R L Jaffe DIS05 Madison Life and Death among the Hadrons R. L. Jaffe DIS05 Madison April 2005 R. L. Jaffe DIS05 Madison April 2005 Update on the Theta

R L Jaffe DIS05 Madison


Life and Death among the Hadrons

Life and Death among the Hadrons

R. L. JaffeDIS05MadisonApril 2005

R. L. JaffeDIS05MadisonApril 2005

Update on the ThetaUpdate on the Theta

Diquark

correlations in

QCD

Diquark

correlations in

QCD



Postmortem on the

Theta

Postmortem on the

Theta• The is in trouble. It may survive, but it is not too early to look at the consequences of its demise

• The is in trouble. It may survive, but it is not too early to look at the consequences of its demiseshould it

occurshould it

occur



• Positive sightings of the Theta• Positive sightings of the Theta

Dzierba, Meyer, Szczepaniak hep-ex/0412077Dzierba, Meyer, Szczepaniak hep-ex/0412077



• Negative non-sightings of the Theta • Negative non-sightings of the Theta

Dzierba, Meyer, Szczepaniak hep-ex/0412077Dzierba, Meyer, Szczepaniak hep-ex/0412077



• Very recent results -- first of a second generation

• Very recent results -- first of a second generation• Reported by R. De Vita for CLAS at APS Tampa 4/17/05

• Reported by R. De Vita for CLAS at APS Tampa 4/17/05



• More detail• More detail



Same reaction, Phys. Lett. B572 (2003)



Implicatio

ns

Implicatio

ns• SU(3) Chiral Soliton Models (Diakonov, Petrov,

Polyakov)

• SU(3) Chiral Soliton Models (Diakonov, Petrov,

Polyakov)• Strong prediction asserted: M=1540 MeV,

= 15 MeV

• Strong prediction asserted: M=1540 MeV,

= 15 MeV• Apparently the model is unreliable, why?• Apparently the model is unreliable, why?

? Truncation of chiral effective lagrangian?? Truncation of chiral effective lagrangian?

? Adiabatic (rigid) excitation?? Adiabatic (rigid) excitation?

? Perturbative implimentation of SU(3)

violation?

? Perturbative implimentation of SU(3)

violation?

Dynamical

balance

Dynamical

balanceAssume that rotational excitations neither deform soliton nor mix with radial excitations. No separation of scales.

Assume that rotational excitations neither deform soliton nor mix with radial excitations. No separation of scales.

No justification to ignoreNo justification to ignore

? Perhaps baryons are not chiral solitons in the

first place!

? Perhaps baryons are not chiral solitons in the

first place!



Implicatio

ns

Implicatio

ns• Quark models, Large Nc (a la Jenkins/Manohar),• Quark models, Large Nc (a la Jenkins/Manohar),

• Never could accommodate narrow width• Never could accommodate narrow width

• No prediction because absolute mass scale of

could not be determined

• No prediction because absolute mass scale of

could not be determined

• Absence of Theta limits the strength of the

correlation (diquark) that has other important

spectroscopic and dynamical implications

• Absence of Theta limits the strength of the

correlation (diquark) that has other important

spectroscopic and dynamical implications

?? ?? ??



LessonsLessons• There really are no (light, narrow) exotics in QCD• There really are no (light, narrow) exotics in QCD

• Phenomenological models should not be taken

very quantitatively, especially for overall scale

(eg. mass of lightest state in sector, or

lightest glueball)

• Phenomenological models should not be taken

very quantitatively, especially for overall scale

(eg. mass of lightest state in sector, or

lightest glueball)• Lattice QCD has not yet progressed to the stage

that it can be decisive

• Lattice QCD has not yet progressed to the stage

that it can be decisive

• Comments do not apply to heavy quark (c and b)

exotics, where different issues apply. See (e.g.)

Stewart, Wessling & Wise, hep-ph/0402076. Not

covered here/ lack of time.

• Comments do not apply to heavy quark (c and b)

exotics, where different issues apply. See (e.g.)

Stewart, Wessling & Wise, hep-ph/0402076. Not

covered here/ lack of time.• A happy accident: the saga of the Theta has

reminded us of the importance of diquark

correlations in QCD

• A happy accident: the saga of the Theta has

reminded us of the importance of diquark

correlations in QCD



Diquarks correlations in

QCD• Color, flavor, spin antisymmetric diquark

dominates

• Color, flavor, spin antisymmetric diquark

dominates

• Spectroscopic consequences

• Exotics in general

• Pentaquarks and related states

• Spectroscopic consequences

• Exotics in general

• Pentaquarks and related states

• Diquarks in deep inelastic processes ?• Diquarks in deep inelastic processes ?

• Phenomenological evidence for diquark

correlations

• Phenomenological evidence for diquark

correlations• Defining diquarks• Defining diquarks

• Spectroscopy in color non-singlet sectors!• Spectroscopy in color non-singlet sectors!

• Conclusions• Conclusions



Correlations and

classification

Correlations and

classification• Confinement• Confinement

• correlations ?

• correlations ?

• Color, flavor, spin antisymmetry

• Color, flavor, spin antisymmetry

• Chiral symmetry breaking

• Chiral symmetry breaking



Classification

Fermi

statistics

Fermi

statistics

– Parity – Parity

+

Parity

+

Parity

ColorColor

Color Color

Leaves only two diquarks in the low energy spectrum

Leaves only two diquarks in the low energy spectrum



Diquarks

Flavor Color Spin

-8

8/3

“Good”“Good”“Bad”“Bad”



• Condensation in quark matter at high density

• Condensation in quark matter at high density• condenses in flavor antisymmetric channel

generating color-flavor locked superconductivity

• condenses in flavor antisymmetric channel generating color-flavor locked superconductivity

Long history in QCD, but never in the mainstream (D. Lichtenberg)Long history in QCD, but never in the mainstream (D. Lichtenberg)

Phenomenological evidence for diquarksPhenomenological evidence for diquarks

• Certain regularities in spectroscopy• Certain regularities in spectroscopy• Absence of• Absence of

• Systematic analysis of baryon and meson resonances.

More later -- A. Selem & F. Wilczek in preparation

• Systematic analysis of baryon and meson resonances.

More later -- A. Selem & F. Wilczek in preparation

• rule in nonleptonic weak decays

• rule in nonleptonic weak decays• dominance gives good description of non-

perturbative effects.• dominance gives good description of non-

perturbative effects.

• Systematic study by Neubert, Stech & collaborators in late 1980’s.

• Systematic study by Neubert, Stech & collaborators in late 1980’s.



Diquark regularities in DIS

• Baryon parton distribution function regularities follow from

• Baryon parton distribution function regularities follow from

• Regularities in fragmentation ratios in to hadrons

• Regularities in fragmentation ratios in to hadrons

Fragmentatio

n ratios

measured

at LEP

(Delphi)

Fragmentatio

n ratios

measured

at LEP

(Delphi)

Known since 1960’sKnown since 1960’s

Recent JLab results

nucl-ex/0308011

Recent JLab results

nucl-ex/0308011



Good diquark, strange

Good diquark, strange

• Formally define color antitriplet diquarks in the presence of an infinitely heavy spectator quark (or Polyakov line)

• Formally define color antitriplet diquarks in the presence of an infinitely heavy spectator quark (or Polyakov line)

• Awaiting lattice calculations, estimate from charm and strange systems:

• Awaiting lattice calculations, estimate from charm and strange systems:

Characterizing diquarksCharacterizing diquarks

Good diquark, non-strange

Good diquark, non-strange

Bad diquark, strange

Bad diquark, strange

Bad diquark, non-strange

Bad diquark, non-strange

Bad diquark, doubly strange

Bad diquark, doubly strange



• Other estimates from charm sector• Other estimates from charm sector

Good - bad mass difference decreases with quark mass.

Good - bad mass difference decreases with quark mass.

Diquark -- heavy quark spin interaction decreases with heavy quark mass and with light quark mass

Diquark -- heavy quark spin interaction decreases with heavy quark mass and with light quark mass

• Conclude: charm baryon masses allow estimate of diquark masses in a heavy quark background. Correlation is ~ 200 MeV. Not huge, but important

• Conclude: charm baryon masses allow estimate of diquark masses in a heavy quark background. Correlation is ~ 200 MeV. Not huge, but important



• Most important: Diquark correlations explain the total (so far) absence of exotics in the light quark spectrum.

• Most important: Diquark correlations explain the total (so far) absence of exotics in the light quark spectrum.

Spectroscopic consequencesSpectroscopic consequences

• Next: Diquark correlations “explain” supernumerary nonet of light scalar mesons as dominantly states

• Next: Diquark correlations “explain” supernumerary nonet of light scalar mesons as dominantly states

• Qualitative regularities in the meson and baryon spectra

• Qualitative regularities in the meson and baryon spectra

• Suggest possible exotics in the heavy quark spectrum.

• Suggest possible exotics in the heavy quark spectrum.



Spectra Spectra

• Baryons• BaryonsFermi statistics kills the singlet and allows only one octet which is a mixture of good and bad diquark except for and

Fermi statistics kills the singlet and allows only one octet which is a mixture of good and bad diquark except for and

• Mesons• Mesons

No Exotics !No Exotics !Lightest multiplet is 0++ nonetLightest multiplet is 0++ nonet



Scalar mesons: a supernumerary nonetScalar mesons: a supernumerary nonet



Spectra Spectra

• Pentaquarks• Pentaquarks

Negative parity, non-exotic, s-waveNegative parity, non-exotic, s-wave

Positive parity, possibly exotic, p-wavePositive parity, possibly exotic, p-wave

Only possible exotic

Only possible exotic

Exotic requires diquarks in an antisymmetric space state (bose statistics) -- heavier, less stable

Exotic requires diquarks in an antisymmetric space state (bose statistics) -- heavier, less stable

• Dibaryons• DibaryonsOnly s-wave is the SU(3)- singlet dihyperon: Only s-wave is the SU(3)- singlet dihyperon: Made heavier by Pauli blockingMade heavier by Pauli blocking



Spectra Summary Spectra Summary

• Generically, no exotics among light (u,d,s)• Generically, no exotics among light (u,d,s)

• Marginal cases: • Marginal cases:

Pentaquark Pentaquark

Dibaryon Dibaryon

• Scalar mesons:• Scalar mesons:

Ground state is a nonet of 0++ mesons resembling known light nonet.

Ground state is a nonet of 0++ mesons resembling known light nonet.

• Heavy quark exotics should be explored more thoroughly

• Heavy quark exotics should be explored more thoroughly



In Deep Inelastic Processes In Deep Inelastic Processes

• Structure function regularities, especially as • Structure function regularities, especially as

• Fragmentation functions• Fragmentation functions

• If diquarks are strongly correlated, baryon fragmentation functions should not be dramatically smaller than meson f.f.

• If diquarks are strongly correlated, baryon fragmentation functions should not be dramatically smaller than meson f.f.

• Data on two particular baryons...• Data on two particular baryons...

Good [u,d] diquark in s-wave

Good [u,d] diquark in s-waveGood [u,d] diquark in p-wave

Good [u,d] diquark in p-wave





Limits on diquarks from higher twist...Limits on diquarks from higher twist... A. Vainshteyn & RLJ

(unpublished)A. Vainshteyn & RLJ

(unpublished)

“But aren’t strong correlations in QCD ruled out by the absence of large twist-four corrections to DIS?”

“How pointlike can diquarks be?”

“But aren’t strong correlations in QCD ruled out by the absence of large twist-four corrections to DIS?”

“How pointlike can diquarks be?” corrections to DIS are known to be small, and limit non-perturbative scales in QCD beyond

corrections to DIS are known to be small, and limit non-perturbative scales in QCD beyond These limits constrain diquarks because twist-four operators include ones sensitive to diquark correlations...

These limits constrain diquarks because twist-four operators include ones sensitive to diquark correlations...



Leading twistLeading twist

However: “Good” diquark is spinless and does not contribute at twist four !However: “Good” diquark is spinless and does not contribute at twist four !

Dimension-6, spin-2 ⇒ twist-4, but only if quarks are coupled to maximum spin.Dimension-6, spin-2 ⇒ twist-4, but only if quarks are coupled to maximum spin.

Twist four -- diquark operator

Twist four -- diquark operator



QCD spectroscopy in color non-singlet sectors

• Neutralize with spectator Wilson line (= infinitely heavy quark)

• (Or with uniform color background charge (how?))• Compare with bottom hadron spectroscopy• And with phenomenological models

• Neutralize with spectator Wilson line (= infinitely heavy quark)

• (Or with uniform color background charge (how?))• Compare with bottom hadron spectroscopy• And with phenomenological models

Mesons

Mesons

Baryons

Baryons

Tetraquark mesonsTetraquark mesonsPentaquark baryonsPentaquark baryons

Even color sextet light quark statesEven color sextet light quark states

• Study correlations in QCD by studying color non-singlet spectroscopy!

• Study correlations in QCD by studying color non-singlet spectroscopy!

• The “ affair” suggests that correlations in QCD can be studied by studying color non-singlet light quark systems neutralized by heavy quark spectator.




• Study correlations in QCD by studying color non-singlet spectroscopy!• Study correlations in QCD by studying color non-singlet spectroscopy!



Example: Classification of ground state Example: Classification of ground state

“Exotics” with unique SU(3) assignments.

“Exotics” with unique SU(3) assignments.“Exotics” mixed by SU(3) violating interactions.

“Exotics” mixed by SU(3) violating interactions.

Total J=3/2 states with Total J=3/2 states with (Ignore for simplicity -- dynamics?)(Ignore for simplicity -- dynamics?)



“Exotics” with unique SU(3) assignments.

“Exotics” with unique SU(3) assignments.“Exotics” mixed by SU(3) violating interactions.

“Exotics” mixed by SU(3) violating interactions.

Non-exotics, mix with single quark states.

Non-exotics, mix with single quark states.

Total J=1/2 states with Total J=1/2 states with (Ignore for simplicity -- dynamics?)(Ignore for simplicity -- dynamics?)



Color triplet spectroscopy Color triplet spectroscopy Spin Isospin Strangeness SU(3)

3/2 1 +1 [15]

3/2 3/2 0 [15]

3/2 1/2 0 [15] + [3] + [6]*

3/2 1 -1 [15] + [6]*

3/2 0 -1 [15] + [3]

3/2 1/2 -2 [15]

3/2 0 +1 [6]*

1/2 1 +1 [15]

1/2 3/2 0 [15]

1/2 1 -1 [15] + [6]

1/2 1/2 -2 [15]

1/2 0 +1 [6]

* This representation only occurs when qq are coupled to 6* This representation only occurs when qq are coupled to 6



Conclusions

• The Theta may have died*

• CSM takes a hit• Quark model, large Nc and other phenomenological

models remain as limited as before.• Jury is still out on heavy quark analogues

• The Theta may have died*

• CSM takes a hit• Quark model, large Nc and other phenomenological

models remain as limited as before.• Jury is still out on heavy quark analogues• The “Theta affair” re-focused attention on

diquarks

• Lots of phenomenological evidence for diquarks• Important spectroscopic consequences, especially

absence of exotics and scalar mesons• Role in DIS --- qualitative --- fragmentation functions

and higher twist• A systematic study of correlations in QCD: light quark

spectroscopy in the color non-singlet sectors

• The “Theta affair” re-focused attention on diquarks

• Lots of phenomenological evidence for diquarks• Important spectroscopic consequences, especially

absence of exotics and scalar mesons• Role in DIS --- qualitative --- fragmentation functions

and higher twist• A systematic study of correlations in QCD: light quark

spectroscopy in the color non-singlet sectors

*Resurrectio

n?

*Resurrectio

n?

Documents

R L Jaffe DIS05 Madison Life and Death among the Hadrons R. L. Jaffe DIS05 Madison April 2005 R. L. Jaffe DIS05 Madison April 2005 Update on the Theta