Structure of strange baryons

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
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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

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S
SU(3) flavor multiplets
0
-1
-2
octet
decuplet
-3
J3/2
J1/2
T3
-1/2
1/2
-1
0
1
-3/2
-1/2
3/2
1/2
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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
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Gell-Mann Okubo mass formula
Equal spacing rule
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SU(6) spin-flavor symmetry
ties together SU(3) multiplets with different
spin and flavor into SU(6) spin-flavor
supermultiplets
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SU(6) spin-flavor supermultiplet
ground state baryon supermultiplet
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Gürsey-Radicati mass formula
SU(6) symmetry breaking part
Relations between octet and decuplet masses
e.g.
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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.
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1/NC expansion of QCD processes
strong coupling
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SU(6) spin-flavor symmetry breaking by
spin-flavor dependent two- and three-quark
operators
These lift the degeneracy between octet and
decuplet baryons.
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SU(3) symmetry breaking
SU(3) symmetry breaking parameter
in the following r0.6
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General spin-flavor operator O
Oi all invariants in spin-flavor space that
are allowed by Lorentz invariance and internal
symmetries of QCD
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Constants A, B, and C parametrize orbital and
color matrix elements. They are determined from
experiment.
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3. Observables

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

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Multipole expansion of baryon charge density
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Charge radius operator
ei...quark charge ?i...quark spin
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Origin of these operator structures
1-quark operator
2-quark operators (exchange currents)
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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
3-quark current
2-quark current
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What is the shape of octet and decuplet baryons?
oblate
prolate
A. J. Buchmann and E. M. Henley, Phys. Rev. C63,
015202 (2001)
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Quadrupole moment operator
two-body
three-body
no one-body contribution
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4. Results
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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))
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Decuplet quadrupole moments
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Similar table for octet-decuplet transition
quadrupole moments
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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)
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Diagonal quadrupole moments
These and the following 7 relations hold
irrespective of how badly SU(3) is broken.
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Transition quadrupole moments
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4 r-dependent relations
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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)
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comparison with experiment
Tiator et al. (2003)
experiment
Blanpied et al. (2001)
experiment
theory
Buchmann et al. (1996)
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data electro-pionproduction curves elastic
neutron form factors
A.J. Buchmann, Phys. Rev. Lett. 93, 212301
(2004).
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transition quadrupole moments
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diagonal quadrupole moments
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Intrinsic quadrupole moment of nucleon
Use r 1 fm, Q0 0.11 fm², then solve for a and b
a/b1.1 large!
A. J. Buchmann and E. M. Henley, Phys. Rev. C63,
015202 (2001)
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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