# Published collaborations 2010 present Rocio BERMUDEZ U Michocan

- Slides: 63

Published collaborations: 2010 -present Rocio BERMUDEZ (U Michoácan); Craig Roberts Physics Division Chen CHEN (ANL, IIT, USTC); Xiomara GUTIERREZ-GUERRERO (U Michoácan); Trang NGUYEN (KSU); Si-xue QIN (PKU); Hannes ROBERTS (ANL, FZJ, UBerkeley); Lei CHANG (ANL, FZJ, PKU); Students Huan CHEN (BIHEP); Early-career Ian CLOËT (UAdelaide); scientists Bruno EL-BENNICH (São Paulo); David WILSON (ANL); Adnan BASHIR (U Michoácan); Stan BRODSKY (SLAC); Gastão KREIN (São Paulo) Roy HOLT (ANL); Mikhail IVANOV (Dubna); Yu-xin LIU (PKU); Robert SHROCK (Stony Brook); Peter TANDY (KSU) Shaolong WAN (USTC)

Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 2

X Confinement Ø Gluon and Quark Confinement – Empirical Fact: No coloured states have yet been observed to reach a detector Ø However – There is no agreed, theoretical definition of light-quark confinement – Static-quark confinement is irrelevant to real-world QCD • There are no long-lived, very-massive quarks • But light-quarks are ubiquitous Ø Flux tubes, linear potentials and string tensions play no role in relativistic quantum field theory with light degrees of freedom. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 3

1993: "for elucidating the quantum structure of electroweak interactions in physics" Regge Trajectories? Ø Martinus Veltmann, “Facts and Mysteries in Elementary Particle Physics” (World Scientific, Singapore, 2003): In time the Regge trajectories thus became the cradle of string theory. Nowadays the Regge trajectories have largely disappeared, not in the least because these higher spin bound states are hard to find experimentally. At the peak of the Regge fashion (around 1970) theoretical physics produced many papers containing families of Regge trajectories, with the various (hypothetically straight) lines based on one or two points only! Phys. Rev. D 62 (2000) 016006 [9 pages] Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 4

Confinement Ø QFT Paradigm: Confinement is expressed through a dramatic change in the analytic structure of propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator – Gribov (1978); Munczek (1983); Stingl (1984); Cahill (1989); Roberts, Williams & Krein (1992); Tandy (1994); … Confined particle Normal particle complex-P 2 timelike axis: P 2<0 o Real-axis mass-pole splits, moving into pair(s) of complex conjugate poles or branch points, or more complicated nonanalyticities … o Spectral density no longer positive semidefinite Craig Roberts: N & N* Structure in Continuum Strong QCD & hence state cannot exist in observable spectrum 15. 08. 12: USC Summer Academy - 56 5

Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 6

Dynamical Chiral Symmetry Breaking ØWhilst confinement is contentious … ØDCSB is a fact in QCD – It is the most important mass generating mechanism for visible matter in the Universe. • Responsible for approximately 98% of the proton’s mass. • Higgs mechanism is (almost) irrelevant to lightquarks. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 7

Frontiers of Nuclear Science: Theoretical Advances C. D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P. C. Tandy, AIP Conf. Proc. 842 (2006) 225 -227 In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies. Mass from nothing! DSE prediction of DCSB confirmed Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 8

Frontiers of Nuclear Science: Theoretical Advances C. D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P. C. Tandy, AIP Conf. Proc. 842 (2006) 225 -227 In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies. Hint of lattice-QCD support for DSE prediction of violation of reflection positivity Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 9

12 Ge. V The Future of JLab Ø Jlab 12 Ge. V: This region scanned by 2<Q 2<9 Ge. V 2 elastic & transition form factors. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 10

K or π The Future of Drell-Yan N Ø Valence-quark PDFs and PDAs probe this critical and complementary region Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 11

Ø Search for exotic hadrons Ø Exploit opportunities provided by new data on nucleon elastic and transition form factors Ø Precision experimental study of valence region, and theoretical computation of distribution functions and distribution amplitudes Ø Develop QCD as a probe for physics beyond the Standard Model Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 12

Discover meaning of confinement, and its relationship to DCSB – the origin of visible mass Ø Search for exotic hadrons Ø Exploit opportunities provided by new data on nucleon elastic and transition form factors Ø Precision experimental study of valence region, and theoretical computation of distribution functions and distribution amplitudes Ø Develop QCD as a probe for physics beyond the Standard Model Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 13

Charting the interaction between light-quarks Process-independent αS(Q 2) This is a well-posed problem whose solution is → unified description of observables an elemental goal of modern hadron physics. The answer provides QCD’s running coupling. Ø Confinement can be related to the analytic properties of QCD's Schwinger functions. Ø Question of light-quark confinement is thereby translated into the challenge of charting the infrared behavior of QCD's universal β-function Ø Through QCD's DSEs, the pointwise behaviour of the β-function determines the pattern of chiral symmetry breaking. Ø DSEs connect β-function to experimental observables. Hence, comparison between computations and observations of o Hadron spectrum, Elastic & transition form factors, Parton distribution fns can be used to chart β-function’s long-range behaviour. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 14

Dichotomy of the pion Goldstone mode fπ Eπ(p 2) = B(p 2) and bound-state Ø Goldstone’s theorem has a pointwise expression in QCD; Namely, in the chiral limit the wave-function for the twobody 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 Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 15

Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 16

Empirical status of the Pion’s valence-quark distributions Pion Ø Owing to absence of pion targets, the pion’s valence-quark distribution functions are measured via the Drell-Yan process: π p → μ+ μ− X Ø Three experiments: CERN (1983 & 1985) and FNAL (1989). No more recent experiments because theory couldn’t even explain these! Ø Problem Conway et al. Phys. Rev. D 39, 92 (1989) Wijesooriya et al. Phys. Rev. C 72 (2005) 065203 PDF behaviour at large-x inconsistent with p. QCD; viz, expt. (1 -x)1+ε cf. QCD (1 -x)2+γ Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 17

Models of the Pion’s valence-quark distributions Pion Ø (1−x)β with β=0 (i. e. , a constant – any fraction is equally probable! ) – Ad. S/QCD models using light-front holography – Nambu–Jona-Lasinio models, when a translationally invariant regularization is used Ø (1−x)β with β=1 – Nambu–Jona-Lasinio NJL models with a hard cutoff – Duality arguments produced by some theorists Ø (1−x)β with 0<β<2 – Relativistic constituent-quark models, with power-law depending on the form of model wave function Ø (1−x)β with 1<β<2 – Instanton-based models, all of which have incorrect large-k 2 behaviour Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 18

Models of the Pion’s valence-quark distributions Pion Ø (1−x)β with β=0 (i. e. , a constant – any fraction is equally probable! ) Completely unsatisfactory. Ø Impossible (1−x) with β=1 to suggest that there’s even qualitative Ø (1−x) with 0<β<2 agreement! – Ad. S/QCD models using light-front holography – Nambu–Jona-Lasinio models, when a translationally invariant regularization is used β – Nambu–Jona-Lasinio NJL models with a hard cutoff – Duality arguments produced by some theorists β – Relativistic constituent-quark models, depending on the form of model wave function Ø (1−x)β with 1<β<2 – Instanton-based models Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 19

DSE prediction of the Pion’s valence-quark distributions Pion Ø Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k 2>>m. G 2 behaviour is (1/k 2)β, Ø Then at a resolving scale Q 0 uπ(x; Q 0) ~ (1 -x)2β namely, the large-x behaviour of the quark distribution function is a direct measure of the momentum-dependence of the underlying interaction. Ø In QCD, β=1 and hence QCD u 2 (x; Q ) ~ (1 -x) π 0 Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 20

DSE prediciton of the Pion’s valence-quark distributions Pion Completely unambigous! Direct connection between u (x; Q ) ~ (1 -x) namely, the large-x behaviour of the quark distribution experiment and theory, function is a direct measure of the momentum-dependence of the underlying interaction. empowering both as tools Ø In QCD, β=1 and hence u (x; Q ) ~ (1 -x) of discovery. Ø Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k 2>m. G 2 behaviour is (1/k 2)β, Ø Then at a resolving scale Q 0 π QCD 2β 0 π 0 2 Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 21

Essentially nonperturbative domain Pion “Model Scale” Ø At what scale Q 0 should the prediction be valid? Ø Hitherto, PDF analyses within models have used the resolving scale Q 0 as a parameter, to be chosen by requiring agreement between the model and lowmoments of the PDF that are determined empirically. Ø Modern DSE studies have exposed a natural value for the model scale; viz. , the gluon mass Q 0 ≈ m. G ≈ 0. 6 Ge. V ≈ 1/0. 33 fm which is the location of the inflexion point in the chiral-limit dressed-quark mass function Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 22

Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 23

Hecht, Roberts, Schmidt Phys. Rev. C 63 (2001) 025213 Reanalysis of qvπ(x) Ø After first DSE computation, the “Conway et al. ” data were reanalysed, this time at next-to-leading-order (Wijesooriya et al. Phys. Rev. C 72 (2005) 065203) Ø The new analysis produced a much larger exponent than initially obtained; viz. , β=1. 87, but now it disagreed equally with model results and the DSE prediction ü NB. Within p. QCD, one can readily understand why adding a higher-order correction leads to a suppression of qvπ(x) at large-x. Ø New experiments were proposed … for accelerators that do not yet exist but the situation remained otherwise unchanged Ø Until the publication of Distribution Functions of the Nucleon and Pion in the Valence Region, Roy J. Holt and Craig D. Roberts, ar. Xiv: 1002. 4666 [nucl-th], Rev. Mod. Phys. 82 (2010) pp. 2991 -3044 Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 24

Distribution Functions of the Nucleon and Pion in the Valence Region, Roy J. Holt and Craig D. Roberts, ar. Xiv: 1002. 4666 [nucl-th], Rev. Mod. Phys. 82 (2010) pp. 2991 -3044 Reanalysis of qvπ(x) Ø This article emphasised and explained the importance of the persistent discrepancy between the DSE result and experiment as a challenge to QCD Ø It prompted another reanalysis of the data, which accounted for a long-overlooked effect: viz. , “soft-gluon resummation, ” – Compared to previous analyses, we include next-to-leading-logarithmic threshold resummation effects in the calculation of the Drell-Yan cross section. As a result of these, we find a considerably softer valence distribution at high momentum fractions x than obtained in previous next-to-leading-order analyses, in line with expectations based on perturbative-QCD counting rules or Dyson-Schwinger equations. Craig Roberts: N & N* Structure in Continuum Strong QCD Aicher, Schäfer, Vogelsang, “Soft-Gluon Resummation and the Valence Parton Distribution Function of the Pion, ” Phys. Rev. Lett. 105 (2010) 252003 15. 08. 12: USC Summer Academy - 56 25

Trang, Bashir, Roberts & Tandy, “Pion and kaon valencequark parton distribution functions, ” ar. Xiv: 1102. 2448 [nucl-th], Phys. Rev. C 83, 062201(R) (2011) [5 pages] Ø Data as reported by. E 615 Ø DSE prediction (2001) Current status of qvπ(x) Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 26

Trang, Bashir, Roberts & Tandy, “Pion and kaon valencequark parton distribution functions, ” ar. Xiv: 1102. 2448 [nucl-th], Phys. Rev. C 83, 062201(R) (2011) [5 pages] Ø Data after inclusion of soft-gluon resummation Ø DSE prediction and modern representation of the data are indistinguishable on the valence-quark domain Ø Emphasises the value of using a single internallyconsistent, wellconstrained framework to correlate and unify the description of hadron observables Current status of qvπ(x) Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 27

Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 28

Expression exact in QCD – no corrections Pion’s valence-quark Distribution Amplitude Ø Reconstruct φπ(x) from moments: entails Pion’s Bethe-Salpeter wave function Ø Contact interaction (1/k 2)ν , ν=0 Straightforward exercise to show ∫ 01 dx xm φπ(x) = fπ 1/(1+m) , hence φπ(x)= fπ Θ(x)Θ(1 -x) Craig Roberts: N & N* Structure in Continuum Strong QCD Work now underway with sophisticated rainbow-ladder interaction: Chang, Cloët, Roberts, Schmidt & Tandy 15. 08. 12: USC Summer Academy - 56 29

Ø Using simple parametrisations of solutions to the gap and Bethe-Salpeter equations, rapid and semiquantitatively reliable estimates can be made for φπ(x) Pion’s valence-quark Distribution Amplitude Leading p. QCD φπ(x)=6 x (1 -x) – (1/k 2)ν=0 – (1/k 2)ν =½ – (1/k 2)ν =1 Ø Again, unambiguous and direct mapping between behaviour of interaction and behaviour of distribution amplitude Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 30

Chang, Cloët, Roberts, Schmidt & Tandy, in progress; Si-xue Qin, Lei Chang, Yu-xin Liu, Craig Roberts and David Wilson, ar. Xiv: 1108. 0603 [nucl-th], Phys. Rev. C 84 042202(R) (2011) Pion’s valence-quark Distribution Amplitude Ø Preliminary results: rainbow-ladder QCD analyses of renormalisation-group-improved (1/k 2)ν =1 interaction Leading p. QCD – humped disfavoured but modest flattening φ (x)=6 x (1 -x) π Ø Such behaviour is only obtained with (1) Running mass in dressed-quark propagators (2) Pointwise expression of Goldstone’s theorem Eπ(k 2) but constant mass quark a 2>0 a 2<0 Reconstructed from 100 moments Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 31

Ø x ≈ 0 & x ≈ 1 correspond to maximum relative momentum within bound -state – expose p. QCD physics Ø x ≈ ½ corresponds to minimum possible relative momentum – behaviour of distribution around midpoint is strongly influence by DCSB Pion’s valence-quark Distribution Amplitude Leading p. QCD φπ(x)=6 x (1 -x) Ø Preliminary results, rainbow-ladder QCD analyses of (1/k 2)ν =1 interaction humped disfavoured but modest flattening Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 32

Ø x ≈ 0 & x ≈ 1 correspond to maximum relative momentum within bound -state – expose p. QCD physics Ø x ≈ ½ corresponds to minimum possible relative momentum – behaviour of distribution around midpoint is strongly influence by DCSB Pion’s valence-quark Distribution Amplitude Leading p. QCD φπ(x)=6 x (1 -x) These computations are the first to offer the possibility of directly exposing DCSB – pointwise – in the light-front frame. Ø Preliminary results, rainbow-ladder QCD analyses of interaction (1/k 2)ν =1 humped disfavoured but modest flattening Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 33

Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 34

Unification of Meson & Baryon Properties Ø Correlate the properties of meson and baryon ground- and excited-states within a single, symmetry-preserving framework Ø Symmetry-preserving means: ü Poincaré-covariant ü Guarantee Ward-Takahashi identities ü Express accurately the pattern by which symmetries are broken Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 35

R. T. Cahill et al. , Austral. J. Phys. 42 (1989) 129 -145 Faddeev Equation quark exchange ensures Pauli statistics quark diquark composed of stronglydressed quarks bound by dressed-gluons Ø Linear, Homogeneous Matrix equation v Yields wave function (Poincaré Covariant Faddeev Amplitude) that describes quark-diquark relative motion within the nucleon Ø Scalar and Axial-Vector Diquarks. . . v Both have “correct” parity and “right” masses v In Nucleon’s Rest Frame Amplitude has s−, p− & d−wave correlations Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 36

Contact Interaction Ø Symmetry-preserving treatment of vector×vector contact interaction is useful tool for the study of phenomena characterised by probe momenta less-than the dressed-quark mass, M. Because: For experimental observables determined by probe momenta Q 2<M 2, contact interaction results are not realistically distinguishable from those produced by the most sophisticated renormalisation-group-improved kernels. Ø Symmetry-preserving regularisation of the contact interaction serves as a useful surrogate, opening domains which analyses using interactions that more closely resemble those of QCD are as yet unable to enter. Ø They’re critical in attempts to use data as tool for charting nature of the quark-quark interaction at long-range; i. e. , identifying signals of the running of couplings and masses in QCD. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 37

Symmetry-preserving treatment of vector contact-interaction: series of papers establishes strengths & limitations. Contact Interaction Ø ar. Xiv: 1204. 2553 [nucl-th] Spectrum of hadrons with strangeness Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Ø ar. Xiv: 1112. 2212 [nucl-th], Phys. Rev. C 85 (2012) 025205 [21 pages] Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts Ø ar. Xiv: 1102. 4376 [nucl-th], Phys. Rev. C 83, 065206 (2011) [12 pages] , π- and ρ-mesons, and their diquark partners, from a contact interaction, H. L. L. Roberts, A. Bashir, L. X. Gutierrez-Guerrero, C. D. Roberts and David J. Wilson Ø ar. Xiv: 1101. 4244 [nucl-th], Few Body Syst. 51 (2011) pp. 1 -25 Masses of ground and excited-state hadrons H. L. L. Roberts, Lei Chang, Ian C. Cloët and Craig D. Roberts Ø ar. Xiv: 1009. 0067 [nucl-th], Phys. Rev. C 82 (2010) 065202 [10 pages] Abelian anomaly and neutral pion production Hannes L. L. Roberts, C. D. Roberts, A. Bashir, L. X. Gutiérrez-Guerrero & P. C. Tandy Ø ar. Xiv: 1002. 1968 [nucl-th], Phys. Rev. C 81 (2010) 065202 (5 pages) Pion form factor from a contact interaction L. Xiomara Gutiérrez-Guerrero, Adnan Bashir, Ian C. Cloët and C. D. Roberts Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 38

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Spectrum of Hadrons with Strangeness Ø Solve gap equation for u & s-quarks Ø Input ratio ms /mu = 24 is consistent with modern estimates Ø Output ratio Ms /Mu = 1. 43 shows dramatic impact of DCSB, even on the s-quark: Ms-ms = 0. 36 Ge. V = M 0 … This is typical of all DSE and lattice studies Ø κ = in-hadron condensate rises slowly with mass of hadron Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 39

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Spectrum of Mesons with Strangeness Ø Solve Bethe-Salpeter equations for mesons and diquarks Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 40

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Spectrum of Mesons with Strangeness Ø Solve Bethe-Salpeter equations for mesons and diquarks Perhaps underestimate radialground splitting by 0. 2 Ge. V ü Computed values for ground-states are greater than the empirical masses, where they are known. ü Typical of DCSB-corrected kernels that omit resonant contributions; i. e. , do not contain effects that may phenomenologically be associated with a meson cloud. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 41

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Spectrum of Diquarks with Strangeness Ø Solve Bethe-Salpeter equations for mesons and diquarks Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 42

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Spectrum of Diquarks with Strangeness Ø Solve Bethe-Salpeter equations for mesons and diquarks ü Level ordering of diquark correlations is same as that for mesons. ü In all diquark channels, except scalar, mass of diquark’s partner meson is a fair guide to the diquark’s mass: o Meson mass bounds the diquark’s mass from below; o Splitting always less than 0. 13 Ge. V and decreases with increasing meson mass Craig Roberts: N & N* Structure in Continuum Strong QCD üScalar channel “special” owing to DCSB 15. 08. 12: USC Summer Academy - 56 43

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Bethe-Salpeter amplitudes Ø Bethe-Salpeter amplitudes are couplings in Faddeev Equation Ø Magnitudes for diquarks follow precisely the meson pattern Craig Roberts: N & N* Structure in Continuum Strong QCD Owing to DCSB, FE couplings in ½- channels are 25 -times weaker than in ½+ ! 15. 08. 12: USC Summer Academy - 56 44

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Spectrum of Baryons with Strangeness Ø Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 45

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Spectrum of Baryons with Strangeness Ø Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. Jülich EBAC Ø As with mesons, computed baryon masses lie uniformly above the empirical values. Ø Success because our results are those for the baryons’ dressedquark cores, whereas empirical values include effects associated with meson-cloud, which typically produce sizable reductions. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 46

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Ø Baryon structure is flavour-blind Structure of Baryons with Strangeness Diquark content Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 47

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, Chang, Roberts, Wan and Wilson & Nucleon and Roper em elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts, ar. Xiv: 1112. 2212 [nucl-th], Phys. Rev. C 85 (2012) 025205 [21 pages] Ø Baryon structure is flavour-blind Structure of Baryons with Strangeness Diquark content 80% 0% 50% Ø Jqq=0 content of J=½ baryons is almost independent of their flavour structure Ø Radial excitation of ground-state octet possess zero scalar diquark content! Ø This is a consequence of DCSB Ø Ground-state (1/2)+ possess unnaturally large scalar diquark content Ø Orthogonality forces radial excitations to possess (almost) none at all! Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 48

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Spectrum of Hadrons with Strangeness Ø Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. (1/2)+ Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 49

ar. Xiv: 1204. 2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, L. Chang, C. D. Roberts, Shaolong Wan and D. J. Wilson Spectrum of Hadrons with Strangeness Ø Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. Ø This level ordering has long been a problem in CQMs with linear or HO (1/2)confinement potentials (1/2)+ Ø Correct ordering owes to DCSB (1/2)+ Craig Roberts: N & N* Structure in Continuum Strong QCD Ø Positive parity diquarks have Faddeev equation couplings 25 times greater than negative parity diquarks Ø Explains why approaches within which DCSB cannot be realised (CQMs) or simulations whose parameters suppress DCSB will both have difficulty reproducing experimental ordering 15. 08. 12: USC Summer Academy - 56 50

I. C. Cloët, C. D. Roberts, et al. ar. Xiv: 0812. 0416 [nucl-th] D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts ar. Xiv: 1112. 2212 [nucl-th], Phys. Rev. C 85 (2012) 025205 [21 pages] Neutron Structure Function at high x SU(6) symmetry Deep inelastic scattering – the Nobel-prize winning quark-discovery experiments Reviews: Ø S. Brodsky et al. NP B 441 (1995) Ø W. Melnitchouk & A. W. Thomas PL B 377 (1996) 11 Ø N. Isgur, PRD 59 (1999) Ø R. J. Holt & C. D. Roberts RMP (2010) Craig Roberts: N & N* Structure in Continuum Strong QCD DSE: “realistic” p. QCD, uncorrelated Ψ DSE: “contact” 0+ qq only Melnitchouk et al. Phys. Rev. D 84 (2011) 117501 Distribution of neutron’s momentum amongst quarks on the valence-quark domain 15. 08. 12: USC Summer Academy - 56 51

Nucleon to Roper Transition Form Factors Ø Extensive CLAS @ JLab Programme has produced the first measurements of nucleon-to-resonance transition form factors I. Aznauryan et al. , Results of the N* Program at JLab ar. Xiv: 1102. 0597 [nucl-ex] Ø Theory challenge is to explain the measurements Ø Notable result is zero in F 2 p→N*, explanation of which is a real challenge to theory. Ø First observation of a zero in a form factor Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 52

Nucleon to Roper Transition Form Factors Ø Extensive CLAS @ JLab Programme has produced the first measurements of nucleon-to-resonance transition form factors I. Aznauryan et al. , Results of the N* Program at JLab ar. Xiv: 1102. 0597 [nucl-ex] Ø Theory challenge is to explain the measurements Ø Notable result is zero in F 2 p→N*, explanation of which is a real challenge to theory. Ø DSE study connects appearance of zero in F 2 p→N* with Solid – DSE Dashed – EBAC Quark Core Near match supports picture of Roper as quark core plus meson cloud ü axial-vector-diquark dominance in Roper resonance ü and structure of form factors of J=1 state Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts, Phys. Rev. C 85 (2012) 025205 [21 pages] Γμ, αβ Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 53

Nucleon to Roper Transition Form Factors Ø Tiator and Vanderhaeghen – in progress – Empirically-inferred light-front-transverse charge density – Positive core plus negative annulus Ø Readily explained by dominance of axial-vector diquark configuration in Roper – Considering isospin and charge Negative d-quark twice as likely to be delocalised from the always-positive core than the positive u-quark d 2 {uu} u + 1 {ud} Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 54

Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 55

QCD is the most interesting part of the standard model - Nature’s only example of an essentially nonperturbative fundamental theory, Ø Confinement with light-quarks is not connected in any known way with a linear potential; not with a potential of any kind. Ø Confinement with light-quarks is associated with a dramatic change in the infrared structure of the parton propagators. Ø Dynamical chiral symmetry breaking, the origin of 98% of visible matter in universe, is manifested unambiguously and fundamentally in an equivalence between the one- and twobody problem in QCD Ø Working together to chart the behaviour of the running masses in QCD, experiment and theory can potentially answer the questions of confinement and dynamical chiral symmetry breaking; a task that currently each alone find hopeless. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 56

Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 57

Universal Misapprehensions Ø Since 1979, DCSB has commonly been associated literally with a spacetimeindependent mass-dimension-three “vacuum condensate. ” Ø Under this assumption, “condensates” couple directly to gravity in general relativity and make an enormous contribution to the cosmological constant Ø Experimentally, the answer is Ωcosm. const. = 0. 76 Ø This mismatch is a bit of a problem. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 58

New Paradigm “in-hadron condensates” Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 59

“Orthodox Vacuum” Ø Vacuum = “frothing sea” u Ø Hadrons = bubbles in that “sea”, d u containing nothing but quarks & gluons interacting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped! ud u u u d Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 60

New Paradigm Ø Vacuum = hadronic fluctuations but no condensates Ø Hadrons = complex, interacting systems within which perturbative behaviour is restricted to just 2% of the interior u d u u u d Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 61

Some Relevant References Ø ar. Xiv: 1202. 2376, Phys. Rev. C 85, 065202 (2012) [9 pages] Confinement contains condensates Stanley J. Brodsky, Craig D. Roberts, Robert Shrock, Peter C. Tandy Ø ar. Xiv: 1109. 2903 [nucl-th], Phys. Rev. C 85 (2012) 012201(Rap. Com), Expanding the concept of in-hadron condensates Lei Chang, Craig D. Roberts and Peter C. Tandy Ø ar. Xiv: 1005. 4610 [nucl-th], Phys. Rev. C 82 (2010) 022201(Rap. Com. ) New perspectives on the quark condensate, Brodsky, Roberts, Shrock, Tandy Ø ar. Xiv: 0905. 1151 [hep-th], PNAS 108, 45 (2011) Condensates in Quantum Chromodynamics and the Cosmological Constant , Brodsky and Shrock, Ø hep-th/0012253 The Quantum vacuum and the cosmological constant problem, Svend Erik Rugh and Henrik Zinkernagel. Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 62

Contents Ø Ø Ø Ø Ø Confinement Dynamical chiral symmetry breaking Dichotomy of the pion Pion valence-quark distribution Pion’s Distribution Amplitude Grand Unification - Mesons and Baryons Neutron Structure Function at high x Nucleon to Roper Transition Form Factors Epilogue New Paradigm “in-hadron condensates” Craig Roberts: N & N* Structure in Continuum Strong QCD 15. 08. 12: USC Summer Academy - 56 63

- Published collaborations Rocio BERMUDEZ U Michocan 2010 present
- Published collaborations 2010 present Rocio BERMUDEZ U Michocan
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