Introduction to Quantum Chromodynamics at Hadron Colliders
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Quantum Field Theory*
Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement. -
Zero-Point Energy in Bag Models
Ooa/ea/oHsnif- ^*7 ( 4*0 0 1 5 4 3 - m . Zero-Point Energy in Bag Models by Kimball A. Milton* Department of Physics The Ohio State University Columbus, Ohio 43210 A b s t r a c t The zero-point (Casimir) energy of free vector (gluon) fields confined to a spherical cavity (bag) is computed. With a suitable renormalization the result for eight gluons is This result is substantially larger than that for a spher ical shell (where both interior and exterior modes are pre sent), and so affects Johnson's model of the QCD vacuum. It is also smaller than, and of opposite sign to the value used in bag model phenomenology, so it will have important implications there. * On leave ifrom Department of Physics, University of California, Los Angeles, CA 90024. I. Introduction Quantum chromodynamics (QCD) may we 1.1 be the appropriate theory of hadronic matter. However, the theory is not at all well understood. It may turn out that color confinement is roughly approximated by the phenomenologically suc cessful bag model [1,2]. In this model, the normal vacuum is a perfect color magnetic conductor, that iis, the color magnetic permeability n is infinite, while the vacuum.in the interior of the bag is characterized by n=l. This implies that the color electric and magnetic fields are confined to the interior of the bag, and that they satisfy the following boundary conditions on its surface S: n.&jg= 0, nxBlg= 0, (1) where n is normal to S. Now, even in an "empty" bag (i.e., one containing no quarks) there will be non-zero fields present because of quantum fluctua tions. -
18. Lattice Quantum Chromodynamics
18. Lattice QCD 1 18. Lattice Quantum Chromodynamics Updated September 2017 by S. Hashimoto (KEK), J. Laiho (Syracuse University) and S.R. Sharpe (University of Washington). Many physical processes considered in the Review of Particle Properties (RPP) involve hadrons. The properties of hadrons—which are composed of quarks and gluons—are governed primarily by Quantum Chromodynamics (QCD) (with small corrections from Quantum Electrodynamics [QED]). Theoretical calculations of these properties require non-perturbative methods, and Lattice Quantum Chromodynamics (LQCD) is a tool to carry out such calculations. It has been successfully applied to many properties of hadrons. Most important for the RPP are the calculation of electroweak form factors, which are needed to extract Cabbibo-Kobayashi-Maskawa (CKM) matrix elements when combined with the corresponding experimental measurements. LQCD has also been used to determine other fundamental parameters of the standard model, in particular the strong coupling constant and quark masses, as well as to predict hadronic contributions to the anomalous magnetic moment of the muon, gµ 2. − This review describes the theoretical foundations of LQCD and sketches the methods used to calculate the quantities relevant for the RPP. It also describes the various sources of error that must be controlled in a LQCD calculation. Results for hadronic quantities are given in the corresponding dedicated reviews. 18.1. Lattice regularization of QCD Gauge theories form the building blocks of the Standard Model. While the SU(2) and U(1) parts have weak couplings and can be studied accurately with perturbative methods, the SU(3) component—QCD—is only amenable to a perturbative treatment at high energies. -
Quantum Mechanics Quantum Chromodynamics (QCD)
Quantum Mechanics_quantum chromodynamics (QCD) In theoretical physics, quantum chromodynamics (QCD) is a theory ofstrong interactions, a fundamental forcedescribing the interactions between quarksand gluons which make up hadrons such as the proton, neutron and pion. QCD is a type of Quantum field theory called a non- abelian gauge theory with symmetry group SU(3). The QCD analog of electric charge is a property called 'color'. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of Particle physics. A huge body of experimental evidence for QCD has been gathered over the years. QCD enjoys two peculiar properties: Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, when you do split the quark the energy is enough to create another quark thus creating another quark pair; they are forever bound into hadrons such as theproton and the neutron or the pion and kaon. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD. Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma. This prediction of QCD was first discovered in the early 1970s by David Politzer and by Frank Wilczek and David Gross. For this work they were awarded the 2004 Nobel Prize in Physics. There is no known phase-transition line separating these two properties; confinement is dominant in low-energy scales but, as energy increases, asymptotic freedom becomes dominant. -
The Eightfold Way Model, the SU(3)-flavour Model and the Medium-Strong Interaction
The Eightfold Way model, the SU(3)-flavour model and the medium-strong interaction Syed Afsar Abbas Jafar Sadiq Research Institute AzimGreenHome, NewSirSyed Nagar, Aligarh - 202002, India (e-mail : [email protected]) Abstract Lack of any baryon number in the Eightfold Way model, and its intrin- sic presence in the SU(3)-flavour model, has been a puzzle since the genesis of these models in 1961-1964. In this paper we show that this is linked to the way that the adjoint representation is defined mathematically for a Lie algebra, and how it manifests itself as a physical representation. This forces us to distinguish between the global and the local charges and between the microscopic and the macroscopic models. As a bonus, a consistent under- standing of the hitherto mysterious medium-strong interaction is achieved. We also gain a new perspective on how confinement arises in Quantum Chro- modynamics. Keywords: Lie Groups, Lie Algegra, Jacobi Identity, adjoint represen- tation, Eightfold Way model, SU(3)-flavour model, quark model, symmetry breaking, mass formulae 1 The Eightfold Way model was proposed independently by Gell-Mann and Ne’eman in 1961, but was very quickly transformed into the the SU(3)- flavour model ( as known to us at present ) in 1964 [1]. We revisit these models and look into the origin of the Eightfold Way model and try to un- derstand as to how it is related to the SU(3)-flavour model. This allows us to have a fresh perspective of the mysterious medium-strong interaction [2], which still remains an unresolved problem in the theory of the strong interaction [1,2,3]. -
Quantum Chromodynamics 1 9
9. Quantum chromodynamics 1 9. QUANTUM CHROMODYNAMICS Revised October 2013 by S. Bethke (Max-Planck-Institute of Physics, Munich), G. Dissertori (ETH Zurich), and G.P. Salam (CERN and LPTHE, Paris). 9.1. Basics Quantum Chromodynamics (QCD), the gauge field theory that describes the strong interactions of colored quarks and gluons, is the SU(3) component of the SU(3) SU(2) U(1) Standard Model of Particle Physics. × × The Lagrangian of QCD is given by 1 = ψ¯ (iγµ∂ δ g γµtC C m δ )ψ F A F A µν , (9.1) q,a µ ab s ab µ q ab q,b 4 µν L q − A − − X µ where repeated indices are summed over. The γ are the Dirac γ-matrices. The ψq,a are quark-field spinors for a quark of flavor q and mass mq, with a color-index a that runs from a =1 to Nc = 3, i.e. quarks come in three “colors.” Quarks are said to be in the fundamental representation of the SU(3) color group. C 2 The µ correspond to the gluon fields, with C running from 1 to Nc 1 = 8, i.e. there areA eight kinds of gluon. Gluons transform under the adjoint representation− of the C SU(3) color group. The tab correspond to eight 3 3 matrices and are the generators of the SU(3) group (cf. the section on “SU(3) isoscalar× factors and representation matrices” in this Review with tC λC /2). They encode the fact that a gluon’s interaction with ab ≡ ab a quark rotates the quark’s color in SU(3) space. -
Supersymmetry Min Raj Lamsal Department of Physics, Prithvi Narayan Campus, Pokhara Min [email protected]
Supersymmetry Min Raj Lamsal Department of Physics, Prithvi Narayan Campus, Pokhara [email protected] Abstract : This article deals with the introduction of supersymmetry as the latest and most emerging burning issue for the explanation of nature including elementary particles as well as the universe. Supersymmetry is a conjectured symmetry of space and time. It has been a very popular idea among theoretical physicists. It is nearly an article of faith among elementary-particle physicists that the four fundamental physical forces in nature ultimately derive from a single force. For years scientists have tried to construct a Grand Unified Theory showing this basic unity. Physicists have already unified the electron-magnetic and weak forces in an 'electroweak' theory, and recent work has focused on trying to include the strong force. Gravity is much harder to handle, but work continues on that, as well. In the world of everyday experience, the strengths of the forces are very different, leading physicists to conclude that their convergence could occur only at very high energies, such as those existing in the earliest moments of the universe, just after the Big Bang. Keywords: standard model, grand unified theories, theory of everything, superpartner, higgs boson, neutrino oscillation. 1. INTRODUCTION unifies the weak and electromagnetic forces. The What is the world made of? What are the most basic idea is that the mass difference between photons fundamental constituents of matter? We still do not having zero mass and the weak bosons makes the have anything that could be a final answer, but we electromagnetic and weak interactions behave quite have come a long way. -
Sakata Model Precursor 2: Eightfold Way, Discovery of Ω- Quark Model: First Three Quarks A
Introduction to Elementary Particle Physics. Note 20 Page 1 of 17 THREE QUARKS: u, d, s Precursor 1: Sakata Model Precursor 2: Eightfold Way, Discovery of ΩΩΩ- Quark Model: first three quarks and three colors Search for free quarks Static evidence for quarks: baryon magnetic moments Early dynamic evidence: - πππN and pN cross sections - R= σσσee →→→ hadrons / σσσee →→→ µµµµµµ - Deep Inelastic Scattering (DIS) and partons - Jets Introduction to Elementary Particle Physics. Note 20 Page 2 of 17 Sakata Model 1956 Sakata extended the Fermi-Yang idea of treating pions as nucleon-antinucleon bound states, e.g. π+ = (p n) All mesons, baryons and their resonances are made of p, n, Λ and their antiparticles: Mesons (B=0): Note that there are three diagonal states, pp, nn, ΛΛ. p n Λ Therefore, there should be 3 independent states, three neutral mesons: π0 = ( pp - nn ) / √2 with isospin I=1 - - p ? π K X0 = ( pp + nn ) / √2 with isospin I=0 0 ΛΛ n π+ ? K0 Y = with isospin I=0 Or the last two can be mixed again… + 0 Λ K K ? (Actually, later discovered η and η' resonances could be interpreted as such mixtures.) Baryons (B=1): S=-1 Σ+ = ( Λ p n) Σ0 = ( Λ n n) mixed with ( Λ p p) what is the orthogonal mixture? Σ- = ( Λ n p) S=-2 Ξ- = ( Λ Λp) Ξ- = ( Λ Λn) S=-3 NOT possible Resonances (B=1): ∆++ = (p p n) ∆+ = (p n n) mixed with (p p p) what is the orthogonal mixture? ∆0 = (n n n) mixed with (n p p) what is the orthogonal mixture? ∆- = (n n p) Sakata Model was the first attempt to come up with some plausible internal structure that would allow systemizing the emerging zoo of hadrons. -
An Introduction to the Quark Model Arxiv:1205.4326V2 [Hep-Ph]
An introduction to the quark model Jean-Marc Richard Université de Lyon & Institut de Physique Nucléaire de Lyon IN2P3-CNRS & UCB, 4 rue Enrico Fermi, 69622 Villeurbanne, France [email protected] May 25, 2012 Abstract This document contains a review on the quark model, prepared for lectures at the Niccolò Cabeo School at Ferrara in May 2012. It includes some historical aspects, the spectral properties of the 2-body and 3-body Schrödinger operators applied to mesons and baryons, the link between meson and baryon spectra, the role of flavour independence, and the speculations about stable or metastable multiquarks. The analogies between few-charge systems and few-quark bound states will be under- lined. Contents 1 Prelude: few charge systems in atomic physics 3 1.1 Introduction . .3 1.2 The atomic two-body problem . .3 1.3 Three-unit-charge ions . .5 arXiv:1205.4326v2 [hep-ph] 24 May 2012 1.4 Three-body exotic ions . .5 1.5 Molecules with four unit charges . .6 2 A brief historical survey 7 2.1 Prehistory . .7 2.2 Early hadrons . .7 2.3 Generalised isospin . .9 2.4 The success of the eightfold way . 10 2.5 The fundamental representation: quarks . 10 2.6 The OZI rule . 12 2.7 First quark models . 13 2.8 Heavy quarks . 14 2.9 Confirmation . 15 1 2 AN INTRODUCTION TO THE QUARK MODEL 3 The quark–antiquark model of mesons 16 3.1 Introduction . 16 3.2 Quantum numbers . 16 3.3 Spin averaged spectrum . 17 3.4 Improvements to the potential . -
The Minkowski Quantum Vacuum Does Not Gravitate
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by KITopen Available online at www.sciencedirect.com ScienceDirect Nuclear Physics B 946 (2019) 114694 www.elsevier.com/locate/nuclphysb The Minkowski quantum vacuum does not gravitate Viacheslav A. Emelyanov Institute for Theoretical Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany Received 9 April 2019; received in revised form 24 June 2019; accepted 8 July 2019 Available online 12 July 2019 Editor: Stephan Stieberger Abstract We show that a non-zero renormalised value of the zero-point energy in λφ4-theory over Minkowski spacetime is in tension with the scalar-field equation at two-loop order in perturbation theory. © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction Quantum fields give rise to an infinite vacuum energy density [1–4], which arises from quantum-field fluctuations taking place even in the absence of matter. Yet, assuming that semi- classical quantum field theory is reliable only up to the Planck-energy scale, the cut-off estimate yields zero-point-energy density which is finite, though, but in a notorious tension with astro- physical observations. In the presence of matter, however, there are quantum effects occurring in nature, which can- not be understood without quantum-field fluctuations. These are the spontaneous emission of a photon by excited atoms, the Lamb shift, the anomalous magnetic moment of the electron, and so forth [5]. This means quantum-field fluctuations do manifest themselves in nature and, hence, the zero-point energy poses a serious problem. -
9. Quantum Chromodynamics 1 9
9. Quantum chromodynamics 1 9. Quantum Chromodynamics Revised September 2017 by S. Bethke (Max-Planck-Institute of Physics, Munich), G. Dissertori (ETH Zurich), and G.P. Salam (CERN).1 This update retains the 2016 summary of αs values, as few new results were available at the deadline for this Review. Those and further new results will be included in the next update. 9.1. Basics Quantum Chromodynamics (QCD), the gauge field theory that describes the strong interactions of colored quarks and gluons, is the SU(3) component of the SU(3) SU(2) U(1) Standard Model of Particle Physics. × × The Lagrangian of QCD is given by 1 = ψ¯ (iγµ∂ δ g γµtC C m δ )ψ F A F A µν , (9.1) q,a µ ab s ab µ q ab q,b 4 µν L q − A − − X µ where repeated indices are summed over. The γ are the Dirac γ-matrices. The ψq,a are quark-field spinors for a quark of flavor q and mass mq, with a color-index a that runs from a =1 to Nc = 3, i.e. quarks come in three “colors.” Quarks are said to be in the fundamental representation of the SU(3) color group. C 2 The µ correspond to the gluon fields, with C running from 1 to Nc 1 = 8, i.e. there areA eight kinds of gluon. Gluons transform under the adjoint representation− of the C SU(3) color group. The tab correspond to eight 3 3 matrices and are the generators of the SU(3) group (cf. -
Basics of Quantum Chromodynamics (Two Lectures)
Basics of Quantum Chromodynamics (Two lectures) Faisal Akram 5th School on LHC Physics, 15-26 August 2016 NCP Islamabad 2015 Outlines • A brief introduction of QCD Classical QCD Lagrangian Quantization Green functions of QCD and SDE’s • Perturbative QCD Perturbative calculation of QCD Green functions Feynman Rules of QCD Renormalization Running of QCD coupling (Asymptotic freedom) • Non-Perturbative QCD Confinement QCD phase transition Dynamical breaking of chiral symmetry Elementary Particle Physics Today Elementary particles: Quarks Leptons Gauge Bosons Higgs Boson (can interact through (cannot interact through (mediate interactions) (impart mass to the elementary strong interaction) strong interaction) particles) 푢 푐 푡 Meson: 푠 = 0,1,2 … Quarks: Hadrons: 1 3 푑 푠 푏 Baryons: 푠 = , , … 2 2 푣푒 푣휇 푣휏 Meson: Baryon Leptons: 푒 휇 휏 Gauge Bosons: 훾, 푊±, 푍0, and 8 gluons 399 Mesons, 574 Baryons have been discovered Higgs Bosons: 퐻 (God/Mother particle) • Strong interaction (Quantum Chromodynamics) • Electro-weak interaction (Quantum electro-flavor dynamics) The Standard Model Explaining the properties of the Hadrons in terms of QCD’s fundamental degrees of freedom is the Problem laying at the forefront of Hadronic physics. How these elementary particles and the SM is discovered? 1. Scattering Experiments Cross sections, Decay Constants, 2. Decay Processes Masses, Spin , Couplings, Form factors, etc. 3. Study of bound states Models Particle Accelerators Models and detectors Experimental Particle Physics Theoretical Particle Particle Physicist Phenomenologist Physicist Measured values of Calculated values of physical observables ≈ physical observables It doesn’t matter how beautifull your theory is, It is more important to have beauty It doesn’t matter how smart you are.