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R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
• Positive sightings of the Theta• Positive sightings of the Theta
Dzierba, Meyer, Szczepaniak hep-ex/0412077Dzierba, Meyer, Szczepaniak hep-ex/0412077
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
• Negative non-sightings of the Theta • Negative non-sightings of the Theta
Dzierba, Meyer, Szczepaniak hep-ex/0412077Dzierba, Meyer, Szczepaniak hep-ex/0412077
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
• 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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
• More detail• More detail
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
Same reaction, Phys. Lett. B572 (2003)
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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!
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
?? ?? ??
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
Correlations and
classification
Correlations and
classification• Confinement• Confinement
• correlations ?
• correlations ?
• Color, flavor, spin antisymmetry
• Color, flavor, spin antisymmetry
• Chiral symmetry breaking
• Chiral symmetry breaking
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
Diquarks
Flavor Color Spin
-8
8/3
“Good”“Good”“Bad”“Bad”
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
• 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.
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
• 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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
• 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.
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
Scalar mesons: a supernumerary nonetScalar mesons: a supernumerary nonet
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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...
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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.
• The “ affair” suggests that correlations in QCD can be studied by studying color non-singlet light quark systems neutralized by heavy quark spectator.
• The “ affair” suggests that correlations in QCD can be studied by studying color non-singlet light quark systems neutralized by heavy quark spectator.
• 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!
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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?)
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
“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?)
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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
R L Jaffe DIS05 Madison
R L Jaffe DIS05 Madison
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?