in QCD. Similarly, we have called an antivortex ponents [22–27] as well as spinor BECs [28]. Similarities of the first (second) component, theu- ¯ (d-)¯ vortex. In the with QCD were found by studying the dynamics of a single presence of the Rabi coupling, the elementally topological objects are composite defects of u- and d-vortices and the solitons connecting them. There are two possibilities for the *meto(at)sci.kj.yamagata-u.ac.jp, nitta(at)phys-h.keio.ac.jp soliton to select the vortices in a pair on its two endpoints: Either a vortex and an antivortex in the same component such Published by the American Physical Society under the terms of the as u andu ¯ (d and d)¯ or vortices in different species such Creative Commons Attribution 4.0 International license. Further as u and d (¯u and d).¯ We have called the former a mesonic distribution of this work must maintain attribution to the author(s) vortex molecule and the latter a baryonic vortex molecule and the published article’s title, journal citation, and DOI. in analogy with QCD. Let us regard quantized circulations 2643-1564/2020/2(3)/033373(31) 033373-1 Published by the American Physical Society MINORU ETO, KAZUKI IKENO, AND MUNETO NITTA PHYSICAL REVIEW RESEARCH 2, 033373 (2020) TABLE I. Topological winding numbers n1, n2, nS,andnR are u-vortices, with the new meson leaving while the new baryon shown. remains at slightly shifted point from the original baryon position. For scattering of a long meson into a baryon, the n1 n2 nS (baryon #) nR (color charge) 2nR recombination takes place also in this case, so that a long and u10 1/21/21kink bend baryon is formed at first stage, and subsequently a d01 1/2 −1/2 −1 long and bent molecule is unstable and soon disintegrates into u¯ −10 −1/2 −1/2 −1 a shorter meson and a shorter baryon. As a result, the final d0¯ −1 −1/21/21state comprises more molecules than the initial configuration, uu¯ 0 0 0 0 0 resembling what happens in real hadron collider experiments. dd¯ 0 0 0 0 0 We exaggeratedly call it a vortical hadron jet in the vortical ud¯ −11 0 −1 −2 hadron collider (VHC) experiment. du¯ 1 −10 1 2We then further discuss a connection between BEC and QCD comparing Polyakov’s dual photon model in 2 + 1 ud 1 1 1 0 0 dimensions to the low-energy effective theory based on two- u¯d¯ −1 −1 −100 component BECs. We also point out that the so-called Okubo- Zweig-Iizuka (OZI) rule [32–34], which is a phenomenologi- cal law concerning final states of hadronic collisions found in nS as the baryon number in QCD and the winding nR of the 1960s [35], seems to hold in vortex molecule collisions in the relative phase between the two components as the color BECs. charge. Then u- and d-vortices carrying fractional baryon- This paper is organized as follows. In Sec. II,weintro- number-like quarks carry a color charge and therefore cannot duce our model and describe mesonic and baryonic vortex exist alone. On the other hand, mesonic moleculesuu ¯ and molecules. In Secs. III and IV, we study the meson-meson dd¯ do not carry the baryon number like mesons, whereas scattering of the same species (¯uu-¯uu) and of the different baryonic molecules ud carry one baryon number, but both do species (¯uu-dd),¯ respectively. In Sec. V, we study the meson- not carry a color charge (color singlets) and therefore can exist baryon scatterings (¯uu and ud). In Sec. VI, we give comments stably. Table I shows a summary of possible states. on a connection between BEC and QCD. Finally, Sec. VII is In this paper, in order to further understand the similarities devoted to a summary and discussion. between BECs and QCD, we focus on the few-body dynamics of vortex molecules, more precisely their collisions, in con- II. HADRONIC VORTEX MOLECULES trast to previous works focusing on dynamics of either sin- gle molecules [14–16] or many molecules describing vortex Theoretically, the dynamics of the condensates i can be lattices [12] or the Berezinskii-Kosterlitz-Thouless transition described by the coupled Gross-Pitaevskii (GP) equations, [17]. Our numerical studies are twofold: the meson-meson ∂ h¯2 scattering and the meson-baryon scattering. First, we investi- ih + ∇2 − g | |2 + g | |2 − μ ¯ ∂ i i 12 ˆi i i gate the meson-meson scattering of the same species (¯uu-¯uu). t 2m =− ω , = , , First, we simulate head-on collisions (zero impact parameter) h¯ ˆi (i 1 2) (1) by varying the incident angle. We show that the constituent ˆ = ˆ = vortices swap the partners in collisions. The recombination where we use the notation 1 2, 2 1, gij represents the can be understood as a collision of the SG and anti-SG atom-atom coupling constants, m is the mass of atom, and μ solitons, and the swapping is nothing but the pair annihilation i represents the chemical potential of each component. The and creation of the confining SG solitons. The simulation with first and second condensates 1,2 are coherently coupled the initial relative angle π happens to show the right-angle through the Rabi (Josephson) terms with the Rabi frequency ω scattering of the two mesons, which is very common among . Experimentally, such a coherent coupling was achieved by relativistic topological solitons. We then develop a useful the JILA group [7]. In the following, we assume description by employing Feynman diagrams to describe the g1 = g2 ≡ g,μ1 = μ2 ≡ μ, (2) various vortex collision events. We also study the meson- meson scatterings with nonzero impact parameter.
Load more

Recommended publications
  • Book of Abstracts Ii Contents
    2014 CAP Congress / Congrès de l’ACP 2014 Sunday, 15 June 2014 - Friday, 20 June 2014 Laurentian University / Université Laurentienne Book of Abstracts ii Contents An Analytic Mathematical Model to Explain the Spiral Structure and Rotation Curve of NGC 3198. .......................................... 1 Belle-II: searching for new physics in the heavy flavor sector ................ 1 The high cost of science disengagement of Canadian Youth: Reimagining Physics Teacher Education for 21st Century ................................. 1 What your advisor never told you: Education for the ’Real World’ ............. 2 Back to the Ionosphere 50 Years Later: the CASSIOPE Enhanced Polar Outflow Probe (e- POP) ............................................. 2 Changing students’ approach to learning physics in undergraduate gateway courses . 3 Possible Astrophysical Observables of Quantum Gravity Effects near Black Holes . 3 Supersymmetry after the LHC data .............................. 4 The unintentional irradiation of a live human fetus: assessing the likelihood of a radiation- induced abortion ...................................... 4 Using Conceptual Multiple Choice Questions ........................ 5 Search for Supersymmetry at ATLAS ............................. 5 **WITHDRAWN** Monte Carlo Field-Theoretic Simulations for Melts of Diblock Copoly- mer .............................................. 6 Surface tension effects in soft composites ........................... 6 Correlated electron physics in quantum materials ...................... 6 The
    [Show full text]
  • Arxiv:2012.15102V2 [Hep-Ph] 13 May 2021 T > Tc
    Confinement of Fermions in Tachyon Matter at Finite Temperature Adamu Issifu,1, ∗ Julio C.M. Rocha,1, y and Francisco A. Brito1, 2, z 1Departamento de F´ısica, Universidade Federal da Para´ıba, Caixa Postal 5008, 58051-970 Jo~aoPessoa, Para´ıba, Brazil 2Departamento de F´ısica, Universidade Federal de Campina Grande Caixa Postal 10071, 58429-900 Campina Grande, Para´ıba, Brazil We study a phenomenological model that mimics the characteristics of QCD theory at finite temperature. The model involves fermions coupled with a modified Abelian gauge field in a tachyon matter. It reproduces some important QCD features such as, confinement, deconfinement, chiral symmetry and quark-gluon-plasma (QGP) phase transitions. The study may shed light on both light and heavy quark potentials and their string tensions. Flux-tube and Cornell potentials are developed depending on the regime under consideration. Other confining properties such as scalar glueball mass, gluon mass, glueball-meson mixing states, gluon and chiral condensates are exploited as well. The study is focused on two possible regimes, the ultraviolet (UV) and the infrared (IR) regimes. I. INTRODUCTION Confinement of heavy quark states QQ¯ is an important subject in both theoretical and experimental study of high temperature QCD matter and quark-gluon-plasma phase (QGP) [1]. The production of heavy quarkonia such as the fundamental state ofcc ¯ in the Relativistic Heavy Iron Collider (RHIC) [2] and the Large Hadron Collider (LHC) [3] provides basics for the study of QGP. Lattice QCD simulations of quarkonium at finite temperature indicates that J= may persists even at T = 1:5Tc [4] i.e.
    [Show full text]
  • Supersymmetric and Conformal Features of Hadron Physics
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 16 October 2018 doi:10.20944/preprints201810.0364.v1 Peer-reviewed version available at Universe 2018, 4, 120; doi:10.3390/universe4110120 Supersymmetric and Conformal Features of Hadron Physics Stanley J. Brodsky1;a 1SLAC National Accelerator Center, Stanford University Stanford, California Abstract. The QCD Lagrangian is based on quark and gluonic fields – not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a repre- sentation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spec- troscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion qq¯ eigenstate has zero mass for mq = 0: A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also 2 −Q2=4κ2 predicts the form of the nonperturbative QCD running coupling: αs(Q ) / e , in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.
    [Show full text]
  • J. Stroth Asked the Question: "Which Are the Experimental Evidences for a Long Mean Free Path of Phi Mesons in Medium?"
    J. Stroth asked the question: "Which are the experimental evidences for a long mean free path of phi mesons in medium?" Answer by H. Stroebele ~~~~~~~~~~~~~~~~~~~ (based on the study of several publications on phi production and information provided by the theory friends of H. Stöcker ) Before trying to find an answer to this question, we need to specify what is meant with "long". The in medium cross section is equivalent to the mean free path. Thus we need to find out whether the (in medium) cross section is large (with respect to what?). The reference would be the cross sections of other mesons like pions or more specifically the omega meson. There is a further reference, namely the suppression of phi production and decay described in the OZI rule. A “blind” application of the OZI rule would give a cross section of the phi three orders of magnitude lower than that of the omega meson and correspondingly a "long" free mean path. In the following we shall look at the phi production cross sections in photon+p, pion+p, and p+p interactions. The total photoproduction cross sections of phi and omega mesons were measured in a bubble chamber experiment (J. Ballam et al., Phys. Rev. D 7, 3150, 1973), in which a cross section ratio of R(omega/phi) = 10 was found in the few GeV beam energy region. There are results on omega and phi production in p+p interactions available from SPESIII (Near- Threshold Production of omega mesons in the Reaction p p → p p omega", Phys.Rev.Lett.
    [Show full text]
  • The Strange Story of the Quantum
    THE STRANGE STORY OF QUANTUM An account for the GENERAL READER of the growth of the IDEAS underlying our present ATOMIC KNOWLEDGE B A N E S H HOFFMANN DEPARTMENT OF MATHEMATICS, QUEENS COLLEGE, NEW YORK Second Edition DOVER PUBLICATIONS, INC. NEW YORK Copyright 1947, by Banesh Hoffmann. Copyright 1959, by Banesh Hoffmann. All rights reserved under Pan American and International Copyright Conventions. Published simultaneously in Canada by McClelland & Stewart, Ltd. This new Dover edition first published in 1959 is an unabridged and corrected republication of the First Edition to which the author has added a 1959 Postscript. Manufactured in the United States of America. Dover Publications, Inc. 180 Varick Street New York 14, N. Y. My grateful thanks are due to my friends Carl G. Hempel, Melber Phillips, and Mark W. Zemansky, f r many valuable sug- gestions, and to the Institute for Advanced Study where this booJc was begun. B. HOFFMCANIST The Institute for Advanced Study Princeton, N, J v February, 1947 ' / fit, (,. ,,,.| CONTENTS Preface ix I PROLOGUE i ACT I II The Quantum is Conceived 16 III It Comes to Light 24 IV Tweedledum and Tweedledee 34 V The Atom of Niels Bohr 43 VI The Atom of Bohr Kneels 60 INTERMEZZO VII Author's Warning to the Reader 70 ACT II VIII The Exploits of the Revolutionary Prince 72 IX Laundry Lists Are Discarded 84 X The Asceticism of Paul 105 XI Electrons Arc Smeared 109 XII Unification 124 XIII The Strange Denouement 140 XIV The New Landscape of Science 174 XV EPILOGUE 200 Postscript: 1999 235 PREFACE THIS book is designed to serve as a guide to those who would explore the theories by which the scientist seeks to comprehend the mysterious world of the atom.
    [Show full text]
  • Understanding the J/Psi Production Mechanism at PHENIX Todd Kempel Iowa State University
    Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2010 Understanding the J/psi Production Mechanism at PHENIX Todd Kempel Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Physics Commons Recommended Citation Kempel, Todd, "Understanding the J/psi Production Mechanism at PHENIX" (2010). Graduate Theses and Dissertations. 11649. https://lib.dr.iastate.edu/etd/11649 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Understanding the J= Production Mechanism at PHENIX by Todd Kempel A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Nuclear Physics Program of Study Committee: John G. Lajoie, Major Professor Kevin L De Laplante S¨orenA. Prell J¨orgSchmalian Kirill Tuchin Iowa State University Ames, Iowa 2010 Copyright c Todd Kempel, 2010. All rights reserved. ii TABLE OF CONTENTS LIST OF TABLES . v LIST OF FIGURES . vii CHAPTER 1. Overview . 1 CHAPTER 2. Quantum Chromodynamics . 3 2.1 The Standard Model . 3 2.2 Quarks and Gluons . 5 2.3 Asymptotic Freedom and Confinement . 6 CHAPTER 3. The Proton . 8 3.1 Cross-Sections and Luminosities . 8 3.2 Deep-Inelastic Scattering . 10 3.3 Structure Functions and Bjorken Scaling . 12 3.4 Altarelli-Parisi Evolution .
    [Show full text]
  • Thermodynamics of Generalizations of Quantum Chromodynamics
    Fantastic Gauge Theories and Where to Find Them: Thermodynamics of Generalizations of Quantum Chromodynamics by Daniel C. Hackett B.A., University of Virginia, 2012 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics 2019 This thesis entitled: Fantastic Gauge Theories and Where to Find Them: Thermodynamics of Generalizations of Quantum Chromodynamics written by Daniel C. Hackett has been approved for the Department of Physics Prof. Thomas DeGrand Prof. Ethan Neil Prof. Anna Hasenfratz Prof. Paul Romatschke Prof. Markus Pflaum Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Hackett, Daniel C. (Ph.D., Physics) Fantastic Gauge Theories and Where to Find Them: Thermodynamics of Generalizations of Quantum Chromodynamics Thesis directed by Prof. Thomas DeGrand Over the past few decades, lattice gauge theory has been successfully employed to study the finite-temperature phase structure of quantum chromodynamics (QCD), the theory of the strong force. While this endeavor is well-established, QCD is only one strongly-coupled quantum field theory in a larger family of similar theories. Using the lattice toolkit originally invented to investigate QCD, we have begun exploring the phase structures of these cousins of QCD. This thesis focuses on generalizations of QCD with multiple different species of fermions charged under distinct representations of the gauge group. I present the results of the first-ever lattice study of the thermodynamics of one such theory, as well as an analytic calculation which predicts the order of the phase transition for all such theories.
    [Show full text]
  • Exploring the Fundamental Properties of Matter with an Electron-Ion Collider
    Exploring the fundamental properties of matter with an Electron-Ion Collider Jianwei Qiu Theory Center, Jefferson Lab Acknowledgement: Much of the physics presented here are based on the work of EIC White Paper Writing Committee put together by BNL and JLab managements, … Eternal Questions People have long asked Where did we come from? The Big Bang theory? What is the world made of? Basic building blocks? What holds it together? Fundamental forces? Where are we going to? The future? Where did we come from? Can we go back in time or recreate the condition of early universe? Going back in time? Expansion of the universe Little Bang in the Laboratory Create a matter (QGP) with similar temperature and energy density BNL - RHIC CERN - LHC Gold - Gold Lead - Lead Relativistic heavy-ion collisions – the little bang q A virtual Journey of Visible Matter: Lorentz Near Quark-gluon Seen contraction collision plasma Hadronization Freeze-out in the detector q Discoveries – Properties of QGP: ² A nearly perfect quantum fluid – NOT a gas! at 4 trillion degrees Celsius, Not, at 10-5 K like 6Li q Questions: ² How the observed particles were emerged (after collision)? Properties of ² Does the initial condition matter (before collision)? visible matter What the world is made of? Human is only a tiny part of the universe But, human is exploring the whole universe! What hold it together? q Science and technology: Particle & Nuclear Physics Nucleon: Proton, or Neutron Nucleon – building block of all atomic matter q Our understanding of the nucleon evolves 1970s
    [Show full text]
  • Color Symmetry and Quark Confinement
    COLOR SYMMETRY AND QUARK CONFINEMENT Proceedings of the TWELFTH�ENCONTRE DE MORIOND. I 2�. Flaine - Haute-Savoie (France) March 6-March 18, 1977 VOL III COLOR SYMMETRY AND QUARK CONFINEMENT edited by TRAN THANH VAN SPONSORED BY INSTITUT NATIONAL DE PHYSIQUE NUCLEAIRE • ET DE PHYSIQUE DES PARTICULES • COMMISSARIAT A L'ENERGIE ATOMIQUE 3 The " Color Symmetry and Quark Confinement ,, Session was organ ized by G. KANE and TRAN THANH VAN J. With the active collaboration of M. CHANOWITZ ...... ___, \. (/ Permanent SecrCtariat . Rencontre de Moriond Laboratoire de Physique Theoriquc B<."ttiment Universite de Paris-Sud 211 - ORSA Y (France) 91405 Tel. 941-73-72 - 941-73-66 4 FOREWORD The Xllth Rencontre de Moriond has devoted a two-day session to the problem of Color Symmetry and Quark Confinement. The talks given at that session are collected in this book with an added pedagogical introduction. It is hoped that this book will be useful to learn about color and how it can be tested experimentally. The review papers summarize the current situation at April-May 1977. I wish to thank all the contributors for the ir efforts in making the ir papers as pedagogical as possible. TRAN THANH VAN J. 5 CONTENTS G. KANE Pedagogi.cal introduction to color calculations 9 CHANOWITZ Color and experiments M. 25 O.W. GREENBERG Unbound color 51 J.D. JACK SON Hadronic wid ths in charmonium 75 J. KRIPFGANZ Parton mode l structure from a confining theory 89 C. �IGG Dilepton production in hadron-hadron collisions and .the "factor of three" from color 93 M.
    [Show full text]
  • The Confinement Problem in Lattice Gauge Theory
    The Confinement Problem in Lattice Gauge Theory J. Greensite 1,2 1Physics and Astronomy Department San Francisco State University San Francisco, CA 94132 USA 2Theory Group, Lawrence Berkeley National Laboratory Berkeley, CA 94720 USA February 1, 2008 Abstract I review investigations of the quark confinement mechanism that have been carried out in the framework of SU(N) lattice gauge theory. The special role of ZN center symmetry is emphasized. 1 Introduction When the quark model of hadrons was first introduced by Gell-Mann and Zweig in 1964, an obvious question was “where are the quarks?”. At the time, one could respond that the arXiv:hep-lat/0301023v2 5 Mar 2003 quark model was simply a useful scheme for classifying hadrons, and the notion of quarks as actual particles need not be taken seriously. But the absence of isolated quark states became a much more urgent issue with the successes of the quark-parton model, and the introduction, in 1972, of quantum chromodynamics as a fundamental theory of hadronic physics [1]. It was then necessary to suppose that, somehow or other, the dynamics of the gluon sector of QCD contrives to eliminate free quark states from the spectrum. Today almost no one seriously doubts that quantum chromodynamics confines quarks. Following many theoretical suggestions in the late 1970’s about how quark confinement might come about, it was finally the computer simulations of QCD, initiated by Creutz [2] in 1980, that persuaded most skeptics. Quark confinement is now an old and familiar idea, routinely incorporated into the standard model and all its proposed extensions, and the focus of particle phenomenology shifted long ago to other issues.
    [Show full text]
  • Pos(LC2019)030
    Color Confinement and Supersymmetric Properties of Hadron Physics from Light-Front Holography Stanley J. Brodsky∗y PoS(LC2019)030 Stanford Linear Accelerator Center, Stanford University, Stanford, CA, 94309 E-mail: [email protected] I review applications of superconformal algebra, light-front holography, and an extended form of conformal symmetry to hadron spectroscopy and dynamics. QCD is not supersymmetrical in the traditional sense – the QCD Lagrangian is based on quark and gluonic fields – not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconfor- mal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The pion qq¯ eigenstate is composite but yet has zero mass for mq = 0: Light-Front Holography also predicts the form of the nonperturbative QCD running coupling: 2 2 2 as(Q ) ∝ exp Q =4k , in agreement with the effective charge determined from measurements − of the Bjorken sum rule. One also obtains viable predictions for tests of hadron dynamics such as spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combined approach of light-front holography and su- perconformal algebra also provides insight into the origin of the QCD mass scale and color con- finement. A key tool is the dAFF principle which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action.
    [Show full text]
  • Kaon to Two Pions Decays from Lattice QCD: ∆I = 1/2 Rule and CP
    Kaon to Two Pions decays from Lattice QCD: ∆I =1/2 rule and CP violation Qi Liu Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2012 c 2012 Qi Liu All Rights Reserved Abstract Kaon to Two Pions decays from Lattice QCD: ∆I =1/2 rule and CP violation Qi Liu We report a direct lattice calculation of the K to ππ decay matrix elements for both the ∆I = 1/2 and 3/2 amplitudes A0 and A2 on a 2+1 flavor, domain wall fermion, 163 32 16 lattice ensemble and a 243 64 16 lattice ensemble. This × × × × is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are non- perturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this work we take a major step towards the computation of the physical K ππ amplitudes by performing → a complete calculation at unphysical kinematics with pions of mass 422MeV and 329MeV at rest in the kaon rest frame. With this simplification we are able to 3 resolve Re(A0) from zero for the first time, with a 25% statistical error on the 16 3 lattice and 15% on the 24 lattice. The complex amplitude A2 is calculated with small statistical errors.
    [Show full text]