1. Structure of strange baryons Alfons Buchmann University of Tuebingen 1.Introduction 2.SU(6) spin-flavor symmetry 3.Observables 4.Results 5.Summary Hyperon 2006, Mainz, 9-13 October 2006

2. 1. Introduction Hadrons with nonzero strangeness add a new dimension to matter provide evidence for larger symmetries are a testing ground of quantum field theories have important astrophysical implications improve our understanding of ordinary matter yet little is known about their spatial structure, such as their size and shape

3. 2. Strong interaction symmetries Strong interactions are approximately invariant under SU(3) flavor and SU(6) spin-flavor symmetry transformations. These symmetries lead to: conservation laws degenerate hadron multiplets relations between observables

4.                  np S T3T3 0 -3 -2 -1/2+1/20+1-3/2-1/2+3/2+1/2 J=1/2 J=3/2 SU(3) flavor multiplets octet decuplet

5. Group algebra relates symmetry breaking within a multiplet (Wigner-Eckart theorem) Y hypercharge S strangeness T 3 isospin symmetry breaking along strangeness direction by hypercharge operator Y Relations between observables M 0, M 1, M 2 from experiment

6. Gell-Mann & Okubo mass formula Equal spacing rule

7. SU(6) spin-flavor symmetry ties together SU(3) multiplets with different spin and flavor into SU(6) spin-flavor supermultiplets

8. SU(6) spin-flavor supermultiplet S T3T3 ground state baryon supermultiplet

9. Gürsey-Radicati mass formula Relations between octet and decuplet masses SU(6) symmetry breaking part e.g.

10. SU(6) spin-flavor is a symmetry of QCD SU(6) symmetry is exact in the large N C limit of QCD. For finite N C, the symmetry is broken. The symmetry breaking operators can be classified according to powers of 1/N C attached to them. This leads to a hierachy in importance of one-, two-, and three-quark operators, i.e., higher order symmetry breaking operators are suppressed by higher powers of 1/N C.

11. 1/N C expansion of QCD processes two-bodythree-body strong coupling

12. SU(6) spin-flavor symmetry breaking by spin-flavor dependent two- and three-quark operators These lift the degeneracy between octet and decuplet baryons.

13. SU(3) symmetry breaking in the following r=0.6 SU(3) symmetry breaking parameter

14. O [i] all invariants in spin-flavor space that are allowed by Lorentz invariance and internal symmetries of QCD one-bodytwo-body three-body General spin-flavor operator O

15. Constants A, B, and C parametrize orbital and color matrix elements. They are determined from experiment.

16. 3. Observables Baryon structure information encoded e.g. in charge form factor: size (charge radii) shape (quadrupole moments)

17. Multipole expansion of baryon charge density

18. Charge radius operator e i...quark charge  i...quark spin

19. 1-quark operator 2-quark operators (exchange currents) Origin of these operator structures

20. SU(6) spin-flavor symmetry breaking by spin-flavor dependent two- and three-quark operators   eiei ekek e.g. electromagnetic current operator e i... quark charge  i ... quark spin m i... quark mass 3-quark current2-quark current

21. What is the shape of octet and decuplet baryons? A. J. Buchmann and E. M. Henley, Phys. Rev. C63, 015202 (2001) prolate oblate

22. Quadrupole moment operator two-body three-body no one-body contribution

23. 4. Results

24. Some relations between charge radii from (*) r²(  - )=0.676 (66) fm² ( A. Buchmann, R. F. Lebed, Phys. Rev. D 67, 016002 (2003)) theoretical range due to size of SU(3) flavor symmetry breaking r²(  - )=0.61(12)(9) fm² (Selex experiment, I. Eschrich et al. PLB522, 233(2001))  equal spacing rule A. J. B., R. F. Lebed, Phys. Rev. D 62, 096005 (2000)

25. Decuplet quadrupole moments

26. Similar table for octet-decuplet transition quadrupole moments

27. Relations between observables There are 18 quadrupole moments, 10 diagonal and 8 tansitional. These are expressed in terms of two constants B and C.  There must be 16 relations between them. 12 relations out of 16 hold irrespective of how badly SU(3) flavor symmetry is broken. A. J. Buchmann and E. M. Henley, Phys. Rev. D65, 07317 (2002)

28. Diagonal quadrupole moments These and the following 7 relations hold irrespective of how badly SU(3) is broken.

29. Transition quadrupole moments

30. 4 r-dependent relations

31. Numerical results Determination of constant B from relation between N  transition quadrupole moment and neutron charge radius r n 2 A. Buchmann, E. Hernandez, A. Faessler, Phys. Rev. C 55, 448 (1997)

32. comparison with experiment experiment theory Tiator et al. (2003) Blanpied et al. (2001) Buchmann et al. (1996)

33. data: electro-pionproduction curves: elastic neutron form factors A.J. Buchmann, Phys. Rev. Lett. 93, 212301 (2004).

34. transition quadrupole moments

35. diagonal quadrupole moments

36. Intrinsic quadrupole moment of nucleon a/b=1.1 large! Use r= 1 fm, Q 0 = 0.11 fm², then solve for a and b A. J. Buchmann and E. M. Henley, Phys. Rev. C63, 015202 (2001)

37. 5. Summary SU(6) spin-flavor analysis  relations between baryon quadrupole moments decuplet baryons have negative quadrupole moments of the order of the neutron charge radius  large oblate intrinsic deformation Experimental determination of Q  is perhaps possible with Panda detector at GSI