Three Mysteries of QCD Diabolical Strange quarks in the nucleonDiabolical Strange quarks in the nucleon Quark correlations and color non-singlet spectroscopyQuark

Three Mysteries of Three Mysteries of QCDQCD

•• Diabolical Strange quarks in the nucleonDiabolical Strange quarks in the nucleon

•• Quark correlations and color non-singlet Quark correlations and color non-singlet spectroscopyspectroscopy

•• Reluctant symmetry: Parity doubling Reluctant symmetry: Parity doubling among the hadrons -- a challenge for among the hadrons -- a challenge for spectroscopyspectroscopy

R. L. Jaffe R. L. Jaffe Workshop on Hadron Structure at J-Workshop on Hadron Structure at J-

ParcParcNovember - December 2o05November - December 2o05

DiabolicalDiabolical

(QCD without (QCD without experimental experimental facilities)facilities)

R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - R. L. Jaffe, Workshop on Hadron Structure at J-Parc, November - December 2o05December 2o05

Why QCD?Why QCD?The perfect (eg. string) The perfect (eg. string) theorytheory

•• 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 phenomenaEmergent phenomena: Confinement, chiral : Confinement, chiral symmetry breaking, hadrons!symmetry breaking, hadrons!

--- at least for light quarks--- at least for light quarks


What’s to be done?What’s to be done?•• Basic QCD dynamics at the scale where hadron’s form is Basic QCD dynamics at the scale where hadron’s form is

not understood.not understood.•• We don’t understand the mechanism of confinement or of We don’t understand the mechanism of confinement or of

chiral symmetry breaking in quantitative terms.chiral symmetry breaking in quantitative terms.•• We don’t understand why quarks are the quasiparticles of We don’t understand why quarks are the quasiparticles of

QCD, even after running through regions of such strong QCD, even after running through regions of such strong renormalization. All the more reason to look for other renormalization. All the more reason to look for other quasiparticles: quasiparticles: pseudoscalar bosonspseudoscalar bosons, , diquarks(!)diquarks(!)

•• We don’t have a satisfactory description of the confined We don’t have a satisfactory description of the confined relativistic bound state to enable us to predict and/or relativistic bound state to enable us to predict and/or interpret information like magnetic moments, excited state interpret information like magnetic moments, excited state spectra, and flavor mixing via OZI rule violation.spectra, and flavor mixing via OZI rule violation.

•• We don’t know how to connect the precise information We don’t know how to connect the precise information obtained with short distance probes at high energies to the obtained with short distance probes at high energies to the properties we would like to understand at hadronic scales properties we would like to understand at hadronic scales --- sum rules, duality, “inclusive-exclusive connection”...--- sum rules, duality, “inclusive-exclusive connection”...


QCD is very difficult at the confinement QCD is very difficult at the confinement scalescale

Domain of the

Hadrons

J-PARC J-PARC


I. I. StrangenessStrangenessIntelligent Intelligent

DesignDesignDiabolical Design Diabolical Design !!Diabolical Design Diabolical Design !!

Light quarksLight quarkschiral dynamicschiral dynamics

Heavy quarksHeavy quarksnon-relativistic non-relativistic

potential potential theorytheoryStrange quarkStrange quark

•• The strange quark mass The strange quark mass is very close to the is very close to the dynamical mass scale of dynamical mass scale of QCDQCD

•• The strange quark content of important hadrons is therefore The strange quark content of important hadrons is therefore remarkably difficult to model and difficult to measure.remarkably difficult to model and difficult to measure.

•• The electric weak charge The electric weak charge matrices of the quarks matrices of the quarks are traceless in flavor are traceless in flavor SU(3)SU(3)

““Belonging to or so evil as to recall the Belonging to or so evil as to recall the Devil”Devil”

•• Important to remember: Symmetry alone tells us nothing about Important to remember: Symmetry alone tells us nothing about strange quark content of nucleonstrange quark content of nucleon


Compare our world to one where Compare our world to one where What do baryon magnetic moments tell us about the u,d, & s quark What do baryon magnetic moments tell us about the u,d, & s quark magnetization in the nucleon?magnetization in the nucleon?

Our world:Our world:

So the strange quark magnetization in the nucleon would have been So the strange quark magnetization in the nucleon would have been known accurately since approximately 1970.known accurately since approximately 1970.

We have to work much harder!We have to work much harder!

A less diabolical world:A less diabolical world:


Brief remark about mechanisms...Brief remark about mechanisms...How do pairs mix into the nucleon How do pairs mix into the nucleon

state?state?•• Flavor singlet? Via gluonsFlavor singlet? Via gluons

•• Flavor skew symmetric? Via Flavor skew symmetric? Via instantonsinstantons

•• Flavor diagonal? Via chiral Flavor diagonal? Via chiral symmetry breakingsymmetry breaking

Some of all of the Some of all of the aboveabove


Mapping the strangeness in the nucleon Mapping the strangeness in the nucleon Ten years progress...Ten years progress...

1111

22223333


Probing the strangeness content of the nucleon with Z Probing the strangeness content of the nucleon with Z exchangeexchange

SAMPLESAMPLESAMPLESAMPLE


Strange quark contribution to the nucleon Strange quark contribution to the nucleon spin...spin...

•• Model independent measurement Model independent measurement possible in possible in elasticelastic neutrino proton neutrino proton scattering at J-Parc.scattering at J-Parc.•• Direct measurement (analogous to magnetic moment in electron Direct measurement (analogous to magnetic moment in electron

scattering)scattering)•• A difficult, but important experimentA difficult, but important experiment•• Free from assumptions about SU(3) violation and low-x Free from assumptions about SU(3) violation and low-x

extrapolationextrapolation•• 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 Standard analysis” of polarized DIS, using EJ-sum rule and hyperon beta-decay axial charges.hyperon beta-decay axial charges.•• Assumes SU(3) symmetry for hyperon axial charges which is Assumes SU(3) symmetry for hyperon axial charges which is

uncertain at the 30% level!uncertain at the 30% level!

••

•• Fragmentation function analysis Fragmentation function analysis by Hermes and COMPASSby Hermes and COMPASS

•• Assumes factorization at relatively low Assumes factorization at relatively low mass scale.mass scale.


II. Quark correlations & Color Non-Singlet II. Quark correlations & Color Non-Singlet SpectroscopySpectroscopy

Quark correlations:Quark correlations:

Many dynamical Many dynamical mechanisms point to QQ mechanisms point to QQ correlations in the correlations in the flavor, spin, and color flavor, spin, and color antisymmetric, positive antisymmetric, positive parity parity “good” “good” diquarkdiquark

•• ConfinementConfinement

•• Chiral symmetry breakingChiral symmetry breaking

•• Quark Quark correlations?correlations?

Message? Message? Lattice QCD Lattice QCD ⇔ ⇔ Phenomenological Phenomenological modelsmodels


Evidence for the “good” diquarkEvidence for the “good” diquark

•• regularities in nucleon distribution functionsregularities in nucleon distribution functions

•• Fragmentation function regularitiesFragmentation function regularities

•• Baryon spin Baryon spin splittings:splittings:

DeRujula, Georgi, DeRujula, Georgi, GlashowGlashow

•• Rule in non-leptonic weak decays Rule in non-leptonic weak decays Neubert, StechNeubert, Stech

•• Total (or perhaps, almost total) absence of exotics Total (or perhaps, almost total) absence of exotics

•• Extra nonet of scalar mesonsExtra nonet of scalar mesonsQuarks correlate in the most Quarks correlate in the most antisymmetricantisymmetric flavor flavor

configurationsconfigurationsRLJRLJ


Only those baryons Only those baryons allowed by allowed by symmetry to contain symmetry to contain pure “good” diquark pure “good” diquark are anomalously are anomalously abundant.abundant.


• 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 Nc

Vary quark massesConstruct 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 Nc

Vary quark massesConstruct hadrons that will perhaps never be observed experimentally.

Lattice QCD --- Experiment --- Model Lattice QCD --- Experiment --- Model buildingbuilding


Color non-singlet spectroscopy on the lattice

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 Mesons

Mesons

Baryons

Baryons

Tetraquark mesonsTetraquark mesons

Pentaquark baryonsPentaquark baryons

[Even color sextet light quark states][Even color sextet light quark states]

Static, infinitely massive, neutralizing antitriplet = Wilson line

Static, infinitely massive, neutralizing antitriplet = Wilson line

Color non-singlet quark source and sinkColor non-singlet quark source and sink


Baryons

Baryons

• Recently implemented by Alexandrou, de Forcrand, Lucini

• Recently implemented by Alexandrou, de Forcrand, Lucini hep-lat/0509113 and C.

Alexandrou JLab Summer Workshop

hep-lat/0509113 and C. Alexandrou JLab Summer

Workshop

• First suggested as a way to study diquark correlations in connection with the Theta.

• First suggested as a way to study diquark correlations in connection with the Theta. RLJ and F. Wilczek hep-ph/0307341 RLJ and F. Wilczek hep-ph/0307341


And more from AdFLAnd more from AdFL

Stimulates further consideration of quark correlations

Stimulates further consideration of quark correlations


• “Schematic

models”

Diquark

dominance

Triquark

correlations

• “Schematic

models”

Diquark

dominance

Triquark

correlations

RLJ & Wilczek; Nussinov; Karliner & LipkinRLJ & Wilczek; Nussinov; Karliner & LipkinKarliner & LipkinKarliner & Lipkin

Proposed correlations?Proposed correlations?• Colorspin -- colormagnetic gluon exchange forces• Colorspin -- colormagnetic gluon exchange forces

DeRujula, Georgi, Glashow; DeGrand, RLJ, Johnson, Kiskis; RLJ; ...DeRujula, Georgi, Glashow; DeGrand, RLJ, Johnson, Kiskis; RLJ; ...

• Instanton dominated

interactions

• Instanton dominated

interactionsShuryak, Oka, ...Shuryak, Oka, ...

• Pseudscalar meson mediated interactions • Pseudscalar meson mediated interactions Georgi & Manohar; Richard, Stancu, Pepin, Glozman, ...Georgi & Manohar; Richard, Stancu, Pepin, Glozman, ...

Not a put

down!

Not a put

down!


Differences

Differences


Internal correlation structureInternal correlation structure

Lightest multipletLightest multiplet

Create states then study correlations in an lattice calculation

Create states then study correlations in an lattice calculation


III. Parity Doubling in the Hadron III. Parity Doubling in the Hadron SpectrumSpectrumMessage?Message?

•• A weak, but nevertheless significant symmetry A weak, but nevertheless significant symmetry between baryons the same I and J and of opposite between baryons the same I and J and of opposite parity.parity.•• Identify and classify baryon and meson Identify and classify baryon and meson resonances above 1.5 GeV, especially Strangeness -1 resonances above 1.5 GeV, especially Strangeness -1 and -2.and -2.•• Semi-Quantitative study of significance of symmetry Semi-Quantitative study of significance of symmetry

in baryon sectorin baryon sector

•• Not “restoration” of Not “restoration” of

•• Could be restoration of in sector Could be restoration of in sector where where

is (for as yet unknown reasons) suppressed. is (for as yet unknown reasons) suppressed. Or, it could be a dynamical symmetry, eg. Or, it could be a dynamical symmetry, eg. conformational conformational

RLJ, Dan Pirjol, & Antonello Scardicchio RLJ, Dan Pirjol, & Antonello Scardicchio hep-ph/0511081hep-ph/0511081

and II in preparationand II in preparation


TypicaTypicall

*F. Iachello, 1989*F. Iachello, 1989

** Trying to do betterTrying to do better

•• Define spectral density for Define spectral density for positive and negative positive and negative parity in each I & J parity in each I & J channel. channel.

•• Test hypothesis that Test hypothesis that spectral functions spectral functions are identical within a are identical within a tolerancetolerance

•• Compare Nature’s Compare Nature’s correlations with a correlations with a “control set” obtained by “control set” obtained by shuffling parities over the shuffling parities over the existing resonances.existing resonances.

•• Include widths and Include widths and reliabilities (stars reliabilities (stars assigned by PDG, *, **, assigned by PDG, *, **, ***, ****)***, ****)


NaturNatureeNaturNaturee

““ControlControls”s”““ControlControls”s”


Nucleons and Nucleons and DeltasDeltas

NucleonNucleonss


Sigmas and Sigmas and LambdasLambdas


Comments on Comments on datadata•• 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. Sigma and Lambda is not convincing. More data needed. For example, many Sigmas in 1.5 -- 2.5 GeV region lack For example, many Sigmas in 1.5 -- 2.5 GeV region lack spin-parity assignments.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 Meson data are even less complete and in many cases controversial.controversial.

•• Could be part of a program to re-examine light hadron Could be part of a program to re-examine light hadron spectroscopy including many beams and processesspectroscopy including many beams and processes


Origins of parity doubling?Origins of parity doubling?•• Not chiral symmetry Not chiral symmetry

restorationrestoration

Cohen & GlozmanCohen & GlozmanJido, Hatsuda, Kunihiro, Oka, HosakaJido, Hatsuda, Kunihiro, Oka, Hosaka

•• Natural idea is that Natural idea is that realized in terms of multiplets (“Wigner-realized in terms of multiplets (“Wigner-Weyl”), would account for parity doubling.Weyl”), would account for parity doubling.

RLJ, Pirjol, ScardicchioRLJ, Pirjol, Scardicchio

•• If one attempts to realize chiral symmetry in a linear way on a subset of states in 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 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 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 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 in the Wigner-Weyl mode, would hold only if certain chirally invariant operators are dynamically suppressed.are dynamically suppressed.

•• However spontaneous symmetry breaking However spontaneous symmetry breaking obstructs this possibilityobstructs this possibility•• When pions transform non-linearly (as When pions transform non-linearly (as required by Goldstone), only irreducible required by Goldstone), only irreducible representations of representations of are isospin multiplets of are isospin multiplets of definite parity.definite parity.•• Attempt to define representation with nontrivial Attempt to define representation with nontrivial parity transformation yields manifold which is parity transformation yields manifold which is simply connected to the standard non-linear simply connected to the standard non-linear representation with trivial parity structure.representation with trivial parity structure.

Linear realization Linear realization between two between two parity eigenstatesparity eigenstates

Linear realization Linear realization between two between two parity eigenstatesparity eigenstates

Standard non-Standard non-linear realizationlinear realizationStandard non-Standard non-linear realizationlinear realization

Arbitrary Arbitrary realizationrealizationArbitrary Arbitrary realizationrealization


What, then, could be the origin of parity What, then, could be the origin of parity doubling?doubling? restoration?restoration?•• This symmetry is explicitly broken by quantum fluctuations This symmetry is explicitly broken by quantum fluctuations

(instantons), without the appearance of Goldstone bosons (instantons), without the appearance of Goldstone bosons (the(the is not massless in the chiral limit) is not massless in the chiral limit)

•• Like any explicitly broken continuous symmetry, it can be Like any explicitly broken continuous symmetry, it can be restored if the matrix elements of the divergence of the restored if the matrix elements of the divergence of the associated Noether current are suppressed.associated Noether current are suppressed.

•• The task becomes to see if the matrix elements of FF-dual The task becomes to see if the matrix elements of FF-dual are suppressed at moderate excitation in the hadron are suppressed at moderate excitation in the hadron spectrum. A project for lattice QCD?spectrum. A project for lattice QCD?



What, then, could be the origin of parity What, then, could be the origin of parity doubling?doubling?Conformational degeneracy?Conformational degeneracy?

•• Any “rigid body” with tri-axial structure and tunneling Any “rigid body” with tri-axial structure and tunneling amplitude between conformations will have parity amplitude between conformations will have parity doubling.doubling.

•• A quark-diquark model of baryons? A quark-diquark model of baryons?


•• Would suggest parity doubling on leading Regge Would suggest parity doubling on leading Regge trajectorytrajectory

•• But it’s a mystery why such an effect should But it’s a mystery why such an effect should dominate for J=1/2, 3/2, etc.dominate for J=1/2, 3/2, etc.


Summary, reflections...Summary, reflections...

•• Despite years of theoretical and experimental Despite years of theoretical and experimental work, QCD still has not yielded the secrets of work, QCD still has not yielded the secrets of confinement dynamics.confinement dynamics.

•• Some aspects may never be understood from first Some aspects may never be understood from first principles (two body scattering at fixed angle, for principles (two body scattering at fixed angle, for example)example)

•• But some problems are crisply defined and beg But some problems are crisply defined and beg for a deeper explanation: 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 The structure of quark correlations and the problem

of exoticsof exotics•• Parity doublingParity doubling•• And others too: vector dominance, the absence of And others too: vector dominance, the absence of

large higher twist effects, the transformation from large higher twist effects, the transformation from current to constituent quarks,...current to constituent quarks,...

Documents

Three Mysteries of QCD Diabolical Strange quarks in the nucleonDiabolical Strange quarks in the nucleon Quark correlations and color non-singlet spectroscopyQuark