Hadron Phenomenology and QCDs DSEs
|
|
- Marjorie Harvey
- 5 years ago
- Views:
Transcription
1 Hadron Phenomenology and QCDs DSEs Lecture 3: Relativistic Scattering and Bound State Equations Ian Cloët University of Adelaide & Argonne National Laboratory Collaborators Wolfgang Bentz Tokai University Craig Roberts Argonne National Laboratory Anthony Thomas University of Adelaide David Wilson Argonne National Laboratory USC Summer Academy on Non-Perturbative Physics, July August 2012
2 Hadron Spectrum In quantum field theory physical states appear as poles in n-point Green Functions For example, the quark antiquark scattering matrix or t-matrix, contains poles for all qq bound states, that is, the physical mesons The quark antiquark t-matrix is obtained by solving the Bethe-Salpeter equation T = K + T K = Γ = Γ K Kernels of gap and BSE must be intimately related 1 = 1 + K For example, consider axial vector Ward Takahashi Identity q µ Γ µ,i 5 (p,p) = S 1 (p )γ τ i τ iγ 5 S 1 (p)+2mγ i π(p,p) frontpage table of contents appendices 2 / 24
3 Inhomogeneous & Homogeneous vertex functions T = K + T K = Γ = Γ K Near a bound state pole of mass m a two-body t-matrix behaves as T (p,k) Γ(p,k) Γ(p,k) p 2 m 2 where p = p 1 +p 2, k = p 1 p 2 Γ(p,k) is the homogeneous Bethe-Salpeter vertex and describes the relative motion of the quark and anti-quark while they form the bound state The inhomogeneous BSE is a generalization and contains all the poles of the t-matrix Γ = + Γ K the first term on the RHS is the elementary driving term the driving term projects out various channels the quark-photon vertex is described by a inhomogeneous BSE frontpage table of contents appendices 3 / 24
4 The Pion How does the pion become (almost) massless when it is composed of two massive constituents The pion is realized as the lowest lying pole in the quark anti-quark t-matrix in the pseudoscalar channel In the NJL model this t-matrix is given by d 4 k T (q),γδ = K,γδ + (2π) 4 K,λǫS(q +k) εε S(k) λ λt (q) ε λ,γδ, γ δ q = γ δ + γ δ ε λ ε λ K = 2iG π (γ 5 τ) (γ 5 τ) λǫ The NJL pion t-matrix is T (q) i,γδ = (γ 5τ i ) 2iG π 1+2G π Π PP (q 2 ) (γ 5τ i ) λǫ The pion mass is then given by: 1+2G π Π PP (q 2 = m 2 π) = 0 frontpage table of contents appendices 4 / 24
5 Pion Bethe-Salpeter Amplitude T = K + T K = Γ = Γ K Recall that near a bound state pole the t-matrix behaves as T (p,k) Γ(p,k) Γ(p,k) p 2 m 2 where p = p 1 +p 2, k = p 1 p 2 Expanding the pion t-matrix about the pole gives T (q) = (γ 5 τ i ) 2iG π 1+2G π Π PP (q 2 ) (γ 5τ i ) ig π q 2 m 2 π(γ 5 τ i )(γ 5 τ i ) Where g π is interpreted as the pion-quark coupling constant 1 g π = Π q 2 PP (q 2 ) q 2 =m 2 π The pion homogeneous BS vertex is therefore: Γ π = g π γ 5 τ i this is a very simple vertex that misses a lot of physics frontpage table of contents appendices 5 / 24
6 The Pion as a Goldstone Boson Using the NJL gap equation and the pion pole condition gives m 2 π = m 2M G π Π (L) AA (m2 π) Therefore in the chiral limit, m 0, the pion is massless In quantum mechanics one could tune a potential to give a massless ground state for a bound state of two massive constituents however quantum mechanics always gives: M bound state M constituents However quantum field theory with DCSB gives: m 2 π m Recall the Gell-Mann Oakes Renner relation f 2 π m 2 π = 1 2 (m u +m d ) ūu+ dd The pion decay constant is given by µ 0 A µ q q a π b (p) = if π p µ δ ab frontpage table of contents appendices 6 / 24
7 ρ a 1 mass splitting The ρ and a 1 are the lowest lying vector (J P = 1 ) and axial-vector (J P = 1 + ) qq bound states: m ρ 770 MeV & m a MeV The masses of these states are given by t-matrix poles in the vector and axial-vector qq channels γ δ q = γ δ + γ δ ε λ ε λ K = 2iG ρ [ (γµ τ) (γ µ τ) γδ +(γ µ γ 5 τ) (γ µ γ 5 τ) γδ ] Chiral symmetry implies one NJL coupling, G ρ. NJL gives m ρ 770 MeV & m a MeV NJL interaction is insufficient to obtain correct ρ a 1 mass splitting The rainbow ladder Maris Tandy DSE model gives m ρ 644 MeV & m a1 759 MeV Clearly something is missing! frontpage table of contents appendices 7 / 24
8 ρ a 1 mass splitting Generalized Quark-Gluon Vertex Recall that going below rainbow ladder by adding σ µν q ν τ 5 (p,p) to quark-gluon vertex, generates quark anomalous magnetic moment An order parameter for dynamical chiral symmetry; Chiral symmetry -0.2 forbids massless particle having -0.4 anomalous magnetic moments p/m E What about the hadron spectrum acm full aem full aem RL Important example of interplay between observables and DSE quark gluon vertex frontpage table of contents appendices 8 / 24
9 An Aside Muon Anomalous Magnetic Moment q µ p p = a exp µ = ± ; a theory µ = ± largest theory error come from HLBL scattering contribution µ ν µ ν µ ν µ ν µ ν q k q k q k q k q k Π µν = l t l t l t l t l t Box diagram contribution is least know only γ µ coupling and VMD has been considered so far we argue that the anomalous magnetic moment term cannot be ignored At least error on a HLBL µ = 8.3± should be much larger Fred Jegerlehner, Andreas Nyffeler, Physics Reports 477 (2009) frontpage table of contents appendices 9 / 24
10 Pion Form Factor Hadron form factors describe its interaction with the electromagnetic current An on-shell pion has one EM form factor l k q θ k π J µ π = (p µ +p µ )F 1 (Q 2 ) π p p In the impulse approximation the pion form factors are given by Γ Γ Γ = Γ Ingredients: dressed quark propagators homogeneous Bethe-Salpeter vertices dressed quark-photon vertex frontpage table of contents appendices 10 / 24
11 Pion Form Factor (2) Pion BSE vertex has the general form ] Γ π (p,k) = γ 5 [E π (p,k)+/pf π (p,k)+/kk pg(p,k)+σ µν k µ p ν H(p,k) Pseudovector component F π (p,k) dominates ultra-violet Perturbative QCD predicts Q 2 F 1π (Q 2 ) Q2 = 16πf 2 π s (Q 2 ) 0.44 s (Q 2 ) DSE finds that pqcd sets in at about Q 2 = 8 GeV 2 frontpage table of contents appendices 11 / 24
12 Some Consequences of Running Quark Mass Pion BSE vertex has the general form ] Γ π (p,k) = γ 5 [E π (p,k)+/pf π (p,k)+/kk pg(p,k)+σ µν k µ p ν H(p,k) In gap equation use simple kernel NJL model with π a 1 mixing g 2 D µν (p k)γ ν (p,k) 1 g m 2 µν γ ν [ ] = Γ π (p,k) = γ 5 Eπ +/pf π G Quark no longer has a running mass Nature of interaction has drastic observable consequences for Q 2 > 0 frontpage table of contents appendices 12 / 24
13 Measuring Pion Form Factor q dσ/dt (µb/gev 2 ) 6 Q 2 =1.60 σ L σ T 2 Q 2 =2.45 p p n t (GeV 2 ) t (GeV 2 ) At low Q 2 pion form factor is measured by scattering a pion from the electron cloud of an atom [t p 2 ] small mass of electron limits this to Q 2 < 0.5 GeV 2 Higher Q 2 experiments have been performed at Jefferson Lab where a virtual photon scatters from a virtual pion that is part of the nucleon wavefunction Initial pion is off its mass shell p 2 0 on mass shell p 2 = m 2 π need to extrapolate to the pion pole p 2 = m 2 π frontpage table of contents appendices 13 / 24
14 Off-Shell Pion Form Factors Fπ,1(p 2, p 2, Q 2 ) t = m 2 π t = 0.2 t = 0.4 Empirical p 2 = m 2 π p 2 = t Fπ,2(p 2, p 2, Q 2 ) t = m 2 π t = 0.2 t = 0.4 p 2 = m 2 π p 2 = t Q 2 (GeV 2 ) Q 2 (GeV 2 ) Initial pion is off its mass shell p 2 < 0 on mass shell p 2 = m 2 π need to extrapolate to the pion pole p 2 = m 2 π However an off-shell pion has two form factors not one and each form factor is a three dimensional function Γ µ π(p,p) = (p µ +p µ )F π1 (p 2,p 2,q 2 )+(p µ p µ )F π2 (p 2,p 2,q 2 ) Using NJL model can determine off-shell pion form factors Potentially important for experimental extraction of F π frontpage table of contents appendices 14 / 24
15 Baryons in the DSEs Baryons are 3-quark bound states with the proton (uud) and neutron (udd) being the most important examples In quantum field theory physical baryons appear as poles in six-point Green Functions Recall that two-body bound states appear as poles in four-point Green Functions and solutions were obtained by solving the Bethe-Salpeter Equation The analogue of the Bethe-Salpeter equation for 3-quark bound states is called the Faddeev equation By definition the Faddeev kernel only contains two-body interactions this is an approximation which is yet to be explored and could have important consequences for QCD Diagrammatically the homogeneous Faddeev equation is given by frontpage table of contents appendices 15 / 24
16 Baryons in the DSEs (2) We will render this problem tractable by making the quark-diquark approximation This is a linear matrix equation, whose solution gives the Baryon wavefunction strictly the Poincaré covariant Faddeev amplitude We will include scalar (J P = 0 +,T = 0) and axial-vector diquarks (J P = 1 +,T = 1) parity dictates that pseudoscalar and vector diquarks must be in an l = 1 state and are therefore suppressed in the nucleon for the negative parity N (1535) the opposite is true The nucleon wavefunction contains S, P and D wave correlations Equation has discrete solutions at p 2 = m 2 i ; nucleon, roper, etc frontpage table of contents appendices 16 / 24
17 What is a Diquark A diquark is a correlated (interacting) quark-quark state This interaction is attractive in the colour 3 (antisymmetric) or colour 6 (symmetric), however only the colour 3 can exist inside a colour singlet nucleon Diquarks are analogous to mesons colour singlet qq bound states Because diquarks are coloured they should not appear as physical states in QCD confinement However in the rainbow ladder approximation and the NJL model diquarks do appear as poles in the qq scattering (t) matrix Lattice QCD also sees evidence for diquarks I. Wetzorke, F. Karsch, hep-lat/ ( 30 3) implies scalar diquark: (flavour- 3, spin-0, colour- 3) (60 3) implies axial-vector diquark: (flavour-6, spin-0, colour- 3) frontpage table of contents appendices 17 / 24
18 Diquarks in The NJL model To describe diquarks in the NJL model one usually rewrites the qq interaction Lagrangian into a qq interaction Lagrangian ( ψγψ ) 2 ( ψω ψt )( ψ T Ωψ ) Ω has quantum numbers if interaction channel Γ Γ Ω Ω The qq NJL Lagrangian in the scalar and axial-vector diquark channels has the form L I = G s [ψγ 5 Cτ 2 A ψ T][ ] ψ T C 1 γ 5 τ 2 A ψ +G a [ψγ µ Cτ i τ 2 A ψ T][ ] ψ T C 1 γ µ τ 2 τ j A ψ +... the first term is the scalar diquark channel (J P = 0 +,T = 0) the second the axial-vector diquark channel (J P = 1 +,T = 1) τ 2 couples isospin of two quarks to T = 0, Cγ 5 couples spin to J = 0, A 3 = 2 λa A = 2,5,7 frontpage table of contents appendices 18 / 24
19 NJL diquarkt-matrices The equation for the qq scattering matrix the Bethe-Salpeter equation has the form T (q),γδ = K,γδ + 1 d 4 k 2 (2π) 4 K,ελS(k) εε S(q k) λλ T (q) ε λ,γδ, γ δ q = γ δ + γ δ ε λ ε λ = γ δ + γ δ ε λ ε λ note symmetry factor of 1 2 (c.f. qq BSE) The Feynman rules for the interaction kernels are K s = 4iG s(γ 5 Cτ 2 A ) (C 1 γ 5 τ 2 A ) γδ K a = 4iG a(γ µ Cτ i τ 2 A ) (C 1 γ µ τ 2 τ i A ) γδ The solution to the BSE is of the form: T (q),γδ = τ(q 2 )Ω Ωγδ τ s (q 2 ) = 4iG s 1+2G s Π s τ µν (q 2 ) a (q) = 4iG a 1+2G a Π a (q 2 ) [g µν +2G a Π a (q 2 ) qµ q ν ] frontpage table of contents appendices 19 / 24 q 2
20 Diquark Propagators The reduced t-matrices are the diquark propagators τ s (q 2 4iG ) = s 1+2G s Π s τ µν 4iG (q 2 ) a (q) = a 1+2G a Π a [g µν +2G (q 2 ) a Π a (q 2 ) qµ q ν q 2 ] Near the pole they behave as elementary propagators T,γδ = γ δ Ω Ω τ(q 2 ) γ δ Ω ig D q 2 MD 2 The diquark masses are therefore given by 1+2G s Π s (q 2 = Ms) 2 = 0 1+2G a Π a (q 2 = Ma) 2 = 0 Ω Expanding Π(q 2 ) near the pole gives the quark-diquark coupling constant gd 2 2 = Π q 2 D (q 2 ) q 2 =M 2 D frontpage table of contents appendices 20 / 24
21 The NJL Faddeev Equation To describe nucleon Faddeev equation kernel must be projected onto colour singlet, spin one-half, isospin one-half & positive parity p = p Make the static approximation to quark exchange kernel: S(p) 1 M Homogeneous Faddeev amplitude with static approximation does not depend of relative momentum between the quark and diquark The Faddeev equation and vertex have the form Γ N (p,s) = K(p)Γ N (p,s) [ ] M Γ N (p,s) = Z N 1 N p0 p µ 2 M N γ γ µ γ 5 u N (p,s) K(p) is the Faddeev kernel Faddeev equation describes the continual recombination of the three quark in quark-diquark configurations frontpage table of contents appendices 21 / 24
22 The NJL Faddeev Equation (2) k p = p p p p k The kernel of this NJL Faddeev eq Γ N (p,s) = K(p)Γ N (p,s) is [ ] [ Γs Γ µ = 3 ] [ Π Ns 3γ γ 5 Π ] Na Γs a M 3γ5 γ µ Π Ns γ γ µ Π Γ Na a, The quark-diquark bubble diagrams are Π Ns (p) = Π µν Na (p) = d 4 k (2π) 4 τ s(p k)s(k) d 4 k (2π) 4 τµν a (p k)s(k) Can now solve for the coefficients 1, 2, 3 this then gives the NJL Faddeev amplitude frontpage table of contents appendices 22 / 24
23 DSE Faddeev Equation The DSE Faddeev equation has far more structure than in NJL For example the DSE Faddeev equation including scalar and axial-vector diquarks reads [ ] S(k,P) d 4 [ ] l S(l,P) A µ i (k,p) u N (p) = (2π) 4 Mµν ij (l;k,p) A j u N (p) ν(l,p) importantly the vertex function depends on the relative momentum, k, between the quark and diquark the Faddeev kernel is M µν ij (l;k,p) S(k,P) and A µ i (k,p) describe the momentum space correlation between the quark and diquark in the nucleon This equation can be solved numerically on a large 2-D grid in k and P However standard practice to use a Chebyshev expansion for S(k,P) & A µ i (k,p) and the solve for the coefficients of the expansion a Chebyshev expansion is an expansion in Chebyshev polynomials frontpage table of contents appendices 23 / 24
24 Table of Contents hadron spectrum vertex functions pion vertex functions goldstone boson ρ a 1 mass splitting muon g 2 pion form factor running quark mass measuring pion form factor off-shell F πs baryons diquarks njl model diquarks njl diquark t-matrices diquark propagators njl faddeev dse faddeev equation frontpage table of contents appendices 24 / 24
QCD and the Nambu Jona-Lasinio Model
Lecture 1 QCD and the Nambu Jona-Lasinio Model Ian Cloët The University of Adelaide & Argonne National Laboratory CSSM Summer School Non-perturbative Methods in Quantum Field Theory 11 th 15 th February
More informationBethe Salpeter studies of mesons beyond rainbow-ladder
Bethe Salpeter studies of mesons beyond rainbow-ladder Richard Williams 1 st June 2010 12th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon College of William and Mary,
More informationA Dyson-Schwinger equation study of the baryon-photon interaction.
A Dyson-Schwinger equation study of the baryon-photon interaction. Diana Nicmorus in collaboration with G. Eichmann A. Krassnigg R. Alkofer Jefferson Laboratory, March 24, 2010 What is the nucleon made
More informationHLbl from a Dyson Schwinger Approach
HLbl from a Dyson Schwinger Approach Richard Williams KFUni Graz Tobias Göcke TU Darmstadt Christian Fischer Uni Gießen INT Workshop on Hadronic Light-by-Light contribution to the Muon Anomaly February
More informationFaddeev equations: a view of baryon properties
E-mail: diana.nicmorus@uni-graz.at G. Eichmann E-mail: ge.eichmann@uni-graz.at A. Krassnigg E-mail: andreas.krassnigg@uni-graz.at R. Alkofer E-mail: reinhard.alkofer@uni-graz.at We present a calculation
More informationCovariance, dynamics and symmetries, and hadron form factors
Covariance, dynamics and symmetries, and hadron form factors Craig D. Roberts cdroberts@anl.gov Physics Division Argonne National Laboratory Exclusive Reactions at High Momentum Transfer, 21-24May/07,
More informationSpectrum of Octet & Decuplet Baryons
Spectrum of Octet & Decuplet Baryons CHEN CHEN The Institute for Theoretical Physics (IFT) Universidade Estadual Paulista (UNESP) Universal Truths & DSEs Spectrum of hadrons (ground, excited and exotic
More informationRichard Williams. Hèlios Sanchis-Alepuz
Richard Williams Hèlios Sanchis-Alepuz Introduction 2 Idea: Information on hadron properties encoded in Green s functions EM form-factors Dyson-Schwinger Approach Nonpert. Covariant Multi-scale Symmetries
More informationRichard Williams C. S. Fischer, W. Heupel, H. Sanchis-Alepuz
Richard Williams C. S. Fischer, W. Heupel, H. Sanchis-Alepuz Overview 2 1.Motivation and Introduction 4. 3PI DSE results 2. DSEs and BSEs 3. npi effective action 6. Outlook and conclusion 5. 3PI meson
More informationBethe Salpeter studies of mesons beyond rainbow-ladder Complutense Unviversity of Madrid
Bethe Salpeter studies of mesons beyond rainbow-ladder Complutense Unviversity of Madrid Richard Williams C. S. Fischer and RW, Phys. Rev. D 78 2008 074006, [arxiv:0808.3372] C. S. Fischer and RW, Phys.
More informationLecture 9. Isospin The quark model
Lecture 9 Isospin The quark model There is one more symmetry that applies to strong interactions. isospin or isotopic spin It was useful in formulation of the quark picture of known particles. We can consider
More informationGian Gopal Particle Attributes Quantum Numbers 1
Particle Attributes Quantum Numbers Intro Lecture Quantum numbers (Quantised Attributes subject to conservation laws and hence related to Symmetries) listed NOT explained. Now we cover Electric Charge
More informationLecture 9 Valence Quark Model of Hadrons
Lecture 9 Valence Quark Model of Hadrons Isospin symmetry SU(3) flavour symmetry Meson & Baryon states Hadronic wavefunctions Masses and magnetic moments Heavy quark states 1 Isospin Symmetry Strong interactions
More informationTetraquarks and Goldstone boson physics
Tetraquarks and Goldstone boson physics Christian S. Fischer Justus Liebig Universität Gießen February 2017 Eichmann, CF, Heupel, PLB 753 (2016) 282-287 Review: Eichmann, Sanchis-Alepuz, Williams, Alkofer,
More informationHLbl from a Dyson Schwinger Approach
HLbl from a Dyson Schwinger Approach Richard Williams KFUni Graz Tobias Göcke TU Darmstadt Christian Fischer Uni Gießen Dissertantenseminar, March 16 th 2011, Graz 1 / 45 Introduction Table of contents
More informationMedium modifications of nucleon electromagnetic form factors
Medium modifications of nucleon electromagnetic form factors arxiv:nucl-th/0506021v1 8 Jun 2005 T. Horikawa Department of Physics, School of Science, Tokai University Hiratsuka-shi, Kanagawa 259-1292,
More informationSKETCHING, TRANSITION FORM FACTORS. Khépani Raya-Montaño University of Michoacan Morelia, Michoacan, Mexico.
SKETCHING, TRANSITION FORM FACTORS Khépani Raya-Montaño University of Michoacan Morelia, Michoacan, Mexico. XXXI RA DPyC. May 24-26, 2017 CINVESTAV-Zacatenco, Ciudad de México Motivation Understanding
More informationQuark-Gluon Vertex Dressing And Meson Masses Beyond Ladder-Rainbow Truncation.
Quark-Gluon Vertex Dressing And Meson Masses Beyond Ladder-Rainbow Truncation. nucl-th/0605057 H.H. Matevosyan 1,2, A.W. Thomas 2, P.C. Tandy 3 1 Department of Physics & Astronomy, Louisiana State University
More informationLecture 8. CPT theorem and CP violation
Lecture 8 CPT theorem and CP violation We have seen that although both charge conjugation and parity are violated in weak interactions, the combination of the two CP turns left-handed antimuon onto right-handed
More informationThe structure of a bound nucleon
The structure of a bound nucleon Ian Cloët (University of Washington) Collaborators Wolfgang Bentz Anthony Thomas (Tokai University) (Adelaide University) Tony s 60 Fest 5 9 Feburary 200 Theme Gain insights
More informationγnn Electrocouplings in Dyson-Schwinger Equations
γnn Electrocouplings in Dyson-Schwinger Equations Jorge Segovia Technische Universität München Physik-Department T30f T30f Theoretische Teilchenund Kernphysik Main collaborators: Craig D. Roberts (Argonne),
More informationQCD Symmetries in eta and etaprime mesic nuclei
QCD Symmetries in eta and etaprime mesic nuclei Steven Bass Chiral symmetry, eta and eta physics: the masses of these mesons are 300-400 MeV too big for them to be pure Goldstone bosons Famous axial U(1)
More informationIntroduction to Quantum Chromodynamics (QCD)
Introduction to Quantum Chromodynamics (QCD) Jianwei Qiu Theory Center, Jefferson Lab May 29 June 15, 2018 Lecture One The plan for my four lectures q The Goal: To understand the strong interaction dynamics
More informationDEEP INELASTIC SCATTERING
DEEP INELASTIC SCATTERING Electron scattering off nucleons (Fig 7.1): 1) Elastic scattering: E = E (θ) 2) Inelastic scattering: No 1-to-1 relationship between E and θ Inelastic scattering: nucleon gets
More informationNucleon, Delta and Nucleon to Delta Electromagnetic Form Factors in DSEs
Nucleon, Delta and Nucleon to Delta Electromagnetic Form Factors in DSEs Jorge Segovia, Ian C. Cloët and Craig D. Roberts Argonne National Laboratory Chen Chen and Shaolong Wan University of Science and
More informationThe Standard Model (part I)
The Standard Model (part I) Speaker Jens Kunstmann Student of Physics in 5 th year at Greifswald University, Germany Location Sommerakademie der Studienstiftung, Kreisau 2002 Topics Introduction The fundamental
More informationOutline. Charged Leptonic Weak Interaction. Charged Weak Interactions of Quarks. Neutral Weak Interaction. Electroweak Unification
Weak Interactions Outline Charged Leptonic Weak Interaction Decay of the Muon Decay of the Neutron Decay of the Pion Charged Weak Interactions of Quarks Cabibbo-GIM Mechanism Cabibbo-Kobayashi-Maskawa
More informationΛ QCD and Light Quarks Contents Symmetries of the QCD Lagrangian Chiral Symmetry and Its Breaking Parity and Handedness Parity Doubling Explicit Chira
Lecture 5 QCD Symmetries & Their Breaking From Quarks to Hadrons Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora Λ QCD and Light Quarks Contents Symmetries of the QCD Lagrangian Chiral Symmetry
More informationIntroduction to Strong Interactions and the Hadronic Spectrum
Introduction to Strong Interactions and the Hadronic Spectrum Milan Vujinovic University of Graz, Graz, Austria Support by FWF Doctoral Program W1203 Hadrons in Vacuum, Nuclei and Stars Institute of Physics,
More informationDr Victoria Martin, Prof Steve Playfer Spring Semester 2013
Particle Physics Dr Victoria Martin, Prof Steve Playfer Spring Semester 2013 Lecture 12: Mesons and Baryons Mesons and baryons Strong isospin and strong hypercharge SU(3) flavour symmetry Heavy quark states
More informationIsospin. K.K. Gan L5: Isospin and Parity 1
Isospin Isospin is a continuous symmetry invented by Heisenberg: Explain the observation that the strong interaction does not distinguish between neutron and proton. Example: the mass difference between
More informationNucleon and Delta Elastic and Transition Form Factors
Nucleon and Delta Elastic and Transition Form Factors Based on: - Phys. Rev. C88 (013) 0301(R), - Few-Body Syst. 54 (013) 1-33, - Few-body Syst. 55 (014) 1185-1. Jorge Segovia Instituto Universitario de
More informationQuantum Numbers. Elementary Particles Properties. F. Di Lodovico c 1 EPP, SPA6306. Queen Mary University of London. Quantum Numbers. F.
Elementary Properties 1 1 School of Physics and Astrophysics Queen Mary University of London EPP, SPA6306 Outline Most stable sub-atomic particles are the proton, neutron (nucleons) and electron. Study
More informationValence quark contributions for the γn P 11 (1440) transition
Valence quark contributions for the γn P 11 (144) transition Gilberto Ramalho (Instituto Superior Técnico, Lisbon) In collaboration with Kazuo Tsushima 12th International Conference on Meson-Nucleon Physics
More informationSUNY Stony Brook August 16, Wolfram Weise. with. Thomas Hell Simon Rössner Claudia Ratti
SUNY Stony Brook August 16, 27 PHASES of QCD POLYAKOV LOOP and QUASIPARTICLES Wolfram Weise with Thomas Hell Simon Rössner Claudia Ratti C. Ratti, M. Thaler, W. Weise: Phys. Rev. D 73 (26) 1419 C. Ratti,
More informationHow nucleon gets its mass
Fiz-Tech, Dec 05, 2006 How nucleon gets its mass Dmitri Diakonov Petersburg Nuclear Physics Institute 1. Quantum Chromodynamics: the theory of strong interactions 2. Chiral symmetry of strong interactions
More informationarxiv:hep-ph/ v4 10 Dec 2005
1 The mass of the nucleon in a chiral quark-diquark model arxiv:hep-ph/0408312v4 10 Dec 2005 Keitaro Nagata 1, Atsushi Hosaka 1 and Laith. J. Abu-Raddad 2 1 Research Center for Nuclear Physics (RCNP),
More informationJanuary 31, PHY357 Lecture 8. Quark composition of hadrons. Hadron magnetic moments. Hadron masses
January 3, 08 PHY357 Lecture 8 Quark composition of hadrons Hadron magnetic moments Hadron masses January 3, 08 Quark rules for building Hadrons! Three types of stable quark configurations established!
More informationLecture II. QCD and its basic symmetries. Renormalisation and the running coupling constant
Lecture II QCD and its basic symmetries Renormalisation and the running coupling constant Experimental evidence for QCD based on comparison with perturbative calculations The road to QCD: SU(3) quark model
More informationDistribution Amplitudes of the Nucleon and its resonances
Distribution Amplitudes of the Nucleon and its resonances C. Mezrag Argonne National Laboratory November 16 th, 2016 In collaboration with: C.D. Roberts and J. Segovia C. Mezrag (ANL) Nucleon DA November
More informationOUTLINE. CHARGED LEPTONIC WEAK INTERACTION - Decay of the Muon - Decay of the Neutron - Decay of the Pion
Weak Interactions OUTLINE CHARGED LEPTONIC WEAK INTERACTION - Decay of the Muon - Decay of the Neutron - Decay of the Pion CHARGED WEAK INTERACTIONS OF QUARKS - Cabibbo-GIM Mechanism - Cabibbo-Kobayashi-Maskawa
More informationThe dissection of γ v N N and γ v N R electromagnetic form factors
The dissection of γ v N N and γ v N R electromagnetic form factors Jorge Segovia Technische Universität München Physik-Department-T30f T30f Theoretische Teilchenund Kernphysik Jorge Segovia (jorge.segovia@tum.de)
More informationDiscrete Transformations: Parity
Phy489 Lecture 8 0 Discrete Transformations: Parity Parity operation inverts the sign of all spatial coordinates: Position vector (x, y, z) goes to (-x, -y, -z) (eg P(r) = -r ) Clearly P 2 = I (so eigenvalues
More informationExotic Hadrons. O Villalobos Baillie MPAGS PP5 November 2015
Exotic Hadrons O Villalobos Baillie MPAGS PP5 November 2015 Allowed hadronic states At the beginning of this course, we stated that there are only two allowed combinations of quarks that give bound hadronic
More informationOutline. Charged Leptonic Weak Interaction. Charged Weak Interactions of Quarks. Neutral Weak Interaction. Electroweak Unification
Weak Interactions Outline Charged Leptonic Weak Interaction Decay of the Muon Decay of the Neutron Decay of the Pion Charged Weak Interactions of Quarks Cabibbo-GIM Mechanism Cabibbo-Kobayashi-Maskawa
More informationOption 212: UNIT 2 Elementary Particles
Department of Physics and Astronomy Option 212: UNIT 2 Elementary Particles SCHEDULE 26-Jan-15 13.00pm LRB Intro lecture 28-Jan-15 12.00pm LRB Problem solving (2-Feb-15 10.00am E Problem Workshop) 4-Feb-15
More informationCovariant quark-diquark model for the N N electromagnetic transitions
Covariant quark-diquark model for the N N electromagnetic transitions Gilberto Ramalho CFTP, Instituto Superior Técnico, Lisbon In collaboration with F. Gross, M.T. Peña and K. Tsushima Nucleon Resonance
More informationBethe Salpeter Meson Masses Beyond Ladder Approximation. Abstract
Kent State U preprint no. KSUCNR-204-02 Bethe Salpeter Meson Masses Beyond Ladder Approximation P. Watson, 1, W. Cassing, 1, and P. C. Tandy 2, 1 Institute for Theoretical Physics, University of Giessen,
More informationDr Victoria Martin, Spring Semester 2013
Particle Physics Dr Victoria Martin, Spring Semester 2013 Lecture 3: Feynman Diagrams, Decays and Scattering Feynman Diagrams continued Decays, Scattering and Fermi s Golden Rule Anti-matter? 1 Notation
More informationLight and strange baryon spectrum from functional methods
Light and strange baryon spectrum from functional methods Christian S. Fischer Justus Liebig Universität Gießen Review: Eichmann, Sanchis-Alepuz, Williams, Alkofer, CF, PPNP 91, 1-100 [1606.09602] Christian
More informationExplanations and Predictions from QCD s DSEs
Explanations and Predictions from QCD s DSEs Jorge Segovia, Ian C. Cloët and Craig D. Roberts Argonne National Laboratory Chen Chen and Shaolong Wan University of Science and Technology of China Physics
More informationThe Quark Parton Model
The Quark Parton Model Quark Model Pseudoscalar J P = 0 Mesons Vector J P = 1 Mesons Meson Masses J P = 3 /2 + Baryons J P = ½ + Baryons Resonances Resonance Detection Discovery of the ω meson Dalitz Plots
More informationL. David Roper
The Heavy Proton L. David Roper mailto:roperld@vt.edu Introduction The proton is the nucleus of the hydrogen atom, which has one orbiting electron. The proton is the least massive of the baryons. Its mass
More informationKern- und Teilchenphysik II Lecture 1: QCD
Kern- und Teilchenphysik II Lecture 1: QCD (adapted from the Handout of Prof. Mark Thomson) Prof. Nico Serra Dr. Marcin Chrzaszcz Dr. Annapaola De Cosa (guest lecturer) www.physik.uzh.ch/de/lehre/phy213/fs2017.html
More informationFundamental Forces. David Morrissey. Key Concepts, March 15, 2013
Fundamental Forces David Morrissey Key Concepts, March 15, 2013 Not a fundamental force... Also not a fundamental force... What Do We Mean By Fundamental? Example: Electromagnetism (EM) electric forces
More informationNucleon Resonance Electro-couplings in Dyson-Schwinger Equations
Nucleon Resonance Electro-couplings in Dyson-Schwinger Equations Jorge Segovia Technische Universität München Physik-Department T30f T30f Theoretische Teilchenund Kernphysik Seminar Theoretical Hadron
More informationHigh Energy Physics. Lecture 9. Deep Inelastic Scattering Scaling Violation. HEP Lecture 9 1
High Energy Physics Lecture 9 Deep Inelastic Scattering Scaling Violation HEP Lecture 9 1 Deep Inelastic Scattering: The reaction equation of DIS is written e+ p e+ X where X is a system of outgoing hadrons
More informationThe symmetries of QCD (and consequences)
The symmetries of QCD (and consequences) Sinéad M. Ryan Trinity College Dublin Quantum Universe Symposium, Groningen, March 2018 Understand nature in terms of fundamental building blocks The Rumsfeld
More informationPhysicsAndMathsTutor.com
OR K π 0 + µ + v ( µ ) M. (a) (i) quark antiquark pair OR qq OR named quark antiquark pair 0 (iii) us (b) (i) Weak any of the following also score mark: weak interaction weak interaction force weak nuclear
More informationQCD in the light quark (up & down) sector (QCD-light) has two mass scales M(GeV)
QCD in the light quark (up & down) sector (QCD-light) has two mass scales M(GeV) 1 m N m ρ Λ QCD 0 m π m u,d In a generic physical system, there are often many scales involved. However, for a specific
More informationRECENT ADVANCES IN THE CALCULATION OF HADRON FORM FACTORS USING DYSON-SCHWINGER EQUATIONS OF QCD
RECENT ADVANCES IN THE CALCULATION OF HADRON FORM FACTORS USING DYSON-SCHWINGER EQUATIONS OF QCD Jorge Segovia Argonne National Laboratory Thomas Jefferson National Accelerator Facility Newport News (Virginia)
More informationPhysics 4213/5213 Lecture 1
August 28, 2002 1 INTRODUCTION 1 Introduction Physics 4213/5213 Lecture 1 There are four known forces: gravity, electricity and magnetism (E&M), the weak force, and the strong force. Each is responsible
More informationIntroduction to particle physics Lecture 6
Introduction to particle physics Lecture 6 Frank Krauss IPPP Durham U Durham, Epiphany term 2009 Outline 1 Fermi s theory, once more 2 From effective to full theory: Weak gauge bosons 3 Massive gauge bosons:
More informationKern- und Teilchenphysik I Lecture 13:Quarks and QCD
Kern- und Teilchenphysik I Lecture 13:Quarks and QCD (adapted from the Handout of Prof. Mark Thomson) Prof. Nico Serra Dr. Patrick Owen, Dr. Silva Coutinho http://www.physik.uzh.ch/de/lehre/phy211/hs2016.html
More informationParticle Physics. Lecture 11: Mesons and Baryons
Particle Physics Lecture 11: Mesons and Baryons Measuring Jets Fragmentation Mesons and Baryons Isospin and hypercharge SU(3) flavour symmetry Heavy Quark states 1 From Tuesday: Summary In QCD, the coupling
More informationIntroduction to particle physics Lecture 7
Introduction to particle physics Lecture 7 Frank Krauss IPPP Durham U Durham, Epiphany term 2009 Outline 1 Deep-inelastic scattering and the structure of protons 2 Elastic scattering Scattering on extended
More informationHadronic light-by-light from Dyson-Schwinger equations
Hadronic light-by-light from Dyson-Schwinger equations Christian S. Fischer Justus Liebig Universität Gießen 23rd of October 2014 Together with Richard Williams, Gernot Eichmann, Tobias Goecke, Jan Haas
More informationIntroduction to Quantum Chromodynamics (QCD)
Introduction to Quantum Chromodynamics (QCD) Jianwei Qiu August 16 19, 018 Four Lectures The 3 rd WHEPS, August 16-4, 018, Weihai, Shandong q The Goal: The plan for my four lectures To understand the strong
More informationOverview. The quest of Particle Physics research is to understand the fundamental particles of nature and their interactions.
Overview The quest of Particle Physics research is to understand the fundamental particles of nature and their interactions. Our understanding is about to take a giant leap.. the Large Hadron Collider
More informationLecture 02. The Standard Model of Particle Physics. Part I The Particles
Lecture 02 The Standard Model of Particle Physics Part I The Particles The Standard Model Describes 3 of the 4 known fundamental forces Separates particles into categories Bosons (force carriers) Photon,
More informationHadronic contributions to the muon g-2
Hadronic contributions to the muon g-2 RICHARD WILLIAMS (HIRSCHEGG 2014) 1 Overview Introduction Hadronic Vacuum Polarisation Hadronic Light-by-Light Scattering Conclusions 2 Overview Introduction Hadronic
More informationA study of π and ρ mesons with a nonperturbative
Journal of Physics: Conference Series PAPER OPEN ACCESS A study of π and ρ mesons with a nonperturbative approach To cite this article: Rocio Bermudez et al 2015 J. Phys.: Conf. Ser. 651 012002 Related
More informationHadronic Resonances in a Hadronic Picture. Daisuke Jido (Nuclear physics group)
Daisuke Jido (Nuclear physics group) Hadrons (particles interacting with strong interactions) are composite objects of quarks and gluons. It has been recently suggested that the structures of some hadrons
More informationBaryonic Spectral Functions at Finite Temperature
Baryonic Spectral Functions at Finite Temperature Masayuki Asakawa Department of Physics, Osaka University July 2008 @ XQCD 2008 QCD Phase Diagram T LHC 160-190 MeV 100MeV ~ 10 12 K RHIC crossover CEP(critical
More informationLecture 2: The First Second origin of neutrons and protons
Lecture 2: The First Second origin of neutrons and protons Hot Big Bang Expanding and cooling Soup of free particles + anti-particles Symmetry breaking Soup of free quarks Quarks confined into neutrons
More informationElectron-positron pairs can be produced from a photon of energy > twice the rest energy of the electron.
Particle Physics Positron - discovered in 1932, same mass as electron, same charge but opposite sign, same spin but magnetic moment is parallel to angular momentum. Electron-positron pairs can be produced
More informationQuark Model. Mass and Charge Patterns in Hadrons. Spin-1/2 baryons: Nucleons: n: MeV; p: MeV
Mass and Charge Patterns in Hadrons To tame the particle zoo, patterns in the masses and charges can be found that will help lead to an explanation of the large number of particles in terms of just a few
More informationGernot Eichmann. The Analytic Structure of the Quark Propagator in the Covariant Faddeev Equation of the Nucleon
Gernot Eichmann The Analytic Structure of the Quark Propagator in the Covariant Faddeev Equation of the Nucleon Diplomarbeit zur Erlangung des Magistergrades der Naturwissenschaften verfasst am Institut
More informationHot and Magnetized Pions
.. Hot and Magnetized Pions Neda Sadooghi Department of Physics, Sharif University of Technology Tehran - Iran 3rd IPM School and Workshop on Applied AdS/CFT February 2014 Neda Sadooghi (Dept. of Physics,
More informationNational Nuclear Physics Summer School Lectures on Effective Field Theory. Brian Tiburzi. RIKEN BNL Research Center
2014 National Nuclear Physics Summer School Lectures on Effective Field Theory I. Removing heavy particles II. Removing large scales III. Describing Goldstone bosons IV. Interacting with Goldstone bosons
More informationPhases and facets of 2-colour matter
Phases and facets of 2-colour matter Jon-Ivar Skullerud with Tamer Boz, Seamus Cotter, Leonard Fister Pietro Giudice, Simon Hands Maynooth University New Directions in Subatomic Physics, CSSM, 10 March
More informationBaryon Resonance Determination using LQCD. Robert Edwards Jefferson Lab. Baryons 2013
Baryon Resonance Determination using LQCD Robert Edwards Jefferson Lab Baryons 2013 Where are the Missing Baryon Resonances? What are collective modes? Is there freezing of degrees of freedom? What is
More informationη π 0 γγ decay in the three-flavor Nambu Jona-Lasinio model
TIT/HEP-38/NP INS-Rep.-3 η π 0 γγ decay in the three-flavor Nambu Jona-Lasinio model arxiv:hep-ph/96053v 8 Feb 996 Y.Nemoto, M.Oka Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 5,
More informationQuark model. Jan 30, 2006 Lecture 8 1
Quark model Jan 30, 2006 Lecture 8 1 Quark model of hadrons!!!! Developed long before QCD was recognized as the appropriate quantum field theory of the strong interactions Postulate that 1.! All baryons
More informationThe SU(3) Group SU(3) and Mesons Contents Quarks and Anti-quarks SU(3) and Baryons Masses and Symmetry Breaking Gell-Mann Okubo Mass Formulae Quark-Mo
Lecture 2 Quark Model The Eight Fold Way Adnan Bashir, IFM, UMSNH, Mexico August 2014 Culiacán Sinaloa The SU(3) Group SU(3) and Mesons Contents Quarks and Anti-quarks SU(3) and Baryons Masses and Symmetry
More informationJacopo Ferretti Sapienza Università di Roma
Jacopo Ferretti Sapienza Università di Roma NUCLEAR RESONANCES: FROM PHOTOPRODUCTION TO HIGH PHOTON VIRTUALITIES ECT*, TRENTO (ITALY), -6 OCTOBER 05 Three quark QM vs qd Model A relativistic Interacting
More informationDiscovery of Pions and Kaons in Cosmic Rays in 1947
Discovery of Pions and Kaons in Cosmic Rays in 947 π + µ + e + (cosmic rays) Points to note: de/dx Bragg Peak Low de/dx for fast e + Constant range (~600µm) (i.e. -body decay) small angle scattering Strange
More informationLOW-ENERGY QCD and STRANGENESS in the NUCLEON
PAVI 09 Bar Harbor, Maine, June 009 LOW-ENERGY QCD and STRANGENESS in the NUCLEON Wolfram Weise Strategies in Low-Energy QCD: Lattice QCD and Chiral Effective Field Theory Scalar Sector: Nucleon Mass and
More informationElectric Dipole Moments and the strong CP problem
Electric Dipole Moments and the strong CP problem We finally understand CP viola3on.. QCD theta term Jordy de Vries, Nikhef, Amsterdam Topical Lectures on electric dipole moments, Dec. 14-16 Introductory
More informationThe Strong Interaction and LHC phenomenology
The Strong Interaction and LHC phenomenology Juan Rojo STFC Rutherford Fellow University of Oxford Theoretical Physics Graduate School course Lecture 2: The QCD Lagrangian, Symmetries and Feynman Rules
More information1 Introduction. 1.1 The Standard Model of particle physics The fundamental particles
1 Introduction The purpose of this chapter is to provide a brief introduction to the Standard Model of particle physics. In particular, it gives an overview of the fundamental particles and the relationship
More informationPartial overview of Dyson-Schwinger approach to QCD and some applications to structure of hadrons a
Partial overview of Dyson-Schwinger approach to QCD and some applications to structure of hadrons a p. 1/30 Partial overview of Dyson-Schwinger approach to QCD and some applications to structure of hadrons
More informationPions are Special Contents Chiral Symmetry and Its Breaking Symmetries and Conservation Laws Goldstone Theorem The Potential Linear Sigma Model Wigner
Lecture 3 Pions as Goldstone Bosons of Chiral Symmetry Breaking Adnan Bashir, IFM, UMSNH, Mexico August 2013 Hermosillo Sonora Pions are Special Contents Chiral Symmetry and Its Breaking Symmetries and
More informationGoldstone bosons in the CFL phase
Goldstone bosons in the CFL phase Verena Werth 1 Michael Buballa 1 Micaela Oertel 2 1 Institut für Kernphysik, Technische Universität Darmstadt 2 Observatoire de Paris-Meudon Dense Hadronic Matter and
More informationFundamental Interactions (Forces) of Nature
Chapter 14 Fundamental Interactions (Forces) of Nature Interaction Gauge Boson Gauge Boson Mass Interaction Range (Force carrier) Strong Gluon 0 short-range (a few fm) Weak W ±, Z M W = 80.4 GeV/c 2 short-range
More information2007 Section A of examination problems on Nuclei and Particles
2007 Section A of examination problems on Nuclei and Particles 1 Section A 2 PHYS3002W1 A1. A fossil containing 1 gramme of carbon has a radioactivity of 0.03 disintegrations per second. A living organism
More informationRichard Williams. Collaborators: Alkofer, Eichmann, Fischer, Heupel, Sanchis-Alepuz
Richard Williams Collaborators: Alkofer, Eichmann, Fischer, Heupel, Sanchis-Alepuz 2 baryons mesons glueballs hybrids tetraquarks pentaquarks Extracting hadron poles from Green s functions 3 Extracting
More information129 Lecture Notes More on Dirac Equation
19 Lecture Notes More on Dirac Equation 1 Ultra-relativistic Limit We have solved the Diraction in the Lecture Notes on Relativistic Quantum Mechanics, and saw that the upper lower two components are large
More informationLectures on Chiral Perturbation Theory
Lectures on Chiral Perturbation Theory I. Foundations II. Lattice Applications III. Baryons IV. Convergence Brian Tiburzi RIKEN BNL Research Center Chiral Perturbation Theory I. Foundations Low-energy
More informationModels of the Nucleon & Parton Distribution Functions
11th CTEQ Summer School on QCD Analysis and Phenomenology Madison, Wisconsin, June 22-30, 2004 Models of the Nucleon & Parton Distribution Functions Wally Melnitchouk Jefferson Lab Outline Introduction
More information