Craig Roberts Physics Division

1. Calories for Quarks Craig Roberts Physics Division

2. Origin of Mass • I will explain this remarkable emergent phenomenon, contained in Nambu's share of the 2008 Nobel Prize, and discuss its connection with the peculiar feature of confinement in QCD; viz., the fact that quarks are forever imprisoned, never reaching the freedom of a particle detector. I will also describe why confinement guarantees that condensates, quantities that were once commonly viewed as constant mass-scales that fill all spacetime, are instead wholly contained within hadrons; and show how contemporary and future terrestrial experiments can help complete the book on the Standard Model Craig Roberts: Calories for Quarks: The Origin of Mass The 2013 Nobel Prize in Physics was awarded to Higgs and Englert following discovery of the Higgs boson at the Large Hadron Collider.  The Higgs boson is often said to give mass to everything.  However, that is wrong.  It only gives mass to some very simple particles, accounting for only one or two percent of the mass of more complex things like atoms, molecules and everyday objects, from your mobile phone to your pet llama.  The vast majority of mass comes from the energy needed to hold quarks together inside nuclei. 

3. Students, Postdocs, Asst. Profs. Collaborators: 2012-Present • Lei Chang (U. Adelaide) • Ian Cloet (ANL) • Bruno El-Bennich(São Paulo); • Adnan BASHIR (U Michoácan); • Stan BRODSKY (SLAC); • Gastão KREIN (São Paulo) • Roy HOLT (ANL); • Yu-xin LIU (PKU); • HervéMoutarde (CEA, Saclay) • Michael RAMSEY-MUSOLF (UM-Amherst) • Alfredo RAYA (U Michoácan); • Jose RodriguezQintero (U. Huelva) • Sebastian SCHMIDT (IAS-FZJ & JARA); • Robert SHROCK (Stony Brook); • Peter TANDY (KSU); • Tony THOMAS (U.Adelaide) • Shaolong WAN (USTC) • Hong-Shi ZONG (Nanjing U) Craig Roberts: Calories for Quarks: The Origin of Mass Rocio BERMUDEZ (U Michoácan); Shi CHAO (Nanjing U) Ming-hui DING (PKU); Fei GAO (PKU) S. HERNÁNDEZ(U Michoácan); Cédric MEZRAG (CEA, Saclay) Trang NGUYEN (KSU); Khépani RAYA (U Michoácan); Hannes ROBERTS (ANL, FZJ, UBerkeley); Chien-Yeah SENG (UM-Amherst) Kun-lun WANG (PKU); Shu-sheng XU (Nanjing U) Chen CHEN (USTC); J. JavierCOBOS-MARTINEZ (U.Sonora); Mario PITSCHMANN (Vienna); Si-xue QIN(U. Frankfurt am Main, PKU); Jorge SEGOVIA (ANL); David WILSON (ODU);

4. Students, Postdocs, Asst. Profs. Collaborators: 2012-Present • Lei Chang (U. Adelaide) • Ian Cloet (ANL) • Bruno El-Bennich(São Paulo); • Adnan BASHIR (U Michoácan); • Stan BRODSKY (SLAC); • Gastão KREIN (São Paulo) • Roy HOLT (ANL); • Yu-xin LIU (PKU); • HervéMoutarde (CEA, Saclay) • Michael RAMSEY-MUSOLF (UW-Mad) • Alfredo RAYA (U Michoácan); • Jose RodriguezQintero (U. Huelva) • Sebastian SCHMIDT (IAS-FZJ & JARA); • Robert SHROCK (Stony Brook); • Peter TANDY (KSU); • Tony THOMAS (U.Adelaide) • Shaolong WAN (USTC) • Hong-Shi ZONG (Nanjing U) Craig Roberts: Calories for Quarks: The Origin of Mass Rocio BERMUDEZ (U Michoácan); Shi CHAO (Nanjing U) Ming-hui DING (PKU); Fei GAO (PKU) S. HERNÁNDEZ(U Michoácan); Cédric MEZRAG (CEA, Saclay) Trang NGUYEN (KSU); Khépani RAYA (U Michoácan); Hannes ROBERTS (ANL, FZJ, UBerkeley); Chien-Yeah SENG (UM-Amherst) Kun-lun WANG (PKU); Shu-sheng XU (Nanjing U) Chen CHEN (USTC); J. JavierCOBOS-MARTINEZ (U.Sonora); Mario PITSCHMANN (Vienna); Si-xue QIN(U. Frankfurt am Main, PKU); Jorge SEGOVIA (ANL); David WILSON (ODU);

5. Standard Model Craig Roberts: Calories for Quarks: The Origin of Mass

6. Standard Model- Formulation Craig Roberts: Calories for Quarks: The Origin of Mass • The Standard Model of Particle Physics is a local gauge field theory, which can be completely expressed in a very compact form • Lagrangian possesses UY(1)xSUL(2)xSUc(3) gauge symmetry • 19 parameters, which must be determined through comparison with experiment • Physics is an empirical science • UY(1)xSUL(2) represents the electroweak theory • 17 of the parameters are here, most of them tied to the Higgs boson, the model’s only fundamental scalar, something like which has now been seen • This sector is essentially perturbative, so the parameters are readily determined • SUc(3) represents the strong interaction component • Just 2 of the parameters are intrinsic to SUc(3) – QCD • However, this is the really interesting sector because it is Nature’s only example of a truly and essentially nonperturbative fundamental theory • Impact of the 2 parameters is not fully known. One might even be zero.

7. Standard Model- Complete? • A number of experimental hints and, almost literally, innumerably many theoretical speculations about other phenomena Craig Roberts: Calories for Quarks: The Origin of Mass • There are certainly phenomena Beyond the Standard Model • Neutrinos have mass, which is not true within the Standard Model • Empirical evidence: νe ↔ νμ, ντ … neutrino flavour is not a constant of motion • The first experiment to detect the effects of neutrino oscillations was Ray Davis' Homestake Experiment in the late 1960s, which observed a deficit in the flux of solar neutrinos νe • Verified and quantified in experiments at the Sudbury Neutrino Observatory

8. Death of Super-String Theory? Craig Roberts: Calories for Quarks: The Origin of Mass

9. Top Open Questions in Physics Craig Roberts: Calories for Quarks: The Origin of Mass

10. Excerpt from the top-10 Craig Roberts: Calories for Quarks: The Origin of Mass • Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap? Quantum chromodynamics is the theory describing the strong nuclear force. Carried by gluons, it binds quarks into particles like protons and neutrons. Apparently, the tiny subparticles are permanently confined: one can't pull a quark or a gluon from a proton because the strong force gets stronger with distance and snaps them right back inside.

11. Quantum Chromodynamics Craig Roberts: Calories for Quarks: The Origin of Mass

12. Quantum Chromodynamics • QCD: The piece of the Standard Model that describes strong interactions. • The physics of neutrons, protons, pions, etc. – i.e., Hadron Physics – is a nonperturbative problem in QCD • Notwithstanding the 2013 Nobel Prize in Physics, the origin of 98% of the visible mass in the Universe is – somehow – found within QCD Craig Roberts: Calories for Quarks: The Origin of Mass

13. Facilities Craig Roberts: Calories for Quarks: The Origin of Mass

14. FacilitiesQCD Machines Craig Roberts: Calories for Quarks: The Origin of Mass • China • Beijing Electron-Positron Collider • Germany • COSY (Jülich Cooler Synchrotron) • ELSA (Bonn Electron Stretcher and Accelerator) • MAMI (Mainz Microtron) • Facility for Antiproton and Ion Research, under construction near Darmstadt. New generation experiments in 2018 (perhaps) • Japan • J-PARC (Japan Proton Accelerator Research Complex), under construction in Tokai-Mura, 150km NE of Tokyo. New generation experiments to begin soon • KEK: Tsukuba, Belle Collaboration • Switzerland (CERN) • Large Hadron Collider: ALICE Detector and COMPASS Detector “Understanding deconfinement and chiral-symmetry restoration”

15. FacilitiesQCD Machines A three dimensional view of the calculated particle paths resulting from collisions occurring within RHIC's STAR detector Craig Roberts: Calories for Quarks: The Origin of Mass • USA • Thomas Jefferson National Accelerator Facility, Newport News, Virginia Nature of cold hadronic matter Upgrade underway Construction cost ≈ $370-million New generation experiments in 2015 • Relativistic Heavy Ion Collider, Brookhaven National Laboratory, Long Island, New York Strong phase transition, 10μs after Big Bang

16. Jefferson Lab Craig Roberts: Calories for Quarks: The Origin of Mass

17. Thomas Jefferson National Accelerator Facility (JLab) Craig Roberts: Calories for Quarks: The Origin of Mass Driving distance: Washington DC to JLab ≈ 270km

18. Thomas Jefferson National Accelerator Facility (JLab) Craig Roberts: Calories for Quarks: The Origin of Mass 1984 … DoE provided initial funding for research, development and design 1987 … Construction began on Continuous Electron Beam Accelerator Facility (CEBAF) - February 13 1994 … Accelerator reached design energy of 4 GeV Construction cost in $FY14 ≈ $1-Billion Goal … Write the book about the strongest force in nature – the force that holds nuclei together – and determine how that force can be explained in terms of the quarks and gluons of quantum chromodynamics (QCD).

19. Thomas Jefferson National Accelerator Facility (JLab) e.g. S. J. Brodsky and G. R. Farrar, Phys. Rev. Lett. 31, 1153 (1973) QCD scaling violations Parton model scaling Craig Roberts: Calories for Quarks: The Origin of Mass One of the primary reasons for building CEBAF/JLab Prediction: at energy-scales greater than some a priori unknown minimum value, Λ, cross-sections and form factors will behave as power = ( number valence-quarks– 1 +Δλ) Δλ=0,1, depending on whether helicity is conserved or flipped … prediction of 1/k2 vector-boson exchange logarithm = distinctive feature & concrete prediction of QCD Claims were made that Λ = 1GeV! So, JLab was initially built to reach 4GeV.

20. Thomas Jefferson National Accelerator Facility (JLab) Particle physics paradigm Particle physics paradigm Craig Roberts: Calories for Quarks: The Origin of Mass • 1994 – 2004 • An enormous number of fascinating experimental results • Including an empirical demonstration that the distribution of charge and magnetisation within the proton are completely different, • Suggesting that quark-quark correlations play a crucial role in nucleon structure • But no sign of parton model scaling and certainly not of scaling violations

21. Thomas Jefferson National Accelerator Facility (JLab) Craig Roberts: Calories for Quarks: The Origin of Mass 2004 … Mission Need Agreed on upgrade of CEBAF (JLab's accelerator) to 12GeV 2014 … 12GeV commissioning beams now being delivered to the experimental halls Final cost of upgrade is approximately $370-Million Physics of JLab at 12GeV arXiv:1208.1244 [hep-ex]

22. What is QCD? Craig Roberts: Calories for Quarks: The Origin of Mass

23. QCD is a Theory (not an effective theory) • wikipedia.org/wiki/Technicolor_(physics) Craig Roberts: Calories for Quarks: The Origin of Mass • Very likely a self-contained, nonperturbativelyrenormalisable and hence well defined Quantum Field Theory This is not true of QED – cannot be defined nonperturbatively • No confirmed breakdown over an enormous energy domain: 0 GeV < E < 8 TeV • Increasingly probable that any extension of the Standard Model will be based on the paradigm established by QCD • Extended Technicolour: electroweak symmetry breaks via a fermion bilinear operator in a strongly-interacting non-Abelian theory. (Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81) • Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg-Landau theory of superconductivity

24. What is QCD? Craig Roberts: Calories for Quarks: The Origin of Mass • Lagrangian of QCD • G = gluon fields • Ψ = quark fields • The key to complexity in QCD … gluon field strength tensor • Generates gluon self-interactions, whose consequences are extraordinary

25. cf.Quantum Electrodynamics Craig Roberts: Calories for Quarks: The Origin of Mass QED is the archetypal gauge field theory Perturbatively simple but nonperturbatively undefined Chracteristic feature: Light-by-light scattering; i.e., photon-photon interaction – leading-order contribution takes place at order α4. Extremely small probability because α4 ≈10-9 !

26. What is QCD? • Relativistic Quantum Gauge Field Theory: • Interactions mediated by vector boson exchange • Vector bosons are perturbatively-massless • Similar interaction in QED • Special feature of QCD – gluon self-interactions 3-gluon vertex 4-gluon vertex Craig Roberts: Calories for Quarks: The Origin of Mass

27. Running couplings Craig Roberts: Calories for Quarks: The Origin of Mass • Quantum gauge-field theories are all typified by the feature that Nothing is Constant • Distribution of charge and mass, the number of particles, etc., indeed, all the things that quantum mechanics holds fixed, depend upon the wavelength of the tool used to measure them • particle number is generally not conserved in quantum field theory • Couplings and masses are renormalised via processes involving virtual-particles. Such effects make these quantities depend on the energy scale at which one observes them

28. QED cf. QCD? 500% 5 x10-5=0.7% Add 3-gluon self-interaction gluon antiscreening fermion screening Craig Roberts: Calories for Quarks: The Origin of Mass • 2004 Nobel Prize in Physics : Gross, Politzer and Wilczek

29. Strong-interaction: QCD • Nature’sonly (now known) example of a truly nonperturbative, fundamental theory • A-priori, no idea as to what such a theory • can produce Craig Roberts: Calories for Quarks: The Origin of Mass • Asymptotically free • Perturbation theory is valid and accurate tool at large-Q2 • Hence chiral limit is defined • Essentiallynonperturbative for Q2 < 2 GeV2

30. Millennium prize of $1,000,000 for proving that SUc(3) gauge theory is mathematically well-defined, which will necessarily prove or disprove the confinement conjecture Confinement? Craig Roberts: Calories for Quarks: The Origin of Mass

31. What is Confinement? Craig Roberts: Calories for Quarks: The Origin of Mass

32. Wilson Loop & the Area Law τ z Linear potential σ = String tension Craig Roberts: Calories for Quarks: The Origin of Mass C is a closed curve in space,   P is the path order operator Now, place static (infinitely heavy) fermionic sources of any charge at positions z0=0 & z=½L Then, evaluate <WC(z, τ)> as a functional integral over gauge-field configurations In the strong-coupling limit, the result can be obtained algebraically; viz., <WC(z, τ)> = exp(-V(z) τ ) where V(z) is the potential between the static sources, which behaves as V(z) = σ z

33. Light quarks & Confinement • Folklore … JLab Hall-DConceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes. Craig Roberts: Calories for Quarks: The Origin of Mass A unit area placed midway between the quarks and perpendicular to the line connecting them intercepts a constant number of field lines, independent of the distance between the quarks. This leads to a constant force between the quarks – and a large force at that, equal to about 16 metric tons.”

34. Light quarks & Confinement Craig Roberts: Calories for Quarks: The Origin of Mass • Problem: Pions They’re extremely light 16 tonnes of force makes a lot of them.

35. Light quarks & Confinement Craig Roberts: Calories for Quarks: The Origin of Mass Problem: 16 tonnes of force makes a lot of pions.

36. G. Bali et al., PoS LAT2005 (2006) 308 Light quarks & Confinement Craig Roberts: Calories for Quarks: The Origin of Mass In the presence of light quarks, pair creation seems to occur non-localized and instantaneously No flux tube in a theory with light-quarks. Flux-tube is not the correct paradigm for confinement in hadron physics

37. Confinement Confined particle Normal particle State described by rapidly damped wave & hence state cannot exist in observable spectrum σ ≈ 1/Im(m) ≈ 1/2ΛQCD≈ ½fm Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or qualitatively analogous structures chracterised by a dynamically generated mass-scale) Craig Roberts: Calories for Quarks: The Origin of Mass • QFT Paradigm: • Confinement is expressed through a dramatic change in the analytic structure of propagators for coloured states • It can almost be read from a plot of the dressed-propagator for a coloured state

38. Plane wave propagation meson meson meson Baryon meson Craig Roberts: Calories for Quarks: The Origin of Mass Feynman propagator for a fermion describes a Plane Wave A fermion begins to propagate It can proceed a long way before undergoing any qualitative changes

39. Quark Fragmentation meson meson meson Baryon meson Confinement is a dynamical phenomenon! σ Craig Roberts: Calories for Quarks: The Origin of Mass A quark begins to propagate But after each “step” of length σ, on average, an interaction occurs, so that the quark loses its identity, sharing it with other partons Finally, a cloud of partons is produced, which coalesces into colour-singlet final states

40. QCD Craig Roberts: Calories for Quarks: The Origin of Mass Remarkably simple Lagrangian density

41. Massless QCD 0 Craig Roberts: Calories for Quarks: The Origin of Mass Remarkably simple Lagrangian density Classically, the massless theory does not possess a mass-scale The theory is “conformally invariant” Everything is massless: gluons and quarks. There are no bound states (no length-scale to define a size) This is not our Universe

42. Massless QCD 0 Craig Roberts: Calories for Quarks: The Origin of Mass Remarkably simple Lagrangian density Define the quantum field theory via a Functional Integral, which generalises the Feynman path integral for quantum mechanics. How does that help?

43. Spontaneous(Dynamical)Chiral Symmetry Breaking Craig Roberts: Calories for Quarks: The Origin of Mass The 2008Nobel Prize in Physics was divided, one half awarded to YoichiroNambu "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"

44. Nambu – Jona-LasinioModel Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961) 345–358 Dynamical Model Of Elementary Particles Based On An Analogy With Superconductivity. II Y. Nambu, G. Jona-Lasinio, Phys.Rev. 124 (1961) 246-254 Craig Roberts: Calories for Quarks: The Origin of Mass • Treats a massless (chirally-invariant) four-fermionLagrangian & solves the gap equation in Hartree-Fock approximation (analogous to rainbow truncation)

45. Chiral Symmetry Craig Roberts: Calories for Quarks: The Origin of Mass • Interacting gauge theories, in which it makes sense to speak of massless fermions, have a nonperturbativechiral symmetry • A related concept is Helicity, which is the projection of a particle’s spin, J, onto it’s direction of motion: • For a massless particle, helicity is a Lorentz-invariant spin-observable λ = ±; i.e., it’s parallel or antiparallel to the direction of motion • Obvious: • massless particles travel at speed of light • hence no observer can overtake the particle and thereby view its momentum as having changed sign

46. Gap Equation Craig Roberts: Calories for Quarks: The Origin of Mass

47. Nambu—Jona-Lasinio Model Free fermion piece Interactions Craig Roberts: Calories for Quarks: The Origin of Mass Gap equation NJL gap equation

48. Critical coupling for dynamical mass generation? NJL model& a mass gap? Craig Roberts: Calories for Quarks: The Origin of Mass • Some algebra ⇒ NJL gap equation is an equation for fermion mass • Chiral limit, m=0 • Clearly, one solution is M=0. • That is the solution in perturbation theory … Start with no mass, end-up with no mass. • Suppose, on the other hand, that M ≠ 0 so that it can be cancelled • This nontrivial solution can exist if-and-only-if one can satisfy 3π2 mG2 = C(M2,1)

49. Critical coupling for dynamical mass generation! NJL model& a mass gap? mG=0.17GeV mG=0.21GeV Dynamical Chiral Symmetry Breaking Craig Roberts: Calories for Quarks: The Origin of Mass • Can one satisfy 3π2 mG2 = C(M2,1) ? • C(M2, 1) = 1 − M2ln [ 1 + 1/M2 ] • Monotonically decreasing function of M • Maximum value at M = 0; viz., C(M2=0, 1) = 1 • Consequently, there is a solution iff3π2 mG2 < 1 • Typical scale for hadron physics: Λ = 1GeV • There is a M≠0 solution iffmG2 < (Λ/(3 π2)) = (0.2 GeV)2 • Interaction strength is proportional to 1/mG2 • Hence, if interaction is strong enough, then one can start with no mass but end up with a massive, perhaps very massive fermion

50. Impact Craig Roberts: Calories for Quarks: The Origin of Mass Appears fairly simple, perhaps, but these two papers have had an enormous impact Together, cited more than 5950 times Google Scholar returns ≈ 9820 items for the term “Nambu – Jona-Lasinio” Defined the paradigm for dynamical chiral symmetry breaking