DOCSLIB.ORG

Quantum Chromodynamics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Chromodynamics Experimental foundations of Quantum Chromodynamics Marcello Fanti University of Milano and INFN M. Fanti (Physics Dep., UniMi) title in footer 1/78 Introduction What we know as of today? In particle collisions we observe a wide plethora of hadrons These are understood to be bound states of quarks: mesons are qq¯, baryons are qqq —andanti-baryons areq ¯q¯q¯. Quarks (and antiquarks) carry a color charge,responsibleforbindingthemintohadrons.Colorsinteractthrough strong interaction,mediatedbygluons,whichalsocarrycolor. Quark-gluon interactions are described by a well-established gauge theory, Quantum Chromodynamics (QCD). Drawbacks: Hadrons do not carry a net color charge None of the experiments ever observed “free quarks” or “free gluons” Such experimental facts cannot be proved from first principles of QCD, although there are good hints from it ... thereforeonehastointroducea furtherpostulate: the “color confinement” the “fundamental particles” (quarks and gluons) cannot be directly studied, their properties can only be inferred ) from measurements on hadrons Despite all that, QCD works pretty well. In these slides we’ll go through the “experimental evidences” of such a theory. M. Fanti (Physics Dep., UniMi) title in footer 2/78 Bibliography Most of what follows is inspired from: F.Halzen and A.D.Martin “Quarks and leptons” — John Wiley & Sons R.Cahn and G.Goldhaber “The experimental foundations of particle physics” — Cambridge University Press D.Griffiths “Introduction to elementary particles” — Wiley-VCH Suggested reading (maybe after studying QCD): http://web.mit.edu/physics/people/faculty/docs/wilczek_nobel_lecture.pdf [Wilczec Nobel Lecture, 2004] M. Fanti (Physics Dep., UniMi) title in footer 3/78 Prequel: electron elastic scattering on pointlike fermion M. Fanti (Physics Dep., UniMi) title in footer 4/78 ef ef elastic scattering ! (“elastic” means that we have the same particles in initial state and final state) Electron scattering on pointlike fermion with charge Qf (e.g. µ)(mediatedbyaphoton) e e p1 (remember: p1 + p2 = p3 + p4) e p3 µ µ ⌫ ⌫ fermionic e.m. currents: J =¯u3γ u1 ; J =¯u4γ u2 g e f q photon propagator: µ⌫ (where q p p —orq p p ?) q2 ⌘ 1 − 3 ⌘ 2 − 4 (not important, as long as we have q2) eQf p2 p4 QED vertices: e and eQf g e2 f f matrix amplitude: = Jµ e µ⌫ eQ J⌫ = Q JµJ M e · · q2 · f · f q2 f e f ,µ ef ef ✓ ◆ ! 4 2 4 2 2 e Qf µ ⌫ e Qf µ ⌫ = (J J )(J J )⇤ = [(¯u γ u )(¯u γ u )] [(¯u γ u )(¯u γ u )]† |M| q4 e f ,µ e f ,⌫ q4 3 1 4 µ 2 3 1 4 ⌫ 2 4 2 e Qf µ ⌫ = (¯u γ u )(¯u γ u )† (¯u γ u )(¯u γ u )† q4 3 1 3 1 4 µ 2 4 ⌫ 2 h µ⌫ i h i Le Lf ,µ⌫ | {z } | {z p/ + m } p/ m For what follows, recall that averaging over spins gives uu¯ = (and likewise, vv¯ = − ) h ispin 2 h ispin 2 Also, recall that u, u¯,γare 4 1, 1 4, 4 4matrices... ⇥ ⇥ ⇥ M. Fanti (Physics Dep., UniMi) title in footer 5/78 ef ef scattering : fermionic tensors ! Few reminders: 0 0 ⌫ 0 ⌫ u¯ u†γ , γ (γ )†γ = γ µ⌫ µ ⌫ ⌘ Le =(¯u3γ u1)(u¯3γ u1)† Tr [ABC ...Z]=Tr [ZABC ...] µ ⌫ 0 =¯u3 γ u1 u1† (γ )† (u3†γ )† p/ + m p/ m ⌫ uu¯ = , vv¯ = − γ h ispin 2 h ispin 2 µ 0 ⌫ 0 µ ⌫ µ⌫ =¯u3 γ u1 u¯1 γ (γ )†γ u3 Tr [γ γ ]=4g µ ⌫ Tr [γ⇢γµγ⌫]=0 = Tr [¯u3 γ u1zu¯1 γ}|u3]{ ⇢ µ σ ⌫ ⇢µ ⌫ ⇢ µ⌫ ⇢⌫ µσ µ ⌫ Tr [γ γ γ γ ]=4(g g g g + g g ) = Tr [u3 u¯3 γ u1 u¯1 γ ] − p/ + me p/ + me Tr 3 γµ 1 γ⌫ −−−! 2 2 hispin 2 1 me me m = Tr p/ γµp/ γ⌫ + Tr p/ γµγ⌫ + Tr γµp/ γ⌫ + e Tr [γµγ⌫] 4 3 1 4 3 4 1 4 = p ph (g ⇢µg ⌫i g ⇢g µ⌫ +hg ⇢⌫g µσ)i + m2 g µ⌫h i 3,⇢ 1,σ − e = pµp⌫ + p⌫pµ p p m2 g µ⌫ 1 3 1 3 − 1 · 3 − e ... andthesameforthepointlike fermion f What if e were e+?? Need to replace u v,thisa↵ects by flipping sign in front of m ! hispin ... but m eventually enters only through m2,sotheresultdoesnotchange! What we are doing is ok for e±f e±f —andlikewisefore±f¯ e±f¯ ) ! ! M. Fanti (Physics Dep., UniMi) title in footer 6/78 ef ef scattering : matrix element ! Lµ⌫ = pµp⌫ + p⌫pµ p p m2 g µ⌫ e 1 3 1 3 − 1 · 3 − e L = p p + p p p p m2 g f ,µ⌫ 2,µ 4,⌫ 2,⌫ 4,µ− 2 · 4 − f µ⌫ Now neglect electron mass (m 0) — means that E , p~ m —butkeep m e ' 1 | 1| e f Lµ⌫ L =[pµp⌫ + p⌫pµ (p p ) g µ⌫] p p + p p p p m2 g e f ,µ⌫ 1 3 1 3 − 1 · 3 2,µ 4,⌫ 2,⌫ 4,µ − 2 · 4 − f µ⌫ =2 (p p )(p p )+(p p )(p p ) m2 (p p ) 1 · 2 3 · 4 1 · 4 ⇥2 · 3 − f 1 · 3 ⇤ ⇥ ⇤ e4Q2 e4Q2 2 = f Lµ⌫ L =2 f (p p )(p p )+(p p )(p p ) m2 (p p ) |M| q4 e f ,µ⌫ q4 1 · 2 3 · 4 1 · 4 2 · 3 − f 1 · 3 ⇥ ⇤ Using p = p + p p and neglecting p2 = p2 = m2 0: 4 1 2 − 3 1 3 e ' e4Q2 2 =2 f 2(p p )(p p )+(p p )(p p p p m2) |M| q4 1 · 2 3 · 2 1 · 3 2 · 1 − 2 · 3 − f ⇥ ⇤ M. Fanti (Physics Dep., UniMi) title in footer 7/78 ef ef scattering : matrix element in LAB frame ! LAB frame : where f is at rest at the beginning, and e moves along the z-axis outgoing( electronE’;E’sinθ,0,E’cosθ) p (E;0, 0, E);p (E 0; E 0 sin ✓, 0, E 0 cos ✓) θ 1 ⌘ 3 ⌘ incoming electron p (m ;0, 0, 0) ; p (E ; p~ ) (E;0,0,E) 2 ⌘ f 4 ⌘ 4 4 p1 p2 = Emf 2 2 · q =(p1 p3) = 2p1 p3 p1 p3 = EE 0(1 cos✓) − − · · − = 2EE 0(1 cos ✓) p p = m E 0 − − 2 · 3 f 2 2 2 2 2 2 Another useful relation: q + p = p (q + p ) = p q +2q p + m = m q +2m (E E 0)=0 2 4) 2 4) · 2 f f ) f − 2 def q ⌫ = E E 0 = (valid for any ef ef elastic scattering) − − 2mf ! 4 2 2 e Qf 2 2 =2 2m EE 0 + EE 0(1 cos ✓)(mf E mf E 0 m ) |M| q4 f − − − f recall identities : 4 2 ⇥e Q 1+cos✓ 1 cos ✓ E ⇤ E 0 1 cos ✓ ✓ f 2 − =sin2 =2 2 2mf EE 0 + − − [2EE 0(1 cos ✓)] 2 2 mf 2 2 − 1+cos✓ 2 ✓ e4Q2 ✓ q2 ✓ =cos = f m2 cos2 sin2 2 2 4EE sin4 ✓ f 2 − 2m2 2 0 2 ✓ ◆ f ✓ ◆ M. Fanti (Physics Dep., UniMi) title in footer 8/78 ef ef scattering : cross-section in LAB frame ! Compute cross-section in LAB frame (where f is at rest at the beginning) p (E;0, 0, E);p (E 0; E 0 sin ✓, 0, E 0 cos ✓) 1 ⌘ 3 ⌘ p (m ;0, 0, 0) ; p (E ; p~ ) 2 ⌘ f 4 ⌘ 4 4 Incoming speeds: v1 = c =1(relativistic electron) and v2 =0.Numberofspinstates:F3 =2and F4 =2 3 2 d p p~ d p~ d⌦ E 0 dE 0 d⌦ Phase space term for relativistic electron: 3 = | 3| | 3| = (where d⌦ d(cos ✓)dφ) 2E3 2E3 2 ⌘ Phase space term for recoiling fermion: 3 d p4 (3) δ(E4 + E 0 mf E) δ (p~3 + p~4 p~1 p~2)δ(E4 + E3 E1 E2) − − 2E − − − − −−!d3p 2(m + E E ) 4 4 f − 0 Recall Fermi’s golden rule for 1, 2 3, 4 processes:R ! 1 d 3p d 3p dσ = 3 F 4 F (2⇡)4 δ(4) (p + p p p ) 2 4(v + v )E E (2⇡)3 2E 3 (2⇡)3 2E 4 3 4 − 1 − 2 |M| 1 2 1 2 ✓ 3 ◆✓ 4 ◆ 1 1 1 2 2 (E 0 dE 0 d⌦) δ(E4 + E 0 E mf ) −−!d3p 4 Em (2⇡) m + E E − − |M| 4 f ✓ f − 0 ◆ R M. Fanti (Physics Dep., UniMi) title in footer 9/78 ef ef scattering : cross-section in LAB frame ! Now, try to elaborate dE 0 δ(E + E 0 E m ) —remember:E is also a function of E 0 4 − − f 4 2 2 2 2 2 2 2 2 For elastic ef ef , E =(p~ ) + m =(p~ p~ ) + m =(E + E 0 2EE 0 cos ✓)+m ! 4 4 f 1 − 3 f − f def δ(E 0 Eelastic0 ) Call f (E 0) = E 0 + E (E + m ) where f (E 0)=0hassomesolutionE 0 = E 0 δ(f (E 0)) = − 4 − f elastic ) f (E ) | 0 0 | 2 @(E 0 + E4 (E + mf )) @E4 1 @(E4 ) f 0(E 0) − =1+ =1+ ⌘ @E 0 @E 0 2 E4 @E 0 2E 0 2E cos ✓ m + E(1 cos ✓) =1+ − = f − 2(m + E E ) m + E E f − 0 f − 0 mf + E E 0 dE 0 δ(E4 + E 0 E mf ) − − − −−dE ! m + E(1 cos ✓) 0 f − 2 R q mf (E E 0) E and (1 cos ✓)= = − mf + E(1 cos ✓)=mf − −2EE 0 EE 0 ) − E 0 e2 Elastic di↵erential cross-section (recall that ↵ = ): 4⇡ dσ 1 E 2 = 0 2 d⌦ 4(2⇡)2m2 E |M| f ✓ ◆ ↵2Q2 E ✓ q2 ✓ = f 0 cos2 sin2 4E 2 sin4 ✓ E 2 − 2m2 2 2 ✓ ◆ f ✓ ◆ M.
Load more

Recommended publications
  • 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]
  • 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]
  • Journal Club Talk on Confinement
    Journal club talk on Confinement Anirban Lahiri Faculty of Physics 1 What is confinement? [1] I First answer begins with an experimental result : the apparent absence of free quarks in Nature. I These are searches for particles with fractional electric charge. I Suppose existence of a scalar which lives in the same representation of quarks and can form a bound state with quarks. If this scalar is not heavy then till date experiments would have detected fractionally charged particle. I Even absence of such phenomenon still leaves the possibility of detecting such a scalar in future. I Despite the fractional electric charge, bound state systems of this sort hardly qualify as free quarks! So the term \quark confinement” must mean something more than just the absence of isolated objects with fractional electric charge. I Fact : Low-lying hadrons can nicely be described in a scheme in which the constituent quarks combine in a color-singlet. I Fact : No evidence for the existence of isolated gluons, or any other particles in the spectrum, in a color non-singlet state. I Quark confinement , color confinement. 2 What is confinement? [1] There are no isolated particles in Nature with non-vanishing color charge. i.e. all asymptotic particle states are color singlets. I This definition confuses confinement with color screening, and applies equally well to spontaneously broken gauge theories, where there is not supposed to be any such thing as confinement. I Discussions on gauge-Higgs theories [2] and \convenient fiction”[3] ........ 3 Regge trajectories [4] What really distinguishes QCD from a Higgs theory with light quarks is the fact that meson states in QCD fall on linear, nearly parallel, Regge trajectories.
    [Show full text]
  • Hidden-Bottom Pentaquarks
    PHYSICAL REVIEW D 99, 014035 (2019) Hidden-bottom pentaquarks † ‡ Gang Yang,1,* Jialun Ping,2, and Jorge Segovia3, 1Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, People’s Republic of China 2Department of Physics and Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023, People’s Republic of China 3Institut de Física d’Altes Energies (IFAE) and Barcelona Institute of Science and Technology (BIST), Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain (Received 19 September 2018; published 25 January 2019) The LHCb Collaboration has recently reported strong evidences of the existence of pentaquark states in þ þ the hidden-charm baryon sector, the so-called Pcð4380Þ and Pcð4450Þ signals. Five-quark bound states in the hidden-charm sector were explored by us using, for the quark-quark interaction, a chiral quark model which successfully explains meson and baryon phenomenology, from the light to the heavy quark sector. We extend herein such study into the hidden-bottom pentaquark sector, analyzing possible bound-states P 1Æ 3Æ 5Æ 1 3 with spin-parity quantum numbers J ¼ 2 , 2 and 2 , and in the 2 and 2 isospin sectors. We do not find positive parity hidden-bottom pentaquark states; however, several candidates with negative parity are found ΣðÞ ¯ ðÞ with dominant baryon-meson structures b B . Their inner structures have been also analyzed with the computation of the distance among any pair of quarks within the bound-state. This exercise reflects that molecular-type bound-states are favored when only color-singlet configurations are considered in the coupled-channels calculation whereas some deeply-bound compact pentaquarks can be found when hidden-color configurations are added.
    [Show full text]
  • Pentaquark and Tetraquark States Arxiv:1903.11976V2 [Hep-Ph]
    Pentaquark and Tetraquark states 1 2 3 4;5 6;7;8 Yan-Rui Liu, ∗ Hua-Xing Chen, ∗ Wei Chen, ∗ Xiang Liu, y Shi-Lin Zhu z 1School of Physics, Shandong University, Jinan 250100, China 2School of Physics, Beihang University, Beijing 100191, China 3School of Physics, Sun Yat-Sen University, Guangzhou 510275, China 4School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China 5Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China 6School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China 7Collaborative Innovation Center of Quantum Matter, Beijing 100871, China 8Center of High Energy Physics, Peking University, Beijing 100871, China April 2, 2019 Abstract The past seventeen years have witnessed tremendous progress on the experimental and theo- retical explorations of the multiquark states. The hidden-charm and hidden-bottom multiquark systems were reviewed extensively in Ref. [1]. In this article, we shall update the experimental and theoretical efforts on the hidden heavy flavor multiquark systems in the past three years. Espe- cially the LHCb collaboration not only confirmed the existence of the hidden-charm pentaquarks but also provided strong evidence of the molecular picture. Besides the well-known XYZ and Pc states, we shall discuss more interesting tetraquark and pentaquark systems either with one, two, three or even four heavy quarks. Some very intriguing states include the fully heavy exotic arXiv:1903.11976v2 [hep-ph] 1 Apr 2019 tetraquark states QQQ¯Q¯ and doubly heavy tetraquark states QQq¯q¯, where Q is a heavy quark.
    [Show full text]
  • QCD, Jets, & Gluons
    QCD, Jets, & Gluons • Quantum Chromodynamics (QCD) • e+ e- → µ+ µ- • e+ e- annihilation to hadrons ( e+ e- → QQ ) J. Brau QCD, Jets and Gluons 1 Quantum Chromodynamics • Another gauge theory, as QED • Interactions described by exchange of massless, spin-1 bosons – so-called “gauge bosons” • Force is long range, due to massless gluons – but long range force is cancelled by combinations of color in mesons and baryons J. Brau QCD, Jets and Gluons 2 The color quantum number • Color was invented to explain: – Δ++ = uuu – e+e- → hadrons – Also explains π0 → γ γ • Color of a quark has three possible values – say red, blue, green • Antiquarks carry anticolor – Anti-red, anti-blue, anti-green • Bosons mediating the quark-quark interaction are called gluons – Gluons are to the strong force what the photon is to the EM force – Gluons carry a color and an anticolor • 9 possible combinations of color and anticolor • rr+gg+bb is color neutral, leaving 8 effective color combinations 4 • Results in potential V = - 3 αs /r + kr J. Brau QCD, Jets and Gluons 3 Color • 3 different color states Hadrons are combinations C – χC = r, g, b of quarks with Y = 0 and C • Color hypercharge I3 = 0 – YC so baryons = r g b & mesons = r anti-r, etc. • Color isospin C – I3 J. Brau QCD, Jets and Gluons 4 Color • In this diagram, the gluon has the color quantum numbers: C C C – I 3 = I 3(r) - I 3(b) = ½ – YC = YC(r) - YC(b) = 1 • So gluon exists in color state J. Brau QCD, Jets and Gluons 5 Quantum Chromodynamics • Important properties of strong interactions distinguishing it from QED: – Color confinement • Observed states have zero color charges.
    [Show full text]
  • Overview of the Future Programs at JLAB and EIC
    Overview of the future programs at JLAB and EIC Jianwei Qiu Theory Center, Jefferson Lab JeffersonOutline Lab of 12 the GeV rest Upgrade of my talk Project The 12 GeV Upgrade greatly expands the research capabilities of Jefferson Lab, adding a fourth experimental hall – D, upgrading existing halls and doubling the power of the lab's accelerator. Maintain capability to delier lower pass beam energies: 2.2, 4.4, 6.6, … Project Scope • Doubling the accelerator beam energy – DONE • New experimental Hall D and beam line – DONE • Civil construction including utilities – DONE TPC = $338M • Upgrades to Experimental Halls B & C – ~99% 99% complete! • Halls B & C Detectors – DONE JLabOutline 12 GeV of Scientificthe rest of Capabilities my talk Outline of the rest of my talk q The next QCD frontier – the “big” questions, … q JLAB12 and the Electron-Ion Collider (EIC) q How JLAB12/EIC could answer the “big” questions? q Path forward to the EIC era – unique role of JLAB12 q Summary The next QCD frontier q What is the role of QCD in the evolution of the universe? q How hadrons are emerged from quarks and gluons? q How does QCD make up the properties of hadrons? Their mass, spin, magnetic moment, … q What is the QCD landscape of nucleon and nuclei? Color Confinement Asymptotic freedom Q (GeV) 200 MeV (1 fm) 2 GeV (1/10 fm) Probing momentum q How do the nuclear force arise from QCD? q ... Have to understand the role of glue! The next QCD frontier q Understanding the glue – the Next QCD Frontier! q Gluons are weird particles! ² Massless, yet, responsible
    [Show full text]