Theoretical Models for Exotic Baryons

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Theoretical Models for Exotic Baryons
Models of the nucleon chiral soliton vs quark
models The strange spin of the nucleon Interpretat
ion of new exotic baryons

• John Ellis
• DESY,
• Feb. 1st, 2005

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Models of the Nucleon
Quarks and/or solitons?
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Models of Nucleon Structure

• Naïve quark model
• MQ 300 MeV
• Wave function QQQ
• Sea of extra qqbar pairs generated perturbatively
• Usual SU(3) multiplets
• Explains OZI rule
• Proton spin Sum of valence quark spins
• Sum of quark spins ½
• Few intrinsic ssbar

• Chiral soliton model
• MU,D few MeV,
• MS 100 MeV
• Intrinsic qqbar pairs in nucleon wave function
• Exotic SU(3) multiplets
• Evasions of OZI rule
• Proton spin Orbital angular momentum
• Sum of quark spins 0
• Many polarized ssbar

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Baryons in Chiral Soliton Model

• Baryons clouds of p, K, ?8 mesons
• ? many ssbar pairs
• Baryon spin due to rotation of meson cloud
• ? Spin orbital angular momentum
• ? no ?0 coupling
• ? ssbar pairs polarized
• Exotic baryons ? excitations of meson cloud

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QCD in Two Dimensions

• Explicit classical soliton _at_ strong coupling
• Finite radius
• Calculable quantum corrections _at_ O(1/Nc)
• Higher multi-qqbar excited states

JE Frishman, in preparation
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Exotic Antidecuplet Predicted in Chiral Soliton
Model
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The Strange Spin of the Nucleon
My personal introduction to chiral soliton models
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Proton Spin in Chiral-Soliton Model

• Proton spin sum rule
• ½ ½(?u ?d ?s) ?G Lz
• ?SM ? small sum of quark contributions to spin
• ?u ?d ?s 0 needs ?s lt 0
• ?SM ? proton spin due to orbital angular
  momentum
• Lz ½
• ?SM ? small gluon contribution to spin
• ?G 0
• in simple extension of ?SM to include gluons
• Predictions subject to 1/Nc, ms corrections
  30?

Brodsky JE Karliner, 1988
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Why Should the Nucleon be Strange?

• The vacuum is strange
• chiral symmetry for p, K mesons ?
• Cannot be expected to disappear when one inserts
  qqq test charge into vacuum
• Expected to be generated in perturbative QCD
• s sbar ? gluon ? quark
• Also, generated by non-perturbative effects
• instantons, chiral soliton models

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Pion-Nucleon s Term

• Measured in low-energy p-N scattering
• Related to strange scalar density
• Two recent determinations
• Maybe y ½ ?

Important later for chiral soliton models of
exotic baryons
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The Strange Spin of the Nucleon

• Naïve interpretation of polarized DIS structure
  fns
• One-particle inclusive particle production
  (HERMES)
• But beware corrections to independent
  fragmentation, positivity bounds

The strange-quark matrix elements in the nucleon
could be small or large, depending on the quantum
numbers
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Measurements of Gluon Polarization
Polarized strangeness ?s or gluons ?G ?s ? ?s
(a/p)?G?
HERMES asymmetry in hadron-pair production at
high pT
SMC asymmetry in hadron-pair production at high
pT
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Most Recent Measurements
PHENIX double helicity asymmetry in pp ?p0 at
high pT
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Compilation of ?G Measurements
Indirect, using polarized structure function
data BBA ?G 1.026 0.549 BBB ?G 0.031
0.669 AAC ?G 0.533 1.931
Direct, using hadron production
asymmetries HERMES _at_ 0.06 lt xG lt 0.28 ?G
0.41 0.18 0.03 SMC _at_ lt?Ggt 0.07 ?G
0.20 0.28 0.10 COMPASS _at_ ltxGgt 0.13 ?G
0.06 0.31 0.06
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Estimates of ?G Integral
Use model shapes for ?G, adjust
normalization BB3 ?G 0.42 0.54 BB4 ?G
0.57 0.69 AAC ?G 0.79 0.39 _at_ Q2 5 GeV2
No hint of large ?G
JE Karliner, hep-ph/0501115
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Comparison with Models for ?G
Need more measurements
JE Karliner, hep-ph/0501115
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Discovery of Exotic Baryons?
Still needs to be confirmed
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The Exotic Revolution?
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Measurements of ? Properties
Stringent upper limits G lt 1(?) MeV from
KN scattering experiments
Inconsistent masses in different experiments?
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Chiral-Soliton Predictions Revisited
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Chiral-Soliton Predictions Revisited
J.E., Karliner Praszalowicz hep-ph/0401127
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Mass Predictions in Chiral Soliton Model
Decuplet-Octet, Antidecuplet-Octet mass
differences where I1, I2 are soliton moments
of inertia. Including corrections of higher order
in Nc and ms where ß, ? related to
soliton moments of inertia Guadagnini
relation

J.E., Karliner Praszalowicz hep-ph/0401127
OK experiment
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Chiral-Soliton Model Parameters
Fix two combinations of a, ß, ? using octet and
decuplet masses Can fix third combination
using p-N S term Using recent range of
values Find
J.E., Karliner Praszalowicz hep-ph/0401127
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Estimating Antidecuplet Masses
Model range for soliton moment of inertia Find
antidecuplet-octet mass difference Antidecuplet
mass splittings Resulting range for T, ?
masses Overall range
J.E., Karliner Praszalowicz hep-ph/0401127
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Exotic Baryon Spectrum s Term
Chiral soliton mass formula
numerically
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Baryon ? Baryon Meson Couplings
Related by generalized Goldberger-Treiman to
axial-current couplings Expressions for
baryon-meson couplings G2 related to
singlet axial-current matrix element
small? Other combinations related to ?, N decay
couplings
J.E., Karliner Praszalowicz hep-ph/0401127
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O(1/Nc) Corrections to Decay Rates
Need to estimate G0,1,2 Estimate G2 from
spin-dependent structure functions Model
calculations ??pN coupling to estimate
G0,1 Estimate of T?KN coupling in this
approximation Significant suppression of T
decay rate not enough?
J.E., Karliner Praszalowicz hep-ph/0401127
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SU(3) Corrections to Decay Rates
SU(3) corrections to pNN coupling SU(3)
corrections to ??pN coupling due to
representation mixing SU(3) corrections to
T?KN coupling due to representation
mixing Large suppression of T decay rate
possible not for other antidecuplet baryons
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Baryon Couplings in Soliton Model
p-Nucleon coupling Consistent with experiment
J.E., Karliner Praszalowicz hep-ph/0401127
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Predictions for Other Exotic Baryons
Masses of 27-plet states Masses for nominal
parameters Mass difference with T in
27-plet Typical value 63 MeV Similarly for
? in 27-plet Typical value 19 MeV Also
35-plet,
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Spectrum of Antidecuplet 27 Baryons
Using ? and ?-- masses
J.E., Karliner Praszalowicz hep-ph/0401127
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Quark Model Approaches
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Understanding T in Quark Language
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Diquark-Triquark Structure?
Karliner Lipkin hep-ph/0307243
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Possible Diquark-Triquark Configurations
Karliner Lipkin hep-ph/0307243
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Estimating T Mass
Karliner Lipkin hep-ph/0307243
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Predictions for Heavy-Flavour Exotics
Karliner Lipkin hep-ph/0307243
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Diquarks
Jaffe Wilczek hep-ph/0307341
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Diquark Model for T Baryon
Jaffe Wilczek hep-ph/0307341
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Predictions Postdictions
Jaffe Wilczek hep-ph/0307341
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Discriminating between Models
also 27 multiplet
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Summary

• Complementary models of nucleon structure
• naïve quark model, chiral soliton
• Experimental evidence of hidden strangeness
• p-N s term, polarized DIS
• Boost for chiral solitons from exotic baryons?
• Predicted in soliton model,
• Spectroscopy depends on p-N s term large?
• New, less naïve quark models
• Expect more twists in the strange, exotic story!

? solitons