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

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

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

                 np S T3T /2+1/20+1-3/2-1/2+3/2+1/2 J=1/2 J=3/2 SU(3) flavor multiplets octet decuplet

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

Gell-Mann & Okubo mass formula Equal spacing rule

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

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

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

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.

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

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

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

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

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

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

Multipole expansion of baryon charge density

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

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

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

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

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

4. Results

Some relations between charge radii from (*) r²(  - )=0.676 (66) fm² ( A. Buchmann, R. F. Lebed, Phys. Rev. D 67, (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, (2000)

Decuplet quadrupole moments

Similar table for octet-decuplet transition quadrupole moments

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, (2002)

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

Transition quadrupole moments

4 r-dependent relations

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)

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

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

transition quadrupole moments

diagonal quadrupole moments

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, (2001)

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