1. Edward Shuryak Stony Brook
Toward dynamical understanding of the diquarks, pentaquarks and dibaryons
Edward Shuryak
Stony Brook
Hadronic physics, Fermilab Oct.2004, Shuryak

2. Small digression: new spectroscopy at T>Tc
We learned recently that the usual mesonic states such as J/ persist above the deconfinement
Hadronic physics, Fermilab Oct.2004, Shuryak

3. Hadronic physics, Fermilab Oct.2004, Shuryak
Moreover, there are multiple colored bound states ES+I.Zahed, hep-ph/
At T>Tc there is no confinement => Hundreds of colored channels as well!
Hadronic physics, Fermilab Oct.2004, Shuryak

4. 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
Hadronic physics, Fermilab Oct.2004, Shuryak

5. 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 N= 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)
Hadronic physics, Fermilab Oct.2004, Shuryak

6. Hadronic physics, Fermilab Oct.2004, Shuryak
The schematic model has new symmetry relations, unlike su(6) between states with different number of quarks!
(ES,Zahed, Phys.Lett.B589:21-27,2004 hep-ph/
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
Hadronic physics, Fermilab Oct.2004, Shuryak

7. Hadronic physics, Fermilab Oct.2004, Shuryak
Pentaquarks from diquarks (3 bodies are like baryons, same Coulomb and confining forces)
Jaffe+Wilczek: 2 scalar diquarks in P-wave: anti-10+8
However  ML=1» 500 MeV is too expensive, M=1880 MeV !
We suggested a scalar+tensor diquarks instead, which leads to a  mass consistent with 1540 MeV in this model
Hadronic physics, Fermilab Oct.2004, Shuryak

8. A non-strange pentaquark
Hadronic physics, Fermilab Oct.2004, Shuryak

9. Hadronic physics, Fermilab Oct.2004, Shuryak
Problems for a schematic model: one 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:
Hadronic physics, Fermilab Oct.2004, Shuryak

10. Corrections to the schematic model
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
Hadronic physics, Fermilab Oct.2004, Shuryak

11. Hadronic physics, Fermilab Oct.2004, Shuryak
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
Hadronic physics, Fermilab Oct.2004, Shuryak

12. Hadronic physics, Fermilab Oct.2004, Shuryak
Example of the correlation functions obtained, normalized to free (perturbative) ones at small time 
Hadronic physics, Fermilab Oct.2004, Shuryak

13. 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
Hadronic physics, Fermilab Oct.2004, Shuryak

14. New diquark-diquark potential: it happens to have a repulsive core!
Hadronic physics, Fermilab Oct.2004, Shuryak

15. The lowest 2-diquark mass (a single diquark M¼ 600 MeV in this run)
Hadronic physics, Fermilab Oct.2004, Shuryak

16. 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
Hadronic physics, Fermilab Oct.2004, Shuryak

17. Hadronic physics, Fermilab Oct.2004, Shuryak
Dibaryon masses
No light states with 3 scalar diquarks are found, for Nf=3 and operators studied
Color-singlet and flavor singlet H has a large mass » 3 GeV
Hadronic physics, Fermilab Oct.2004, Shuryak

18. 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.
Hadronic physics, Fermilab Oct.2004, Shuryak

19. Hadronic physics, Fermilab Oct.2004, Shuryak
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
Scalar+tensor diquarks get good masses for pentaquarks but not dibaryons (ES_Zahed)
Dynamical studies of diquark-diquark interaction are in progress, (D.Pertot+ES)
repuslive core found. No light dibaryons for sure, so far no clear light pentaquarks either
Hadronic physics, Fermilab Oct.2004, Shuryak