Craig Roberts Physics Division

1. Prospects for the physics of cold, sparse hadrons Craig Roberts Physics Division

2. Students Postdocs Asst. Profs. Collaborators: 2011-Present • Adnan BASHIR (U Michoácan); • Stan BRODSKY (SLAC); • Gastão KREIN (São Paulo) • Roy HOLT (ANL); • Mikhail IVANOV (Dubna); • Yu-xin LIU (PKU); • Michael RAMSEY-MUSOLF (UW-Mad) • Alfredo RAYA (U Michoácan); • Sebastian SCHMIDT (IAS-FZJ & JARA); • Robert SHROCK (Stony Brook); • Peter TANDY (KSU); • Tony THOMAS (U.Adelaide) • Shaolong WAN (USTC) Prospects for the physics of cold, sparse hadrons (72p) Rocio BERMUDEZ (U Michoácan); Chen CHEN (ANL, IIT, USTC); Xiomara GUTIERREZ-GUERRERO (U Michoácan); Trang NGUYEN (KSU); Khépani Raya (U Michoácan); Hannes ROBERTS (ANL, FZJ, UBerkeley); Chien-Yeah SENG (UW-Mad) Kun-lun WANG (PKU); J. JavierCOBOS-MARTINEZ (U.Sonora); Mario PITSCHMANN (ANL & UW-Mad); Si-xue QIN(U. Frankfurt am Main); Jorge SEGOVIA (ANL); David WILSON (ODU); Lei CHANG (FZJ); Ian CLOËT (ANL); Bruno EL-BENNICH (São Paulo);

3. Science Challenges for the coming decade: 2013-2022 Prospects for the physics of cold, sparse hadrons (72p) • Exploit opportunities provided by new data on hadron elastic and transition form factors • Chart infrared evolution of QCD’s coupling and dressed-masses • Reveal correlations that are key to nucleon structure • Expose the facts or fallacies in modern descriptions of hadron structure

4. Science Challenges for the coming decade: 2013-2022 Prospects for the physics of cold, sparse hadrons (72p) • Precision experimental study of valence region (Bjorken-x> 0.5), and theoretical computation of distribution functions and distribution amplitudes • Computation is critical, parametrisation is inadequate • Without computation, no amount of data will reveal anything about the theory underlying the phenomena of strong interaction physics

5. Overarching Science Challenges for the coming decade: 2013-2022 Discover meaning of confinement, and its relationship to DCSB – the origin of visible mass Prospects for the physics of cold, sparse hadrons (72p)

6. What is QCD? Prospects for the physics of cold, sparse hadrons (72p)

7. QCD is a Theory (not an effective theory) Prospects for the physics of cold, sparse hadrons (72p) • 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 < 8000 GeV • Increasingly likely 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

8. Contrast: so-called Effective Field Theories Can Cannot • QCD appears valid at all energy scales that have been tested so far: no breakdown below • E ≈ 60000 mπ • Cannot be used to test QCD • Any mismatch between • EF-Theory and experiment owes to an error in the formulation of one or conduct of the other Prospects for the physics of cold, sparse hadrons (72p) EFTs applicable over a very restricted energy domain; e.g., ChPT known to breakdown for E > 2mπ Can be used to help explore how features of QCD influence observables

9. 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 Prospects for the physics of cold, sparse hadrons (72p) • Asymptotically free • Perturbation theory is valid and accurate tool at large-Q2 • Hence chiral limit is defined • Essentiallynonperturbative for Q2 < 2 GeV2

10. What is Confinement? Prospects for the physics of cold, sparse hadrons (72p)

11. Light quarks & Confinement • Folklore … Hall-DConceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes. Prospects for the physics of cold, sparse hadrons (72p) 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.”

12. Light quarks & Confinement Prospects for the physics of cold, sparse hadrons (72p) • Problem: 16 tonnes of force makes a lot of pions.

13. Light quarks & Confinement Prospects for the physics of cold, sparse hadrons (72p) Problem: 16 tonnes of force makes a lot of pions.

14. G. Bali et al., PoS LAT2005 (2006) 308 Light quarks & Confinement Prospects for the physics of cold, sparse hadrons (72p) 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

15. Confinement Confined particle Normal particle complex-P2 complex-P2 timelike axis: P2<0 s ≈ 1/Im(m) ≈ 1/2ΛQCD≈ ½fm • Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities • State described by rapidly damped wave & hence state cannot exist in observable spectrum Prospects for the physics of cold, sparse hadrons (72p) • 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

16. Light quarks & Confinement Prospects for the physics of cold, sparse hadrons (72p) • In the study of hadrons, attention should turn from potential models toward the continuum bound-state problem in quantum field theory • Such approaches offer the possibility of posing simultaneously the questions • What is confinement? • What is dynamical chiral symmetry breaking? • How are they related? Is it possible that two phenomena, so critical in the Standard Model and tied to the dynamical generation of a mass-scale in QCD, can have different origins and fates?

17. Dynamical ChiralSymmetry Breaking Prospects for the physics of cold, sparse hadrons (72p)

18. Dynamical Chiral Symmetry Breaking Prospects for the physics of cold, sparse hadrons (72p) • DCSB is a fact in QCD • Dynamical, not spontaneous • Add nothing to QCD , no Higgs field, nothing! • Effect achieved purely through the quark+gluon dynamics. • It’s the most important mass generating mechanism for visible matter in the Universe. • Responsible for ≈98% of the proton’s mass. • Higgs mechanism is (almost) irrelevant to light-quarks. • Just like gluons and quarks, and for the same reasons, condensates are confined within hadrons. • There are no vacuum condensates.

19. “Orthodox Vacuum” u d u u d u u u d Prospects for the physics of cold, sparse hadrons (72p) Vacuum = “frothing sea” Hadrons = bubbles in that “sea”, containing nothing but quarks & gluons interacting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!

20. Background Prospects for the physics of cold, sparse hadrons (72p) Worth noting that nonzero vacuum expectation values of local operators in QCD—the so-called vacuum condensates—are phenomenological parameters, which were introduced at a time of limited computational resources in order to assist with the theoretical estimation of essentially nonperturbative strong-interaction matrix elements. A universality of these condensates was assumed, namely, that the properties of all hadrons could be expanded in terms of the same condensates. While this helps to retard proliferation, there are nevertheless infinitely many of them. As qualities associated with an unmeasurable state (the vacuum), such condensates do not admit direct measurement. Practitioners have attempted to assign values to them via an internally consistent treatment of many separate empirical observables. However, only one, the so-called quark condensate, is attributed a value with any confidence.

21. Confinement contains condensates Prospects for the physics of cold, sparse hadrons (72p)

22. “Orthodox Vacuum” u d u u d u u u d Prospects for the physics of cold, sparse hadrons (72p) Vacuum = “frothing sea” Hadrons = bubbles in that “sea”, containing nothing but quarks & gluons interacting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!

23. New Paradigm u d u u d u u u d Prospects for the physics of cold, sparse hadrons (72p) Vacuum = hadronic fluctuations but no condensates Hadrons = complex, interacting systems within which perturbativebehaviour is restricted to just 2% of the interior

24. Paradigm shift:In-Hadron Condensates “Void that is truly empty solves dark energy puzzle” Rachel Courtland, New Scientist 4th Sept. 2010 • Cosmological Constant: • Putting QCD condensates back into hadrons reduces the • mismatch between experiment and theory by a factor of 1046 • Possibly by far more, if technicolour-like theories are the correct • paradigm for extending the Standard Model Prospects for the physics of cold, sparse hadrons (72p) “EMPTY space may really be empty. Though quantum theory suggests that a vacuum should be fizzing with particle activity, it turns out that this paradoxical picture of nothingness may not be needed. A calmer view of the vacuum would also help resolve a nagging inconsistency with dark energy, the elusive force thought to be speeding up the expansion of the universe.”

25. Relevant References Prospects for the physics of cold, sparse hadrons (72p) arXiv:1202.2376, Phys. Rev. C 85 (2012) 065202 Confinement contains condensates Stanley J. Brodsky, Craig D. Roberts, Robert Shrock, Peter C. Tandy arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(RapCom), Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. Tandy arXiv:1005.4610 [nucl-th], Phys. Rev. C82 (2010) 022201(RapCom.) New perspectives on the quark condensate, Brodsky, Roberts, Shrock, Tandy arXiv:0905.1151 [hep-th], PNAS 108, 45 (2011) Condensates in Quantum Chromodynamics and the Cosmological Constant, Brodsky and Shrock, hep-th/0012253 The Quantum vacuum and the cosmological constant problem, Svend Erik Rugh and HenrikZinkernagel.

26. DCSB C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227 • In QCD, all “constants” of quantum mechanics are actually strongly momentum dependent: couplings, number density, mass, etc. • So, a quark’s mass depends on its momentum. • Mass function can be calculated and is depicted here. • Continuum- and Lattice-QCD Mass from nothing! • are in agreement: the vast bulk of the light-quark mass comes from a cloud of gluons, dragged along by the quark as it propagates. Prospects for the physics of cold, sparse hadrons (72p)

27. Enigma of Mass Prospects for the physics of cold, sparse hadrons (72p)

28. Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273  Pion’s Goldberger-Treiman relation Pseudovector components necessarily nonzero. Cannot be ignored! Miracle: two body problem solved, almost completely, once solution of one body problem is known Exact in Chiral QCD Prospects for the physics of cold, sparse hadrons (72p) • Pion’s Bethe-Salpeter amplitude Solution of the Bethe-Salpeter equation • Dressed-quark propagator • Axial-vector Ward-Takahashi identity entails

29. Dichotomy of the pionGoldstone mode and bound-state fπ Eπ(p2) = B(p2) Prospects for the physics of cold, sparse hadrons (72p) • Goldstone’s theorem has a pointwise expression in QCD; Namely, in the chiral limit the wave-function for the two-body bound-state Goldstone mode is intimately connected with, and almost completely specified by, the fully-dressed one-body propagator of its characteristic constituent • The one-body momentum is equated with the relative momentum of the two-body system

30. Enigma of mass fπ Eπ(p2) = B(p2) Prospects for the physics of cold, sparse hadrons (72p) • The quark level Goldberger-Treiman relation shows that DCSB has a very deep and far reaching impact on physics within the strong interaction sector of the Standard Model; viz., Goldstone's theorem is fundamentally an expression of equivalence between the one-body problem and the two-body problem in the pseudoscalar channel.  • This emphasises that Goldstone's theorem has a pointwise expression in QCD • Hence, pion properties are an almost direct measure of the dressed-quark mass function.  • Thus, enigmatically, the properties of the masslesspion are the cleanest expression of the mechanism that is responsible for almost all the visible mass in the universe.

31. In QCD, Gluons, too, become massive Prospects for the physics of cold, sparse hadrons (72p) Not just quarks … Gluons also have a gap equation … 1/k2behaviour signals essential singularity in the running coupling: Impossible to reach in perturbation theory

32. Valence quarks Parton structure of hadrons Prospects for the physics of cold, sparse hadrons (72p)

33. Deep inelastic scattering Probability that a quark/gluon within the target will carry a fraction x of the bound-state’s light-front momentum Distribution Functions of the Nucleon and Pion in the Valence Region, Roy J. Holt and Craig D. Roberts, arXiv:1002.4666 [nucl-th], Rev. Mod. Phys. 82 (2010) pp. 2991-3044 Prospects for the physics of cold, sparse hadrons (72p) • Quark discovery experiment at SLAC (1966-1978, Nobel Prize in 1990) • Completely different to elastic scattering • Blow the target to pieces instead of keeping only those events where it remains intact. • Cross-section is interpreted as a measurement of the momentum-fraction probability distribution for quarks and gluons within the target hadron: q(x), g(x)

34. Parton Structure of Hadrons Prospects for the physics of cold, sparse hadrons (72p) • Valence-quark structure of hadrons • Definitive of a hadron – it’s how we tell a proton from a neutron • Expresses charge; flavour; baryon number; and other Poincaré-invariant macroscopic quantum numbers • Via evolution, determines background at LHC • Sea-quark distributions • Flavour content, asymmetry, intrinsic: yes or no? • Any nontrivial answers are essentially nonperturbative features of QCD

35. Parton Structure of Hadrons Prospects for the physics of cold, sparse hadrons (72p) • Light front provides a link with quantum mechanics • If a probability interpretation is ever valid, then it’s in the infinite-momentum frame • Enormous amount of intuitively expressive information about hadrons & processes involving them is encoded in • Parton distribution functions • Generalisedparton distribution functions • Transverse-momentum-dependent parton distribution functions • Information will be revealed by the measurement of these functions – so long as they can be calculated Success of programme demands very close collaboration between experiment and theory

36. Parton Structure of Hadrons Prospects for the physics of cold, sparse hadrons (72p) • Need for calculation is emphasised by Saga of pion’s valence-quark distribution: • 1989: uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD; • 2001: DSE- QCD predicts uvπ ~ (1-x)2 argues that distribution inferred from data can’t be correct;

37. Parton Structure of Hadrons Prospects for the physics of cold, sparse hadrons (72p) • Need for calculation is emphasised by Saga of pion’s valence-quark distribution: • 1989: uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD; • 2001: DSE- QCD predicts uvπ ~ (1-x)2 argues that distribution inferred from data can’t be correct; • 2010: NLO reanalysis including soft-gluon resummation, inferred distribution agrees with DSE and QCD

38. Pion’s valence-quark Distribution Amplitude Pion’s Bethe-Salpeter wave function Whenever a nonrelativistic limit is realistic, this would correspond to the Schroedinger wave function. Prospects for the physics of cold, sparse hadrons (72p) Exact expression in QCD for the pion’s valence-quark parton distribution amplitude Expression is Poincaré invariant but a probability interpretation is only valid in the light-front frame because only therein does one have particle-number conservation. Probability that a valence-quark or antiquark carries a fraction x=k+ / P+ of the pion’s light-front momentum { n2=0, n.P = -mπ}

39. Pion’s valence-quark Distribution Amplitude Pion’s Bethe-Salpeter wave function Prospects for the physics of cold, sparse hadrons (72p) Moments method is ideal for φπ(x): entails Contact interaction (1/k2)ν , ν=0 Straightforward exercise to show ∫01 dxxmφπ(x) = fπ1/(1+m) , hence φπ(x)= fπ Θ(x)Θ(1-x)

40. Pion’s valence-quark Distribution Amplitude Prospects for the physics of cold, sparse hadrons (72p) The distribution amplitude φπ(x) is actually dependent on the momentum-scale at which a particular interaction takes place; viz., φπ(x)= φπ(x,Q) One may show in general that φπ(x) has an expansion in terms of Gegenbauer–α=3/2 polynomials: Only even terms contribute because the neutral pion is an eigenstate of charge conjugation, so φπ(x)=φπ(1-x) Evolution, analogous to that of the parton distribution functions, is encoded in the coefficients an(Q)

41. Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude Prospects for the physics of cold, sparse hadrons (72p) • However, practically, in reconstructing φπ(x) from its moments, it is better to use Gegenbauer–α polynomials and then rebuild the Gegenbauer–α=3/2 expansion from that. • Better means – far more rapid convergence because Gegenbauer–α=3/2 is only accurate near ΛQCD/Q=0. • One nontrivial Gegenbauer–α polynomial provides converged reconstruction cf. more than SEVEN Gegenbauer–α=3/2 polynomials • Results have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available. • xα (1-x)α, with α=0.3

42. Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude • This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB. • Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result Asymptotic φπ(x)=6 x (1-x) DB RL Prospects for the physics of cold, sparse hadrons (72p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB

43. Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude These computations are the first to directly expose DCSB – pointwise – on the light-front; i.e., in the infinite momentum frame. • This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB. • Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result Asymptotic DB RL Prospects for the physics of cold, sparse hadrons (72p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB

44. Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 Dilation of pion’s wave function is measurable in pion’s electromagnetic form factor at JLab12 A-rated:E12-06-10 • Established a one-to-one connection between DCSB and the pointwise form of the pion’s wave function. • Dilation measures the rate at which dressed-quark approaches the asymptotic bare-parton limit • Experiments at JLab12 can empirically verify the behaviour of M(p), and hence chart the IR limit of QCD Prospects for the physics of cold, sparse hadrons (72p)

45. Pion distribution amplitude from lattice-QCD, I.C. Cloëtet al. arXiv:1306.2645 [nucl-th] Lattice comparisonPion’s valence-quark PDA V. Braun et al., PRD 74 (2006) 074501 • Lattice-QCD • => one nontrivial moment: • <(2x-1)2> = 0.27 ± 0.04 • Legend • Solid = DB (Best) DSE • Dashed = RL DSE • Dotted (black) = 6 x (1-x) • Dot-dashed = midpoint lattice; and the yellow shading exhibits band allowed by lattice errors • DBα=0.31 but 10% a2<0 • RL α=0.29 and 0% a2 φπ~ xα (1-x)α α=0.35 +0.32 = 0.67 - 0.24 = 0.11 Prospects for the physics of cold, sparse hadrons (72p) Employ the generalised-Gegenbauer method described previously (and in Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]).

46. Pion distribution amplitude from lattice-QCD, I.C. Cloëtet al. arXiv:1306.2645 [nucl-th] Lattice comparisonPion’s valence-quark PDA Prospects for the physics of cold, sparse hadrons (72p) • Establishes that contemporary DSE- and lattice-QCD computations, at the same scale, agree on the pointwise form of the pion's PDA, φπ(x). • This unification of DSE- and lattice-QCD results expresses a deeper equivalence between them, expressed, in particular, via the common behaviour they predict for the dressed-quark mass-function, which is both • a definitive signature of dynamical chiral symmetry breaking • and the origin of the distribution amplitude's dilation.

47. Pion distribution amplitude from lattice-QCD, I.C. Cloëtet al. arXiv:1306.2645 [nucl-th] When is asymptotic PDA valid? asymptotic 4 GeV2 100 GeV2 • Consequently, the asymptotic distribution, • φπasy(x), is a poor approximation to the pion's PDA • at all such scales that are either currently accessible or • foreseeable in experiments on pion elastic and transition form factors. • Thus, related expectations based on φπasy(x) should be revised. Prospects for the physics of cold, sparse hadrons (72p) Under leading-order evolution, the PDA remains broad to Q2>100 GeV2 Feature signals persistence of the influence of dynamical chiral symmetry breaking.

48. Pion distribution amplitude from lattice-QCD, I.C. Cloëtet al. arXiv:1306.2645 [nucl-th] When is asymptotic PDA valid? Q2=27 GeV2 This is not δ(x)! Prospects for the physics of cold, sparse hadrons (72p) φπasy(x) can only be a good approximation to the pion's PDA when it is accurate to write uvπ (x) ≈ δ(x) for the pion's valence-quark distribution function. This is far from valid at currently accessible scales

49. ElasticScattering Prospects for the physics of cold, sparse hadrons (72p)

50. Pion electromagnetic form factor at spacelikemomentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th] Charged pionelastic form factor • P. Maris & P.C. Tandy,Phys.Rev. C62 (2000) 055204: numerical procedure is practically useless for Q2>4GeV2, so prediction ends! • Algorithm developed for pion PDA overcomes this obstacle • Solves the practical problem of continuing from Euclidean metric formulation to Minkowski space Prospects for the physics of cold, sparse hadrons (72p)