Toward dynamical understanding of the diquarks, pentaquarks and dibaryons

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Toward dynamical understanding of the diquarks,
pentaquarks and dibaryons

• Edward Shuryak
• Stony Brook

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Small digression new spectroscopy at TgtTc
We learned recently that the usual mesonic states
such as J/? persist above the deconfinement
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Moreover, there are multiple colored bound
statesESI.Zahed, hep-ph/0403127

• At TgtTc there is no confinement gt Hundreds of
  colored channels as well!

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Why diquarks and which ones?

• Instanton-induced t Hooft interaction has a
  strength 1/(Nc-1) in qq relative to bar-qq
• T. Schafer, E.Shuryak and Verbaarschot, Nucl.
  Phys. B412 (1994) 143. instanton liquid model
  very different N, ? correlators
• (soon confirmed by lattice, Negele et al)
• scalar mass is close to constituent quark mass
  in this model (400 MeV) namely MScalar 450 MeV
  and tensor MT 570 MeV

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What is the instanton liquid model?

• All gauge fields are due to instantons
• All quark fields are due to instanton zero modes
• It typically uses N200-300 instantons in a 4d
  Euclidean box and can be considered as N-body
  quark calculaiton all known correlation
  functions with light quarks agree with lattice
  ones (but they are much much cheaper)

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The schematic model has new symmetry relations,
unlike su(6) between states with different number
of quarks! (ES,Zahed, Phys.Lett.B58921-27,2004
hep-ph/0310270 Scalar diquarks are treated at
the same level as the constituent quarks So
?,pentaquarks and dibaryons can all be considered
to be 3-body objects
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Pentaquarks from diquarks(3 bodies are like
baryons, same Coulomb and confining forces)

• JaffeWilczek 2 scalar diquarks in P-wave
  anti-108
• However ? ML1 500 MeV is too expensive, M?1880
  MeV !
• We suggested a scalartensor diquarks instead,
  which leads to a ? mass consistent with 1540 MeV
  in this model

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A non-strange pentaquark
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Problems for a schematic modelone should not
trust it because of dibaryons
The famous H dibaryon in such notations is
So 3 diquarks are not identical and Formally BOSE
SYMMETRY does not apply One get then rather
light H! Contradicts to the fact that none of the
searches has found it! Rapp,Schafer,ES,Velkovsky,
Ann.phys.280(200)35 Suggested a P-wave state
(like Jaffe-Wilczek later for ?) motivated by a
repulsion in the s-wave
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Corrections to the schematic model

1. 2 instantons create independent attraction for 2
   diquarks this is included

(b) Diquarks have dentical quarks inside their
exchange leads to repulsive Pauli potetial
(c) The same strange quarks can be used for both
instanton this generates an attractive
interaction absent for a charm quark
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An attempt to do 4,5,6 quarks states in
ILM Non-local sources Allow for p-waves (Not
usually studied On the lattice!)
The issue of diquark interaction can be
addressed With correlation function with4-quark
propagators. The exchange diagram above is
included with the minus sign
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Example of the correlation functions obtained,
normalized to free (perturbative) ones at small
time ?
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Two ways to use the correlators

• The usual one go to the largest ? (Euclidean
  time) possible, get a mass from
• K exp(-M?) (very difficult)
• New one Measure the effective energy of a state
  at small ?, V(r) of the objects we put in by hand
  at distance r

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New diquark-diquark potential it happens to have
a repulsive core!
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The lowest 2-diquark mass(a single diquark M¼
600 MeV in this run)
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6 quark correlators and dibaryons
Inserting 3 diquarks at distance d from each
other allows to get also P-waves All
antisymmetrization diagrams included! Cases
studied
3-diquark Potentials can be defined in a similar
way Their core is large if all 3 are
close Approximate additivity of the core is found
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Dibaryon masses

• No light states with 3 scalar diquarks are found,
  for Nf3 and operators studied
• Color-singlet and flavor singlet H has a large
  mass 3 GeV

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Outreach to other fields

• The interaction of diquarks is obviously
  important for high density QCD. Defines whether
  BCS-BEC transition (or qq with zero binding) can
  be seen in this case
• Strongly coupled fermionic atoms repulsion
  between fermionic pairs (molecules) is known
  to be central to understanding Of this system.

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Conclusions

• Scalar and even tensor diquarks are dynamically
  generated by instantons and form self-bound
  clusters inside baryons, even without confinement
• Scalar diquark is as small and as heavy as a
  constituent quark and has the same color
  schematic model counts bodies and has new
  symmetries
• Scalartensor diquarks get good masses for
  pentaquarks but not dibaryons (ES_Zahed)
• Dynamical studies of diquark-diquark interaction
  are in progress, (D.PertotES)
• repuslive core found. No light dibaryons for
  sure, so far no clear light pentaquarks either