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Dyson Schwinger Equations for Hadron Physics

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  1. Dyson Schwinger Equationsfor Hadron Physics Craig D. RobertsPhysics DivisionArgonne National Laboratory & School of PhysicsPeking University Transition Region

  2. Hadron Physics “Hadron physics is unique at the cutting edge of modern science because Nature has provided us with just one instance of a fundamental strongly-interacting theory; i.e., Quantum Chromodynamics (QCD). The community of science has never before confronted such a challenge as solving this theory.” Craig Roberts, Physics Division: DSEs for Hadron Physics

  3. NSACLong Range Plan Craig Roberts, Physics Division: DSEs for Hadron Physics “A central goal of (DOE Office of ) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD.”

  4. What is QCD? Craig Roberts, Physics Division: DSEs for Hadron Physics

  5. What is QCD? • Relativistic Quantum Gauge Theory: • Interactions mediated by vector boson exchange • Vector bosons are perturbatively-massless Craig Roberts, Physics Division: DSEs for Hadron Physics

  6. What is QCD? • Relativistic Quantum Gauge Theory: • Interactions mediated by vector boson exchange • Vector bosons are perturbatively-massless • Similar interaction in QED Craig Roberts, Physics Division: DSEs for Hadron Physics

  7. What is QCD? • Relativistic Quantum Gauge Theory: • Interactions mediated by vector boson exchange • Vector bosons are perturbatively-massless • Similar interaction in QED • Special feature of QCD – gluon self-interactions, which completely change the character of the theory 3-gluon vertex 4-gluon vertex Craig Roberts, Physics Division: DSEs for Hadron Physics

  8. QED cf. QCD? Running coupling Craig Roberts, Physics Division: DSEs for Hadron Physics

  9. QED cf. QCD? Running coupling Add 3-gluon self-interaction Craig Roberts, Physics Division: DSEs for Hadron Physics

  10. QED cf. QCD? gluon antiscreening fermion screening Craig Roberts, Physics Division: DSEs for Hadron Physics

  11. QED cf. QCD? gluon antiscreening fermion screening Craig Roberts, Physics Division: DSEs for Hadron Physics • 2004 Nobel Prize in Physics : Gross, Politzer and Wilczek

  12. Simple picture- Proton Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange Craig Roberts, Physics Division: DSEs for Hadron Physics

  13. Simple picture- Pion Two quantum-mechanical constituent-quarks - particle+antiparticle -interacting via a potential, derived from one constituent-gluon exchange Craig Roberts, Physics Division: DSEs for Hadron Physics

  14. Modern Miraclesin Hadron Physics Craig Roberts, Physics Division: DSEs for Hadron Physics • proton = three constituent quarks • Mproton ≈ 1GeV • Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV

  15. Modern Miraclesin Hadron Physics Craig Roberts, Physics Division: DSEs for Hadron Physics • proton = three constituent quarks • Mproton ≈ 1GeV • Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV • pion = constituent quark + constituent antiquark • Guess Mpion ≈ ⅔ × Mproton≈ 700MeV

  16. Modern Miraclesin Hadron Physics Craig Roberts, Physics Division: DSEs for Hadron Physics • proton = three constituent quarks • Mproton ≈ 1GeV • Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV • pion = constituent quark + constituent antiquark • Guess Mpion ≈ ⅔ × Mproton≈ 700MeV • WRONG . . . . . . . . . . . . . . . . . . . . . . Mpion = 140MeV

  17. Modern Miraclesin Hadron Physics Craig Roberts, Physics Division: DSEs for Hadron Physics • proton = three constituent quarks • Mproton ≈ 1GeV • Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV • pion = constituent quark + constituent antiquark • Guess Mpion ≈ ⅔ × Mproton≈ 700MeV • WRONG . . . . . . . . . . . . . . . . . . . . . . Mpion = 140MeV • Rho-meson • Also constituent quark + constituent antiquark – just pion with spin of one constituent flipped • Mrho ≈ 770MeV ≈ 2 × Mconstituent−quark

  18. Modern Miraclesin Hadron Physics Craig Roberts, Physics Division: DSEs for Hadron Physics • proton = three constituent quarks • Mproton ≈ 1GeV • Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV • pion = constituent quark + constituent antiquark • Guess Mpion ≈ ⅔ × Mproton≈ 700MeV • WRONG . . . . . . . . . . . . . . . . . . . . . . Mpion = 140MeV • Rho-meson • Also constituent quark + constituent antiquark – just pion with spin of one constituent flipped • Mrho ≈ 770MeV ≈ 2 × Mconstituent−quark What is “wrong” with the pion?

  19. Dichotomy of the pion Craig Roberts, Physics Division: DSEs for Hadron Physics • How does one make an almost massless particle from two massive constituent-quarks? • Naturally, one could always tune a potential in quantum mechanics so that the ground-state is massless • However: current-algebra (1968) • This is impossible in quantum mechanics, for which one always finds:

  20. NSACLong Range Plan? • What is a constituent quark, a constituent-gluon? Craig Roberts, Physics Division: DSEs for Hadron Physics

  21. NSACLong Range Plan? • What is a constituent quark, a constituent-gluon? • Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom? Craig Roberts, Physics Division: DSEs for Hadron Physics

  22. NSACLong Range Plan? • What is a constituent quark, a constituent-gluon? • Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom? Craig Roberts, Physics Division: DSEs for Hadron Physics • If not, with what should they be replaced?

  23. NSACLong Range Plan? • What is a constituent quark, a constituent-gluon? • Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom? Craig Roberts, Physics Division: DSEs for Hadron Physics • If not, with what should they be replaced? • What is the meaning of the NSAC Challenge?

  24. QCD’s Challenges • Quark and Gluon Confinement • No matter how hard one strikes the proton, • one cannot liberate an individual quark or gluon Craig Roberts, Physics Division: DSEs for Hadron Physics

  25. QCD’s Challenges • Quark and Gluon Confinement • No matter how hard one strikes the proton, • one cannot liberate an individual quark or gluon Craig Roberts, Physics Division: DSEs for Hadron Physics • Dynamical Chiral Symmetry Breaking Very unnatural pattern of bound state masses; e.g., Lagrangian (pQCD) quark mass is small but . . . no degeneracy between JP=+ and JP=− (parity partners)

  26. QCD’s Challenges • Quark and Gluon Confinement • No matter how hard one strikes the proton, • one cannot liberate an individual quark or gluon Craig Roberts, Physics Division: DSEs for Hadron Physics • Dynamical Chiral Symmetry Breaking Very unnatural pattern of bound state masses; e.g., Lagrangian (pQCD) quark mass is small but . . . no degeneracy between JP=+ and JP=− (parity partners) • Neither of these phenomena is apparent in QCD’s LagrangianYetthey are the dominant determiningcharacteristics of real-world QCD.

  27. QCD’s ChallengesUnderstand emergent phenomena • Quark and Gluon Confinement • No matter how hard one strikes the proton, • one cannot liberate an individual quark or gluon Craig Roberts, Physics Division: DSEs for Hadron Physics • Dynamical Chiral Symmetry Breaking Very unnatural pattern of bound state masses; e.g., Lagrangian (pQCD) quark mass is small but . . . no degeneracy between JP=+ and JP=− (parity partners) • Neither of these phenomena is apparent in QCD’s LagrangianYetthey are the dominant determiningcharacteristics of real-world QCD. • QCD – Complex behaviour arises from apparently simple rules.

  28. Why don’t we juststop talking & solve the problem? Craig Roberts, Physics Division: DSEs for Hadron Physics • Emergent phenomena can’t be studied using perturbation theory

  29. Why don’t we juststop talking & solve the problem? Craig Roberts, Physics Division: DSEs for Hadron Physics • Emergent phenomena can’t be studied using perturbation theory • So what? Same is true of bound-state problems in quantum mechanics!

  30. Why don’t we juststop talking & solve the problem? Craig Roberts, Physics Division: DSEs for Hadron Physics • Emergent phenomena can’t be studied using perturbation theory • So what? Same is true of bound-state problems in quantum mechanics! • Differences: • Here relativistic effects are crucial – virtual particles Quintessence of Relativistic Quantum Field Theory • Interaction between quarks – the Interquark Potential – Unknown throughout > 98% of the pion’s/proton’s volume!

  31. Why don’t we juststop talking & solve the problem? Craig Roberts, Physics Division: DSEs for Hadron Physics • Emergent phenomena can’t be studied using perturbation theory • So what? Same is true of bound-state problems in quantum mechanics! • Differences: • Here relativistic effects are crucial – virtual particles Quintessence of Relativistic Quantum Field Theory • Interaction between quarks – the Interquark Potential – Unknown throughout > 98% of the pion’s/proton’s volume! • Understanding requires ab initio nonperturbative solution of fully-fledged interacting relativistic quantum field theory

  32. Universal Truths Craig Roberts, Physics Division: DSEs for Hadron Physics • Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron'scharacterising properties amongst its QCD constituents.

  33. Universal Truths Craig Roberts, Physics Division: DSEs for Hadron Physics • Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron'scharacterising properties amongst its QCD constituents. • Dynamical Chiral Symmetry Breaking (DCSB) is most important mass generating mechanism for visible matter in the Universe. Higgs mechanism is (almost) irrelevant to light-quarks.

  34. Universal Truths Craig Roberts, Physics Division: DSEs for Hadron Physics • Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron'scharacterising properties amongst its QCD constituents. • Dynamical Chiral Symmetry Breaking (DCSB) is most important mass generating mechanism for visible matter in the Universe. Higgs mechanism is (almost) irrelevant to light-quarks. • Running of quark mass entails that calculations at even modest Q2 require a Poincaré-covariant approach. Covariance requires existence of quark orbital angular momentum in hadron's rest-frame wave function.

  35. Universal Truths Craig Roberts, Physics Division: DSEs for Hadron Physics • Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron'scharacterising properties amongst its QCD constituents. • Dynamical Chiral Symmetry Breaking (DCSB) is most important mass generating mechanism for visible matter in the Universe. Higgs mechanism is (almost) irrelevant to light-quarks. • Running of quark mass entails that calculations at even modest Q2 require a Poincaré-covariant approach. Covariance requires existence of quark orbital angular momentum in hadron's rest-frame wave function. • Confinement is expressed through a violent change of the propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator. It is intimately connected with DCSB.

  36. How can we tackle the SM’sStrongly-interacting piece? Craig Roberts, Physics Division: DSEs for Hadron Physics

  37. How can we tackle the SM’sStrongly-interacting piece? Craig Roberts, Physics Division: DSEs for Hadron Physics The Traditional Approach – Modelling

  38. How can we tackle the SM’sStrongly-interacting piece? Craig Roberts, Physics Division: DSEs for Hadron Physics The Traditional Approach – Modelling – has its problems.

  39. How can we tackle the SM’sStrongly-interacting piece? – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom Craig Roberts, Physics Division: DSEs for Hadron Physics Lattice-QCD

  40. How can we tackle the SM’sStrongly-interacting piece? – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom – Approximately 500 people worldwide & 20-30 people per collaboration. Craig Roberts, Physics Division: DSEs for Hadron Physics Lattice-QCD –

  41. A Compromise?Dyson-Schwinger Equations Craig Roberts, Physics Division: DSEs for Hadron Physics

  42. A Compromise?Dyson-Schwinger Equations Craig Roberts, Physics Division: DSEs for Hadron Physics • 1994 . . . “As computer technology continues to improve, lattice gauge theory [LGT] will become an increasingly useful means of studying hadronic physics through investigations of discretised quantum chromodynamics [QCD]. . . . .”

  43. A Compromise?Dyson-Schwinger Equations Craig Roberts, Physics Division: DSEs for Hadron Physics • 1994 . . . “However, it is equally important to develop other complementary nonperturbative methods based on continuum descriptions. In particular, with the advent of new accelerators such as CEBAF (VA) and RHIC (NY), there is a need for the development of approximation techniques and models which bridge the gap between short-distance, perturbative QCD and the extensive amount of low- and intermediate-energy phenomenology in a single covariant framework. . . . ”

  44. A Compromise?Dyson-Schwinger Equations Craig Roberts, Physics Division: DSEs for Hadron Physics • 1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.”

  45. A Compromise?Dyson-Schwinger Equations Craig Roberts, Physics Division: DSEs for Hadron Physics • 1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.” C. D. Roberts and A. G. Williams, “Dyson-Schwinger equations and their application to hadronic physics,” Prog. Part. Nucl. Phys. 33, 477 (1994) [arXiv:hep-ph/9403224]. (473 citations)

  46. A Compromise?Dyson-Schwinger Equations Craig Roberts, Physics Division: DSEs for Hadron Physics • 1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.” C. D. Roberts and A. G. Williams, “Dyson-Schwinger equations and their application to hadronic physics,” Prog. Part. Nucl. Phys. 33, 477 (1994) [arXiv:hep-ph/9403224]. (473 citations)

  47. A Compromise?DSEs • Dyson (1949) & Schwinger (1951) . . . One can derive a system of coupled integral equations relating all the Green functions for a theory, one to another. Craig Roberts, Physics Division: DSEs for Hadron Physics

  48. A Compromise?DSEs • Dyson (1949) & Schwinger (1951) . . . One can derive a system of coupled integral equations relating all the Green functions for a theory, one to another. • Gap equation: • fermion self energy • gauge-boson propagator • fermion-gauge-boson vertex Craig Roberts, Physics Division: DSEs for Hadron Physics

  49. A Compromise?DSEs • Dyson (1949) & Schwinger (1951) . . . One can derive a system of coupled integral equations relating all the Green functions for a theory, one to another. • Gap equation: • fermion self energy • gauge-boson propagator • fermion-gauge-boson vertex • These are nonperturbative equivalents in quantum field theory to the Lagrange equations of motion. • Essential in simplifying the general proof of renormalisability of gauge field theories. Craig Roberts, Physics Division: DSEs for Hadron Physics

  50. Dyson-SchwingerEquations Craig Roberts, Physics Division: DSEs for Hadron Physics • Well suited to Relativistic Quantum Field Theory • Simplest level: Generating Tool for Perturbation Theory . . . Materially Reduces Model-Dependence • NonPerturbative, Continuum approach to QCD • Hadrons as Composites of Quarks and Gluons • Qualitative and Quantitative Importance of: • Dynamical Chiral Symmetry Breaking – Generation of fermionmass from nothing • Quark & Gluon Confinement – Coloured objects not detected, not detectable?