Three Mysteries of QCD Diabolical Strange quarks in the nucleonDiabolical Strange quarks in the nucleon Quark correlations and color non-singlet spectroscopyQuark correlations and color non-singlet spectroscopy Reluctant symmetry: Parity doubling among the hadrons -- a challenge for spectroscopyReluctant symmetry: Parity doubling among the hadrons -- a challenge for spectroscopy R. L. Jaffe Workshop on Hadron Structure at J-Parc November - December 2o05 Diabolical (QCD without experimental facilities) (QCD without experimental facilities)

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Why QCD? The perfect (eg. string) theory No parametersNo parameters All interactions dictated by symmetriesAll interactions dictated by symmetries Highly non-trivial vacuumHighly non-trivial vacuum A warm up for the “Theory of Everything”A warm up for the “Theory of Everything” Emergent phenomena: Confinement, chiral symmetry breaking, hadrons!Emergent phenomena: Confinement, chiral symmetry breaking, hadrons! --- at least for light quarks --- at least for light quarks

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05

What’s to be done? Basic QCD dynamics at the scale where hadron’s form is not understood.Basic QCD dynamics at the scale where hadron’s form is not understood. We don’t understand the mechanism of confinement or of chiral symmetry breaking in quantitative terms.We don’t understand the mechanism of confinement or of chiral symmetry breaking in quantitative terms. We don’t understand why quarks are the quasiparticles of QCD, even after running through regions of such strong renormalization. All the more reason to look for other quasiparticles: pseudoscalar bosons, diquarks(!)We don’t understand why quarks are the quasiparticles of QCD, even after running through regions of such strong renormalization. All the more reason to look for other quasiparticles: pseudoscalar bosons, diquarks(!) We don’t have a satisfactory description of the confined relativistic bound state to enable us to predict and/or interpret information like magnetic moments, excited state spectra, and flavor mixing via OZI rule violation.We don’t have a satisfactory description of the confined relativistic bound state to enable us to predict and/or interpret information like magnetic moments, excited state spectra, and flavor mixing via OZI rule violation. We don’t know how to connect the precise information obtained with short distance probes at high energies to the properties we would like to understand at hadronic scales --- sum rules, duality, “inclusive-exclusive connection”...We don’t know how to connect the precise information obtained with short distance probes at high energies to the properties we would like to understand at hadronic scales --- sum rules, duality, “inclusive-exclusive connection”...

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 QCD is very difficult at the confinement scale Domain of the Hadrons J-PARC

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 I. Strangeness Intelligent Design Diabolical Design ! Light quarks chiral dynamics Heavy quarks non-relativistic potential theory Strange quark The strange quark mass is very close to the dynamical mass scale of QCDThe strange quark mass is very close to the dynamical mass scale of QCD The strange quark content of important hadrons is therefore remarkably difficult to model and difficult to measure.The strange quark content of important hadrons is therefore remarkably difficult to model and difficult to measure. The electric weak charge matrices of the quarks are traceless in flavor SU(3)The electric weak charge matrices of the quarks are traceless in flavor SU(3) “Belonging to or so evil as to recall the Devil” Important to remember: Symmetry alone tells us nothing about strange quark content of nucleonImportant to remember: Symmetry alone tells us nothing about strange quark content of nucleon

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Compare our world to one where What do baryon magnetic moments tell us about the u,d, & s quark magnetization in the nucleon? Our world: So the strange quark magnetization in the nucleon would have been known accurately since approximately We have to work much harder! A less diabolical world:

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Brief remark about mechanisms... How do pairs mix into the nucleon state? Flavor singlet? Via gluonsFlavor singlet? Via gluons Flavor skew symmetric? Via instantonsFlavor skew symmetric? Via instantons Flavor diagonal? Via chiral symmetry breakingFlavor diagonal? Via chiral symmetry breaking Some of all of the above

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Mapping the strangeness in the nucleon Ten years progress

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Probing the strangeness content of the nucleon with Z exchange Probing the strangeness content of the nucleon with Z exchange SAMPLESAMPLE

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Strange quark contribution to the nucleon spin... Model independent measurement possible in elastic neutrino proton scattering at J-Parc.Model independent measurement possible in elastic neutrino proton scattering at J-Parc. Direct measurement (analogous to magnetic moment in electron scattering)Direct measurement (analogous to magnetic moment in electron scattering) A difficult, but important experimentA difficult, but important experiment Free from assumptions about SU(3) violation and low-x extrapolationFree from assumptions about SU(3) violation and low-x extrapolation Had been an objective of LSND, but never achieved!Had been an objective of LSND, but never achieved! J-Parc...J-Parc... “Standard analysis” of polarized DIS, using EJ-sum rule and hyperon beta-decay axial charges.“Standard analysis” of polarized DIS, using EJ-sum rule and hyperon beta-decay axial charges. Assumes SU(3) symmetry for hyperon axial charges which is uncertain at the 30% level!Assumes SU(3) symmetry for hyperon axial charges which is uncertain at the 30% level! Fragmentation function analysis by Hermes and COMPASSFragmentation function analysis by Hermes and COMPASS Assumes factorization at relatively low mass scale.Assumes factorization at relatively low mass scale.

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 II. Quark correlations & Color Non-Singlet Spectroscopy Quark correlations: Many dynamical mechanisms point to QQ correlations in the flavor, spin, and color antisymmetric, positive parity “good” diquark ConfinementConfinement Chiral symmetry breakingChiral symmetry breaking Quark correlations?Quark correlations? Message? Lattice QCD ⇔ Phenomenological models

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Evidence for the “good” diquark regularities in nucleon distribution functions regularities in nucleon distribution functions Fragmentation function regularitiesFragmentation function regularities Baryon spin splittings:Baryon spin splittings: DeRujula, Georgi, Glashow Rule in non-leptonic weak decays Rule in non-leptonic weak decays Neubert, Stech Total (or perhaps, almost total) absence of exoticsTotal (or perhaps, almost total) absence of exotics Extra nonet of scalar mesonsExtra nonet of scalar mesons Quarks correlate in the most antisymmetric flavor configurations RLJ

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Only those baryons allowed by symmetry to contain pure “good” diquark are anomalously abundant.

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Given development of lattice QCD, why not just dispense with phenomenological models? Because whole areas of hadron physics will never (?) be amenable to lattice methods. Scattering, production, structure functions, fragmentation, diffractive phenomena (the Pomeron), polarization phenomena, resonance widths... Use lattice to gain insight into QCD dynamics, even in “alternative realities”, not accessible to experiment. Vary N c Vary quark masses Construct hadrons that will perhaps never be observed experimentally. Given development of lattice QCD, why not just dispense with phenomenological models? Because whole areas of hadron physics will never (?) be amenable to lattice methods. Scattering, production, structure functions, fragmentation, diffractive phenomena (the Pomeron), polarization phenomena, resonance widths... Use lattice to gain insight into QCD dynamics, even in “alternative realities”, not accessible to experiment. Vary N c Vary quark masses Construct hadrons that will perhaps never be observed experimentally. Lattice QCD --- Experiment --- Model building

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Color non-singlet spectroscopy on the lattice Neutralize with spectator Wilson line (= infinitely heavy quark) Compare with bottom hadron spectroscopy (in principle) And with phenomenological models Neutralize with spectator Wilson line (= infinitely heavy quark) Compare with bottom hadron spectroscopy (in principle) And with phenomenological models Meson s Baryon s Tetraquark mesons Pentaquark baryons [Even color sextet light quark states] Static, infinitely massive, neutralizing antitriplet = Wilson line Color non-singlet quark source and sink

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Baryon s Recently implemented by Alexandrou, de Forcrand, Lucini hep-lat/ and C. Alexandrou JLab Summer Workshop First suggested as a way to study diquark correlations in connection with the Theta. RLJ and F. Wilczek hep-ph/

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 And more from AdFL Stimulates further consideration of quark correlations

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 “Schematic models” Diquark dominance Triquark correlations “Schematic models” Diquark dominance Triquark correlations RLJ & Wilczek; Nussinov; Karliner & Lipkin Karliner & Lipkin Proposed correlations? Colorspin -- colormagnetic gluon exchange forces DeRujula, Georgi, Glashow; DeGrand, RLJ, Johnson, Kiskis; RLJ;... Instanton dominated interactions Shuryak, Oka,... Pseudscalar meson mediated interactions Georgi & Manohar; Richard, Stancu, Pepin, Glozman,... Not a put down!

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Difference s

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Internal correlation structure Lightest multipletmultiplet Lightest multipletmultiplet Create states then study correlations in an lattice calculation

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 III. Parity Doubling in the Hadron Spectrum Message? A weak, but nevertheless significant symmetry between baryons the same I and J and of opposite parity.A weak, but nevertheless significant symmetry between baryons the same I and J and of opposite parity. Identify and classify baryon and meson resonances above 1.5 GeV, especially Strangeness -1 and -2.Identify and classify baryon and meson resonances above 1.5 GeV, especially Strangeness -1 and -2. Semi-Quantitative study of significance of symmetry in baryon sectorSemi-Quantitative study of significance of symmetry in baryon sector Not “restoration” ofNot “restoration” of Could be restoration of in sector whereCould be restoration of in sector where is (for as yet unknown reasons) suppressed. Or, it could be a dynamical symmetry, eg. conformational is (for as yet unknown reasons) suppressed. Or, it could be a dynamical symmetry, eg. conformational RLJ, Dan Pirjol, & Antonello Scardicchio hep- ph/ and II in preparation

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Typical *F. Iachello, 1989 * Trying to do better Define spectral density for positive and negative parity in each I & J channel.Define spectral density for positive and negative parity in each I & J channel. Test hypothesis that spectral functionsTest hypothesis that spectral functions are identical within a tolerance Compare Nature’s correlations with a “control set” obtained by shuffling parities over the existing resonances.Compare Nature’s correlations with a “control set” obtained by shuffling parities over the existing resonances. Include widths and reliabilities (stars assigned by PDG, *, **, ***, ****)Include widths and reliabilities (stars assigned by PDG, *, **, ***, ****)

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 NatureNature “Controls”“Controls”

Nucleons and Deltas Nucleons

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Sigmas and Lambdas

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Comments on data Nucleon and Delta parity doubling correlation is significant.Nucleon and Delta parity doubling correlation is significant. Sigma and Lambda is not convincing. More data needed. For example, many Sigmas in GeV region lack spin-parity assignments.Sigma and Lambda is not convincing. More data needed. For example, many Sigmas in GeV region lack spin-parity assignments. Insufficient data on Cascades for meaningful analysisInsufficient data on Cascades for meaningful analysis Meson data are even less complete and in many cases controversial.Meson data are even less complete and in many cases controversial. Could be part of a program to re-examine light hadron spectroscopy including many beams and processesCould be part of a program to re-examine light hadron spectroscopy including many beams and processes

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Origins of parity doubling? Not chiral symmetry restorationNot chiral symmetry restoration Cohen & Glozman Jido, Hatsuda, Kunihiro, Oka, Hosaka Natural idea is that realized in terms of multiplets (“Wigner-Weyl”), would account for parity doubling.Natural idea is that realized in terms of multiplets (“Wigner-Weyl”), would account for parity doubling. RLJ, Pirjol, Scardicchio If one attempts to realize chiral symmetry in a linear way on a subset of states in a world with spontaneous symmetry breaking and massless pions, the chiral symmetry in fact gives no relations among the properties of these states, such as masses and couplings. Such predictions, that are typical of a symmetry realized in the Wigner-Weyl mode, would hold only if certain chirally invariant operators are dynamically suppressed.If one attempts to realize chiral symmetry in a linear way on a subset of states in a world with spontaneous symmetry breaking and massless pions, the chiral symmetry in fact gives no relations among the properties of these states, such as masses and couplings. Such predictions, that are typical of a symmetry realized in the Wigner-Weyl mode, would hold only if certain chirally invariant operators are dynamically suppressed. However spontaneous symmetry breaking obstructs this possibilityHowever spontaneous symmetry breaking obstructs this possibility When pions transform non-linearly (as required by Goldstone), only irreducible representations ofWhen pions transform non-linearly (as required by Goldstone), only irreducible representations of are isospin multiplets of definite parity. are isospin multiplets of definite parity. Attempt to define representation with nontrivial parity transformation yields manifold which is simply connected to the standard non-linear representation with trivial parity structure.Attempt to define representation with nontrivial parity transformation yields manifold which is simply connected to the standard non-linear representation with trivial parity structure. Linear realization between two parity eigenstates Standard non-linear realization Arbitrary realization

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 What, then, could be the origin of parity doubling? restoration? restoration? This symmetry is explicitly broken by quantum fluctuations (instantons), without the appearance of Goldstone bosons (theThis symmetry is explicitly broken by quantum fluctuations (instantons), without the appearance of Goldstone bosons (the is not massless in the chiral limit) is not massless in the chiral limit) Like any explicitly broken continuous symmetry, it can be restored if the matrix elements of the divergence of the associated Noether current are suppressed.Like any explicitly broken continuous symmetry, it can be restored if the matrix elements of the divergence of the associated Noether current are suppressed. The task becomes to see if the matrix elements of FF-dual are suppressed at moderate excitation in the hadron spectrum. A project for lattice QCD?The task becomes to see if the matrix elements of FF-dual are suppressed at moderate excitation in the hadron spectrum. A project for lattice QCD? Like any explicitly broken continuous symmetry, it can be restored if the matrix elements of the divergence of the associated Noether current are suppressed.Like any explicitly broken continuous symmetry, it can be restored if the matrix elements of the divergence of the associated Noether current are suppressed.

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 What, then, could be the origin of parity doubling? Conformational degeneracy? Any “rigid body” with tri-axial structure and tunneling amplitude between conformations will have parity doubling.Any “rigid body” with tri-axial structure and tunneling amplitude between conformations will have parity doubling. A quark-diquark model of baryons?A quark-diquark model of baryons? Like any explicitly broken continuous symmetry, it can be restored if the matrix elements of the divergence of the associated Noether current are suppressed.Like any explicitly broken continuous symmetry, it can be restored if the matrix elements of the divergence of the associated Noether current are suppressed. Would suggest parity doubling on leading Regge trajectoryWould suggest parity doubling on leading Regge trajectory But it’s a mystery why such an effect should dominate for J=1/2, 3/2, etc.But it’s a mystery why such an effect should dominate for J=1/2, 3/2, etc.

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05 Summary, reflections... Despite years of theoretical and experimental work, QCD still has not yielded the secrets of confinement dynamics.Despite years of theoretical and experimental work, QCD still has not yielded the secrets of confinement dynamics. Some aspects may never be understood from first principles (two body scattering at fixed angle, for example)Some aspects may never be understood from first principles (two body scattering at fixed angle, for example) But some problems are crisply defined and beg for a deeper explanation:But some problems are crisply defined and beg for a deeper explanation: The role of the strange quark in the nucleonThe role of the strange quark in the nucleon [The role of gluons in the nucleon][The role of gluons in the nucleon] The structure of quark correlations and the problem of exoticsThe structure of quark correlations and the problem of exotics Parity doublingParity doubling And others too: vector dominance, the absence of large higher twist effects, the transformation from current to constituent quarks,...And others too: vector dominance, the absence of large higher twist effects, the transformation from current to constituent quarks,...