The Spin Structure of the Nucleon

Total Page:16

File Type:pdf, Size:1020Kb

The Spin Structure of the Nucleon JLAB-PHY-18-2760 SLAC{PUB{17279 The Spin Structure of the Nucleon Alexandre Deur Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA Stanley J. Brodsky SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309, USA Guy F. de T´eramond Universidad de Costa Rica, San Jos´e,Costa Rica July 17, 2018 [email protected], arXiv:1807.05250v1 [hep-ph] 13 Jul 2018 [email protected], [email protected], This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Contract DE-AC02-76SF00515. Abstract We review the present understanding of the spin structure of protons and neutrons, the fundamental building blocks of nuclei collectively known as nucleons. The field of nu- cleon spin provides a critical window for testing Quantum Chromodynamics (QCD), the gauge theory of the strong interactions since it involves fundamental aspects of hadron structure, and it can be probed in detail in experiments, particularly deep inelastic lepton scattering on polarized targets. QCD was initially probed in high energy deep inelastic lepton scattering with unpo- larized beams and targets. With time, interest shifted from testing perturbative QCD to illuminating the nucleon structure itself. In fact, the spin degrees of freedom of hadrons provide an essential and detailed verification of both perturbative and nonperturbative QCD dynamics. Nucleon spin was initially thought of coming mostly from the spin of its quark constituents, based on intuition from the parton model. However, the first experiments showed that this expectation was incorrect. It is now clear that nucleon physics is much more complex, involving quark orbital angular momenta as well as gluonic and sea quark contributions. Thus, the nucleon spin structure remains a most active aspect of QCD research, involving important advances such as the developments of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Elastic and inelastic lepton-proton scattering, as well as photoabsorption experi- ments provide various ways to investigate non-perturbative QCD. Fundamental sum rules { such as the Bjorken sum rule for polarized photoabsorption on polarized nucle- ons { are also in the non-perturbative domain. This realization triggered a vigorous program to link the low energy effective hadronic description of the strong interactions to fundamental quarks and gluon degrees of freedom of QCD. This has also led to the development of holographic QCD ideas based on the AdS/CFT or gauge/gravity cor- respondence, a novel approach providing a well-founded semiclassical approximation to QCD. Any QCD-based model of the nucleon's spin and dynamics must also successfully account for the observed spectroscopy of hadrons. Analytic calculations of the hadron spectrum, a long sought goal of QCD research, has now being realized using light-front holography and superconformal quantum mechanics, a formalism consistent with the results from nucleon spin studies. We begin this review with a phenomenological description of nucleon structure in general and of its spin structure in particular, aimed to engage non-specialist readers. Next, we discuss the nucleon spin structure at high energy, including topics such as 2 Dirac's front form and light-front quantization which provide a frame-independent, rel- ativistic description of hadron structure and dynamics, the derivation of spin-sum rules, and a direct connection to the QCD Lagrangian. We then discuss experimental and theoretical advances in the nonperturbative domain { in particular the development of light-front holographic QCD and superconformal quantum mechanics, its predictions for the spin content of nucleons, the computation of PDFs and of hadron masses. Contents 1 Preamble5 2 Overview of QCD and the nucleon structure8 2.1 Charged lepton-nucleon scattering . 10 2.1.1 The first Born approximation . 10 2.1.2 Kinematics . 11 2.1.3 General expression of the reaction cross-section . 12 2.1.4 Leptonic and hadronic tensors, and cross-section parameterization 13 2.1.5 Asymmetries . 14 2.2 Nucleon-Nucleon scattering . 15 2.3 e+ e− annihilation . 17 3 Constraints on spin dynamics from scattering processes 17 3.1 Deep inelastic scattering (DIS) . 17 3.1.1 Mechanism . 17 3.1.2 Bjorken scaling . 18 3.1.3 DIS: QCD on the Light-front . 18 3.1.4 Formalism and structure functions . 25 3.1.5 Single-spin asymmetries (SSA) . 27 3.1.6 Photo-absorption asymmetries . 27 3.1.7 Structure function extraction . 29 3.1.8 The Parton Model . 30 3.1.9 The nucleon spin sum rule and the \spin crisis" . 35 3.1.10 Definitions of the spin sum rule components . 37 3.2 The resonance region . 40 3.2.1 Constituent Quark Models . 41 3.2.2 The Resonance Spectrum of Nucleons . 43 3 3.2.3 A link between DIS and resonances: hadron-parton duality . 44 3.3 Elastic and quasi-elastic scatterings . 44 3.3.1 Elastic cross-section . 45 3.3.2 Quasi-elastic scattering . 48 3.4 Summary . 49 4 Computation methods 49 4.1 The Operator Product Expansion (OPE) . 51 4.2 Lattice gauge theory . 53 4.2.1 Calculations of structure functions . 55 4.2.2 Direct calculation of hadronic PDFs: Matching LFQCD to LGT 56 4.3 Chiral perturbation theory . 57 4.3.1 Chiral symmetry in QCD . 57 4.3.2 Connection to conformal symmetry . 58 4.4 The light-front holographic QCD approximation . 58 4.5 Summary . 60 5 Sum rules 60 5.1 General formalism . 61 5.2 GDH and forward spin polarizability sum rules . 61 5.3 δLT sum rule . 63 5.4 The Burkhardt-Cottingham sum rule . 63 5.5 Sum rules for deep inelastic scattering (DIS) . 64 5.6 Color polarizabilities . 69 6 World data and global analyses 69 6.1 Experiments and World data . 69 6.2 Global analyses . 72 6.3 PQCD in the high-xBj domain . 74 6.3.1 A1 in the DIS at high-xBj ...................... 75 6.3.2 Quark models and other predictions of A1 for high-xBj DIS . 75 6.3.3 A1 results . 76 0 6.4 Results on the polarized partial cross-sections σTT and σLT ........ 77 6.5 Results on the generalized GDH integral . 78 6.6 Moments of g1 and g2 ............................ 78 6.6.1 Extractions of the g1 first moments . 79 4 6.6.2 Data and theory comparisons . 79 6.6.3 Results on Γ2 and on the BC and ELT sum rules . 81 6.7 Generalized spin polarizabilities γ0, δLT ................... 82 6.7.1 Results on γ0 ............................. 82 6.7.2 The δLT puzzle . 83 6.8 d2 results . 83 6.8.1 Results on the neutron . 84 6.8.2 Results on the Proton . 84 6.8.3 Discussion . 84 6.9 Higher-twist contributions to Γ1, g1 and g2 ................ 85 6.9.1 Leading and higher-twist analysis of Γ1 .............. 85 6.9.2 Color polarizabilities and confinement force . 87 6.9.3 Higher twist studies for g1, A1, g2 and A2 ............. 87 6.10 Study of the hadron-parton spin duality . 89 6.11 Nucleon spin structure at high energy . 90 6.11.1 General conclusions . 90 6.11.2 Individual contributions to the nucleon spin . 91 6.11.3 High-energy picture of the nucleon spin structure . 95 6.11.4 Pending Questions . 97 6.11.5 Contributions from lower energy data . 97 7 Perspectives: the hadron mass spectrum 99 8 Outlook 101 1 Preamble The study of the individual contributions to the nucleon spin provides a critical window for testing detailed predictions of Quantum Chromodynamics (QCD) for the internal quark and gluon structure of hadrons. Fundamental spin predictions can be tested experimentally to high precision, particularly in measurements of deep inelastic scattering (DIS) of polarized leptons on polarized proton and nuclear targets. The spin of the nucleons was initially thought to originate simply from the spin of the constituent quarks, based on intuition from the parton model. However, experiments have shown that this expectation was incorrect. It is now clear that nucleon spin physics is much more complex, involving quark and gluon orbital angular momenta (OAM) as 5 well as gluon spin and sea-quark contributions. Contributions to the nucleon spin in fact originate from the nonperturbative dynamics associated with color confinement as well as from perturbative (pQCD) evolution. Thus, nucleon spin structure has become an active aspect of QCD research, incorporating important theoretical advances such as the development of generalized parton distributions (GPD) and transverse momentum distributions (TMD). Fundamental sum rules, such as the Bjorken sum rule for polarized DIS or the Drell-Hearn-Gerasimov sum rule for polarized photoabsorption cross sections, constrain critically the spin structure. In addition, elastic lepton-nucleon scattering and other exclusive processes, e.g. Deeply Virtual Compton Scattering (DVCS), also determine important aspects of nucleon spin dynamics. This has led to a vigorous theoretical and experimental program to obtain an effective hadronic description of the strong force in terms of the basic quark and gluon fields of QCD. Furthermore, the theoretical program for determining the spin structure of hadrons has benefited from advances in lattice gauge theory simulations of QCD and the recent development of light-front holographic QCD ideas based on the AdS/CFT correspondence, an approach to hadron structure based on the holographic embedding of light-front dynamics in a higher dimensional gravity theory, together with the constraints imposed by the underlying superconformal alge- braic structure. This novel approach to nonperturbative QCD and color confinement has provided a well-founded semiclassical approximation to QCD. QCD-based models of the nucleon spin and dynamics must also successfully account for the observed spectroscopy of hadrons. Analytic calculations of the hadron spectrum, a long-sought goal, are now being carried out using Lorentz frame-independent light-front holographic methods.
Recommended publications
  • Electron-Nucleon Scattering at LDMX for DUNE
    Snowmass Letter of Intent: Snowmass Topical Groups: NF6, RF6, TF11 Electron-Nucleon Scattering at LDMX for DUNE Torsten Akesson1, Artur Ankowski2, Nikita Blinov3, Lene Kristian Bryngemark4, Pierfrancesco Butti2, Caterina Doglioni1, Craig Dukes5, Valentina Dutta6, Bertrand Echenard7, Thomas Eichlersmith8, Ralf Ehrlich5, Andrew Furmanski∗8, Niramay Gogate9, Mathew Graham2, Craig Group5, Alexander Friedland2, David Hitlin7, Vinay Hegde9, Christian Herwig3, Joseph Incandela6, Wesley Ketchumy3, Gordan Krnjaic3, Amina Li6, Shirley Liz2,3, Dexu Lin7, Jeremiah Mans8, Cristina Mantilla Suarez3, Phillip Masterson6, Martin Meier8, Sophie Middleton7, Omar Moreno2, Geoffrey Mullier1, Tim Nelson2, James Oyang7, Gianluca Petrillo2, Ruth Pottgen1, Stefan Prestel1, Luis Sarmiento1, Philip Schuster2, Hirohisa Tanaka2, Lauren Tompkins4, Natalia Toro2, Nhan Tran§3, and Andrew Whitbeck9 1Lund University 2Stanford Linear Accelerator Laboratory 3Fermi National Accelerator Laboratory 4Stanford University 5University of Virginia 6University of California Santa Barbara 7California Institute of Technology 8University of Minnesota 9Texas Tech University ABSTRACT We point out that the LDMX (Light Dark Matter eXperiment) detector design, conceived to search for sub-GeV dark matter, will also have very advantageous characteristics to pursue electron-nucleus scattering measurements of direct relevance to the neutrino program at DUNE and elsewhere. These characteristics include a 4-GeV electron beam, a precision tracker, electromagnetic and hadronic calorimeters with near 2p azimuthal acceptance from the forward beam axis out to 40◦ angle, and low reconstruction energy threshold. LDMX thus could provide (semi)exclusive cross section measurements, with∼ detailed information about final-state electrons, pions, protons, and neutrons. We compare the predictions of two widely used neutrino generators (GENIE, GiBUU) in the LDMX region of acceptance to illustrate the large modeling discrepancies in electron-nucleus interactions at DUNE-like kinematics.
    [Show full text]
  • (E) Slac Measurement of the Neutron Spin Structure
    Sr.AC-PUB-b217 _ _ "" --7 (- 7 _ -_ • / April 1993 (E) DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. SLAC MEASUREMENT OF THE NEUTRON SPIN STRUCTURE FUNCTION Emlyn llughes Representing the Efd2 Collaboration Stanford l,inear Accelerator Center Stanford, CA 94309, USA ABSTRACT A measurement of the nucleon spin asymmetries from deep inelastic scattering of polarized electrons by polarize.d alle has been performed. The neutron spin structure flmction gn is extracted and used to test the Bjorken sum rule. The neutron integral assuming a simple Regge theory extrapolation at low x is fo_gr_(x)dx = -0.022 + 0.011. Combined with the EMC proton results, the l_jorken sum rule predicts a neutron integral of ._ .qr_(x)dx = -0.065:t:0.018. Presented at the 2Sth Rencontres de Moriond QCD and Hi@ Energy tJadronic Interactiot's l.es Arcs, France, March 20-28,1993 *Work supported l.y Deparlment of Energy contract I-)ti-ACO3-7(,SI:(It}515 "' ': " "; ...
    [Show full text]
  • From Quark and Nucleon Correlations to Discrete Symmetry and Clustering
    From quark and nucleon correlations to discrete symmetry and clustering in nuclei G. Musulmanbekov JINR, Dubna, RU-141980, Russia E-mail: [email protected] Abstract Starting with a quark model of nucleon structure in which the valence quarks are strongly correlated within a nucleon, the light nu- clei are constructed by assuming similar correlations of the quarks of neighboring nucleons. Applying the model to larger collections of nucleons reveals the emergence of the face-centered cubic (FCC) sym- metry at the nuclear level. Nuclei with closed shells possess octahedral symmetry. Binding of nucleons are provided by quark loops formed by three and four nucleon correlations. Quark loops are responsible for formation of exotic (borromean) nuclei, as well. The model unifies independent particle (shell) model, liquid-drop and cluster models. 1 Introduction arXiv:1708.04437v2 [nucl-th] 19 Sep 2017 Historically there are three well known conventional nuclear models based on different assumption about the phase state of the nucleus: the liquid-drop, shell (independent particle), and cluster models. The liquid-drop model re- quires a dense liquid nuclear interior (short mean-free-path, local nucleon interactions and space-occupying nucleons) in order to predict nuclear bind- ing energies, radii, collective oscillations, etc. In contrast, in the shell model each point nucleon moves in mean-field potential created by other nucleons; the model predicts the existence of nucleon orbitals and shell-like orbital- filling. The cluster models require the assumption of strong local-clustering 1 of particularly the 4-nucleon alpha-particle within a liquid or gaseous nuclear interior in order to make predictions about the ground and excited states of cluster configurations.
    [Show full text]
  • First Results of the Cosmic Ray NUCLEON Experiment
    Prepared for submission to JCAP First results of the cosmic ray NUCLEON experiment E. Atkin,a V. Bulatov,b V. Dorokhov,b N. Gorbunov,c;d S. Filippov,b V. Grebenyuk,c;d D. Karmanov,e I. Kovalev,e I. Kudryashov,e A. Kurganov,e M. Merkin,e A. Panov,e;1 D. Podorozhny,e D. Polkov,b S. Porokhovoy,c V. Shumikhin,a L. Sveshnikova,e A. Tkachenko,c;f L. Tkachev,c;d A. Turundaevskiy,e O. Vasiliev ande A. Voronine aNational Research Nuclear University “MEPhI”, Kashirskoe highway, 31. Moscow, 115409, Russia bSDB Automatika, Mamin-Sibiryak str, 145, Ekaterinburg, 620075, Russia cJoint Institute for Nuclear Research, Dubna, Joliot-Curie, 6, Moscow region, 141980, Russia d arXiv:1702.02352v2 [astro-ph.HE] 2 Jul 2018 “DUBNA” University, Universitetskaya str., 19, Dubna, Moscow region, 141980, Russia eSkobeltsyn Institute of Nuclear Physics, Moscow State University, 1(2), Leninskie gory, GSP-1, Moscow, 119991, Russia f Bogolyubov Institute for Theoretical Physics, 14-b Metrolohichna str., Kiev, 03143, Ukraine 1Corresponding author. E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], tfl[email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract.
    [Show full text]
  • 14. Structure of Nuclei Particle and Nuclear Physics
    14. Structure of Nuclei Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 14. Structure of Nuclei 1 In this section... Magic Numbers The Nuclear Shell Model Excited States Dr. Tina Potter 14. Structure of Nuclei 2 Magic Numbers Magic Numbers = 2; 8; 20; 28; 50; 82; 126... Nuclei with a magic number of Z and/or N are particularly stable, e.g. Binding energy per nucleon is large for magic numbers Doubly magic nuclei are especially stable. Dr. Tina Potter 14. Structure of Nuclei 3 Magic Numbers Other notable behaviour includes Greater abundance of isotopes and isotones for magic numbers e.g. Z = 20 has6 stable isotopes (average=2) Z = 50 has 10 stable isotopes (average=4) Odd A nuclei have small quadrupole moments when magic First excited states for magic nuclei higher than neighbours Large energy release in α, β decay when the daughter nucleus is magic Spontaneous neutron emitters have N = magic + 1 Nuclear radius shows only small change with Z, N at magic numbers. etc... etc... Dr. Tina Potter 14. Structure of Nuclei 4 Magic Numbers Analogy with atomic behaviour as electron shells fill. Atomic case - reminder Electrons move independently in central potential V (r) ∼ 1=r (Coulomb field of nucleus). Shells filled progressively according to Pauli exclusion principle. Chemical properties of an atom defined by valence (unpaired) electrons. Energy levels can be obtained (to first order) by solving Schr¨odinger equation for central potential. 1 E = n = principle quantum number n n2 Shell closure gives noble gas atoms. Are magic nuclei analogous to the noble gas atoms? Dr.
    [Show full text]
  • Electron- Vs Neutrino-Nucleus Scattering
    Electron- vs Neutrino-Nucleus Scattering Omar Benhar INFN and Department of Physics Universita` “La Sapienza” I-00185 Roma, Italy NUFACT11 University of Geneva, August 2nd, 2011 Neutrino-nucleus scattering . impact of the flux average . flux-averaged electron scattering x-section: a numerical experiment . contributions of reaction mechanisms other than quasi elastic single nucleon knock out to the MiniBooNE CCQE data sample Summary & Outlook Outline Electron scattering . standard data representation . theoretical description: the impulse approximation Omar Benhar (INFN, Roma) NUFACT11 Geneva 02/08/2011 2 / 24 Summary & Outlook Outline Electron scattering . standard data representation . theoretical description: the impulse approximation Neutrino-nucleus scattering . impact of the flux average . flux-averaged electron scattering x-section: a numerical experiment . contributions of reaction mechanisms other than quasi elastic single nucleon knock out to the MiniBooNE CCQE data sample Omar Benhar (INFN, Roma) NUFACT11 Geneva 02/08/2011 2 / 24 Outline Electron scattering . standard data representation . theoretical description: the impulse approximation Neutrino-nucleus scattering . impact of the flux average . flux-averaged electron scattering x-section: a numerical experiment . contributions of reaction mechanisms other than quasi elastic single nucleon knock out to the MiniBooNE CCQE data sample Summary & Outlook Omar Benhar (INFN, Roma) NUFACT11 Geneva 02/08/2011 2 / 24 The inclusive electron-nucleus x-section The x-section of the process e
    [Show full text]
  • The Spin of the Proton
    The spin of the proton Bo-Qiang Ma (马伯强) Peking Univ (北京大学) ? The 7th Workshop on Hadron Physics in China and Opportunities Worldwide August 3-7, 2015, Duke Kunshan University Collaborators: Enzo Barone, Stan Brodsky, Jacques Soffer, Andreas Schafer, Ivan Schmidt, Jian-Jun Yang, Qi-Ren Zhang and students: Bowen Xiao, Zhun Lu, Bing Zhang, Jun She, Jiacai Zhu, Xinyu Zhang, Tianbo Liu 3 It has been 30 years of the proton “spin crisis” or “spin puzzle” • Spin Structure: experimentally u d s 0.020 u d s 0.3 spin “crisis” or “puzzle”: where is the proton’s missing spin? The Proton “Spin Crisis” In contradiction with the naïve quark model expectation: u d s 0.3 Why there is the proton spin puzzle/crisis? • The quark model is very successful for the classification of baryons and mesons • The quark model is good to explain the magnetic moments of octet baryons • The quark model gave the birth of QCD as a theory for strong interaction So why there is serious problem with spin of the proton in the quark model? The parton model (Feynman 1969) Infinite • photon scatters incoherently off Momentum massless, pointlike, spin-1/2 quarks Frame • probability that a quark carries fraction of parent proton’s momentum is q(), (0< < 1) 1 2 2 F2 (x) d eq q( ) (x ) eq x q(x) 0 q,q q,q 4 1 1 xu(x) x d(x) x s(x) ... 9 9 9 •the functions u(x), d(x), s(x), … are called parton distribution functions (pdfs) - they encode information about the proton’s deep structure •Parton model is established under the collinear approxiamtion: The transversal motion of partons is neglected or integrated over.
    [Show full text]
  • Solid Polarized Targets for Nuclear and Particle Physics Experiments
    P1: NBL October 6, 1997 15:46 Annual Reviews AR043-03 Annu. Rev. Nucl. Part. Sci. 1997. 47:67–109 Copyright c 1997 by Annual Reviews Inc. All rights reserved ! SOLID POLARIZED TARGETS FOR NUCLEAR AND PARTICLE PHYSICS EXPERIMENTS D. G. Crabb Physics Department, University of Virginia, Charlottesville, Virginia 22901 W. Meyer Institut fur¨ Experimentalphysik I, Ruhr-Universitat¨ Bochum, Bochum, Germany KEY WORDS: dynamic polarization, nucleon spin structure, lepton scattering, cryogenics, asymmetry ABSTRACT The development, in the early 1960s, of the dynamic nuclear polarization process in solid diamagnetic materials, doped with paramagnetic radicals, led to the use of solid polarized targets in numerous nuclear and particle physics experiments. Since then steady progress has been made in all contributing subsystems so that proton polarizations near 100% and deuteron polarizations higher than 50% have been achieved in various materials. More radiation-resistant materials, such as ammonia, have made it possible to perform experiments with high beam intensi- ties and experiments that benefit from 4He cooling at 1K and high magnetic fields. The development of dilution refrigerators have allowed frozen spin operation so that experiments with large angular acceptance for the scattered particles have by University of Virginia Libraries on 05/18/07. For personal use only. become routine. Many experiments have taken advantage of these developments and many more are being planned, especially with electromagnetic probes. Annu. Rev. Nucl. Part. Sci. 1997.47:67-109. Downloaded from arjournals.annualreviews.org CONTENTS 1. INTRODUCTION . 68 2. POLARIZATION MECHANISMS . 71 2.1 Thermal Equilibrium Polarization . 72 2.2 Solid-State Effect . 72 2.3 Equal Spin Temperature Theory .
    [Show full text]
  • In-Medium QCD Sum Rules for Ω Meson, Nucleon and D Meson QCD-Summenregeln F ¨Ur Im Medium Modifizierte Ω-Mesonen, Nukleonen Und D-Mesonen
    Institut f¨ur Theoretische Physik Fakult¨at Mathematik und Naturwissenschaften Technische Universit¨at Dresden In-Medium QCD Sum Rules for ω Meson, Nucleon and D Meson QCD-Summenregeln f ¨ur im Medium modifizierte ω-Mesonen, Nukleonen und D-Mesonen Dissertation zur Erlangung des akademischen Grades Doctor rerum naturalium vorgelegt von Ronny Thomas geboren am 7. Februar 1978 in Dresden C Dresden 2008 To Andrea and Maximilian Eingereicht am 07. Oktober 2008 1. Gutachter: Prof. Dr. Burkhard K¨ampfer 2. Gutachter: Prof. Dr. Christian Fuchs 3. Gutachter: PD Dr. Stefan Leupold Verteidigt am 28. Januar 2009 Abstract The modifications of hadronic properties caused by an ambient nuclear medium are investigated within the scope of QCD sum rules. This is exemplified for the cases of the ω meson, the nucleon and the D meson. By virtue of the sum rules, integrated spectral densities of these hadrons are linked to properties of the QCD ground state, quantified in condensates. For the cases of the ω meson and the nucleon it is discussed how the sum rules allow a restriction of the parameter range of poorly known four-quark condensates by a comparison of experimental and theoretical knowledge. The catalog of independent four-quark condensates is covered and relations among these condensates are revealed. The behavior of four-quark condensates under the chiral symmetry group and the relation to order parameters of spontaneous chiral symmetry breaking are outlined. In this respect, also the QCD condensates appearing in differences of sum rules of chiral partners are investigated. Finally, the effects of an ambient nuclear medium on the D meson are discussed and relevant condensates are identified.
    [Show full text]
  • The Electron Ion Collider (EIC)
    7/18/16 EIC Lecture 2 at NNPSS 2016 at MIT 1 The Electron Ion Collider (EIC) Abhay Deshpande Lecture 2: What do we need polarized beams? Nucleon Spin Structure: What’s the problem? 2. Quantum Chromodynamics: The Fundamental Description of the Heart of Visible Matter Sidebar 2.6: Nucleon Spin: So Simple and Yet So Complex The simple fact that the proton carries spin 1/2, quark spins to account for most of the proton’s spin measured in units of Planck’s famous constant, is but were quite surprised when experiments at CERN exploited daily in thousands of magnetic resonance and other laboratories showed that the spins of all imaging images worldwide. Because the proton is a quarks and antiquarks combine to account for no more composite system, its spin is generated from its quark than about 30% of the total. This result has led nuclear 7/18/16 EIC Lecture 2 at NNPSS 2016 at MIT and gluon constituents. Physicists’ evolving appreciation scientists2. Quantum to address Chromodynamics: the more daunting The Fundamental challenges2 Description of the Heart of Visible Matter of how the spin might be generated, and of how much involved in measuring the other possible contributions to we have yet to understand about it, is an illustrative the spin illustrated in Figure 1. The gluons also have an Thecase study nucleon of how seemingly simple spin properties of visible intrinsic spin (1 unit) and might be “polarized” (i.e., might matter emerge from complex QCD interactions. have a preferential orientation of their spins along or puzzle….
    [Show full text]
  • Measurements of the Nucleon Spin- Structure Functions in and Above the Resonance Region for the Hall-B Eg1experiment at Jefferson Laboratory
    Measurements of the Nucleon Spin- Structure Functions in and Above the Resonance Region for the Hall-B EG1Experiment at Jefferson Laboratory Robert Fersch Christopher Newport University Jefferson Laboratory (CLAS Collaboration) Structure of the Nucleon Unpolarized distributions q, g f(x) Transversity δq δf(x) 3 d.o.f. completely Helicity describe the nucleon at Δf(x) leading twist when kT = 0 Δq, Δg Structure of the Nucleon Unpolarized distributions q, g f(x) Transversity δq δf(x) 3 d.o.f. completely Helicity describe the nucleon at Δf(x) leading twist when kT = 0 Δq, Δg Helicity: Δq = q+ – q– Incident electron couples to quarks of opposite longitudinal spin 2 Structure function g1(x,Q ) ~ σ1/2 – σ3/2 Requires longitudinally polarized beam and target The EG1 experiment ran in CLAS for 7 months 2000-2001 4 beam energies used (1.6, 2.5, 4.2, 5.7 GeV) CEBAF Large Acceptance Spectrometer (Hall-B) at Jefferson Lab (~70%) polarized electron beam in energies up to 6 GeV The EG1 experiment ran in CLAS for 7 months 2000-2001 4 beam energies used (1.6, 2.5, 4.2, 5.7 GeV) CEBAF Large Acceptance Spectrometer (Hall-B) at Jefferson Lab Drift Chambers (momentum reconstruction) Scintillation Counters (time- of-flight, PID) Cherenkov Counters and Electromagnetic Calorimeters (separation of electrons from light hadrons) The EG1 experiment ran in CLAS for 7 months 2000-2001 4 beam energies used (1.6, 2.5, 4.2, 5.7 GeV) CLAS Longitudinally Polarized Target 15 15 - NH3 and ND3 target cells - Typical polarizations of 75% (H) and 30% (D) 12 - C and LHe target cells for unpolarized background subtraction ammonia target cell The EG1 experiment ran in CLAS for 7 months 2000-2001 4 beam energies used (1.6, 2.5, 4.2, 5.7 GeV) Kinematic coverage & statistics Many papers already published using EG1 data (including a study of Bloom-Gilman duality): • N.
    [Show full text]
  • Transverse Spin Structure of the Nucleon
    NS65CH18-Yuan ARI 9 September 2015 14:34 Transverse Spin Structure of the Nucleon Matthias Grosse Perdekamp1 and Feng Yuan2 1Physics Department, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801; email: [email protected] 2Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720; email: [email protected] Annu. Rev. Nucl. Part. Sci. 2015. 65:429–56 Annu. Rev. Nucl. Part. Sci. 2015.65:429-456. Downloaded from www.annualreviews.org Keywords Access provided by University of California - Berkeley on 10/21/15. For personal use only. First published online as a Review in Advance on transversity, QCD, parton distributions, deep-inelastic scattering August 3, 2015 The Annual Review of Nuclear and Particle Science Abstract is online at nucl.annualreviews.org We review the current status and future perspectives of theory and exper- This article’s doi: iments of transverse spin phenomena in high-energy scattering processes 10.1146/annurev-nucl-102014-021948 off nucleon targets and related issues in nucleon structure and QCD. Copyright c 2015 by Annual Reviews. ⃝ Systematic exploration of transverse spin effects requires measurements All rights reserved in polarized deep-inelastic scattering, polarized pp collisions, and e+e− annihilations. Sophisticated QCD-based techniques are also needed to analyze the experimental data sets. 429 NS65CH18-Yuan ARI 9 September 2015 14:34 Contents 1.INTRODUCTION............................................................ 430 2. TRANSVERSE SPIN PHENOMENA IN EXPERIMENTS. 432 2.1. Lepton–Nucleon Scattering . 432 2.2. e+e− Annihilations.......................................................... 434 2.3. Nucleon–Nucleon Scattering . 434 2.4. Transverse Spin Phenomena in High-Energy Experiments ................... 435 3. TRANSVERSE SPIN STRUCTURE OF THE NUCLEON .
    [Show full text]