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Structure of strange baryons

Structure of strange baryons. Alfons Buchmann University of Tuebingen. Introduction SU(6) spin-flavor symmetry Observables Results Summary. Hyperon 2006, Mainz, 9-13 October 2006. 1. Introduction. Hadrons with nonzero strangeness add a new dimension to matter

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Structure of strange baryons

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  1. Structure of strange baryons Alfons Buchmann University of Tuebingen • Introduction • SU(6) spin-flavor symmetry • Observables • Results • 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. S n p D- D0 D+ D++ S*+ S*- S*0 S+ S0 S- L0 X*- X*0 X- X0 W SU(3) flavor multiplets 0 -1 -2 octet decuplet -3 J=3/2 J=1/2 T3 -1 -1/2 0 +1/2 +1 -3/2 -1/2 +1/2 +3/2

  5. symmetry breaking along strangeness direction by hypercharge operator Y Relations between observables Group algebra relates symmetry breaking within a multiplet (Wigner-Eckart theorem) Y hypercharge S strangeness T3 isospin M0, M1, M2 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. S T3 SU(6) spin-flavor supermultiplet ground state baryon supermultiplet

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

  10. SU(6) spin-flavor is a symmetry of QCD SU(6) symmetry is exact in the large NC limit of QCD. For finite NC,the symmetry is broken. The symmetry breaking operators can be classified according to powers of 1/NC 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/NC.

  11. two-body three-body 1/NC expansion of QCD processes 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 SU(3) symmetry breaking parameter in the following r=0.6

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

  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 ei...quark charge i...quark spin

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

  20. ek ei g g SU(6) spin-flavor symmetry breaking by spin-flavor dependent two- and three-quark operators e.g. electromagnetic current operator ei ... quark charge si ... quark spin mi ... quark mass 2-quark current 3-quark current

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

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

  23. 4. Results

  24. Some relations between charge radii A. J. B., R. F. Lebed, Phys. Rev. D 62, 096005 (2000) S equal spacing rule from (*) r²(S-)=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(S-)=0.61(12)(9) fm² (Selex experiment, I. Eschrich et al. PLB522, 233(2001))

  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 rn2 A. Buchmann, E. Hernandez, A. Faessler, Phys. Rev. C 55, 448 (1997)

  32. comparison with experiment Tiator et al. (2003) experiment Blanpied et al. (2001) experiment theory 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 Use r= 1 fm, Q0= 0.11 fm², then solve for a and b a/b=1.1 large! 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

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