Helicity amplitudes and electromagnetic decays of strange baryon resonances

1
Helicity amplitudes and electromagnetic decays of
strange baryon resonances
Tim Van Cauteren, Jan Ryckebusch,
SSF, Ghent University
Bernard Metsch, Herbert-R. Petry
HISKP, Bonn University
Arxivnucl-th/0509047
2
Outline

• Motivation.
• Bonn constituent-quark model.
• Helicity amplitudes. Results for
• (J1/2, 3/2) L?L and L?S0
• (J1/2, 3/2) S0?L and S0,?S0,
• Conclusions and outlook.

3
u-channel Diagram

• Photon couples to Y() in u-channel of kaon
  production from the nucleon.
• The EM form factors of this g-Y() vertex are
  not known experimentally.

Can we compute these form factors ?
4
Uncertainties in the Isobar Model
p(e,eK)L

• Usual ansatz for the unmeasured EM form factors
  dipoles with cutoffs 0.4 lt L lt 1.0 GeV.
• Uncertainties up to 50.
• Can we reduce these uncertainties ?

S. Janssen et al., Phys. Rev. C67, R052201
(2003). R. M. Mohring et al. (Hall C, JLab),
Phys. Rev. C67, 055205 (2003).
5
Bethe-Salpeter Equation

• The Bethe-Salpeter amplitudes can be calculated
  from the integral equation with interaction
  kernels as integral kernels.
• We use instantaneous forces a 3q confining
  interaction and a 2q residual interaction, the t
  Hooft instanton induced interaction.

6
Current Matrix Elements
7
Helicity Amplitudes (HAs)

• Definitions

8
L (J 1/2)
L ? L(1116)
L ? S0(1193)
(MeV)
(MeV)
9
L (J 3/2)
L ? L(1116)
L ? S0(1193)
-0.038
-0.070
10
Isospin Asymmetries
11
L Conclusions

• The first excited state of a certain spin and
  parity couples considerably stronger to a photon
  with intermediate virtuality Q2 than to a real
  photon.
• The lowest-lying Ls with certain quantum
  numbers decay preferably the the L(1116) the 2nd
  and 3rd excited states decay preferentially to
  the S0(1193).
• The computed widths for the S01(1405) ? L(1116)
  and S01(1405) ? S0(1193) EM decays are larger
  than the experimentally known values. This lends
  support to the special structure of this
  resonance.
• The width for the S01(1670) ? S0(1193) EM decay
  turns out to be rather large.

12
S0 (J 1/2)
S0 ? L(1116)
S0 ? S0(1193)
13
S (J 1/2)
S- ? S-(1193)
S ? S(1193)
14
S0 (J 3/2)
S0 ? L(1116)
S0 ? S0(1193)
15
S (J 3/2)
S- ? S-(1193)
S ? S(1193)
16
S Conclusions

• The first excited state of a certain spin and
  parity can couple considerably stronger to a
  photon with intermediate virtuality Q2 than to a
  real photon.
• The EM decay width of a S to the S ground
  state can be considerably larger for the S0 to
  the S0(1193), e.g. for the P11(1660).
• Very large widths are reported for the S11(1620),
  decaying electromagnetically to the L and S
  ground states.

17
Conclusions Outlook

• The computed helicity amplitudes show which
  hyperons and hyperon resonances couple more or
  less strongly to real and virtual photons.
• One can predict which hyperon resonances will
  contribute preferentially to the p(e,eK)L and
  which to the p(e,eK)S process, and this for Q2
  up to 6.0 GeV2.
• Some S resonances can contribute significantly
  to the p(e,eK0)S, but not to the p(e,eK)S0
  process.
• Further work implementation of helicity
  amplitudes into an isobar model GPDs.

18
Kaon Electroproduction
p(e,eK)Y

• An electron interacts electromagnetically with a
  proton, resulting in the creation of a kaon and
  hyperon.
• A kaon is a strongly interacting boson (meson)
  with a strange valence (anti-)quark.
• The lepton part is described by QED, the hadron
  part by QED and QCD ? model.

19
Conclusions (1)

• The p(e,eK)Y process is most easily described in
  terms of hadrons ? isobar model.
• The input parameters (coupling constants, form
  factors) are properties of the hadrons involved
  in the reaction, and they are not always known
  experimentally. This induces a large degree of
  uncertainty.
• This holds particular true if the involved hadron
  is a hyperon or hyperon resonance, for which the
  experimental information concerning their
  electromagnetic properties is rather poor.
• To controle the induced uncertainties, the
  unmeasured electromagnetic properties of Y()s
  can be computed in the Lorentz-covariant Bonn
  constituent quark model.

20
Qg F2/F1

• Perturbative QCD predicts that g2 for the
  proton, yet measurements show that g is around 1.
• For the L hyperon, the computed ratio is constant
  in the interval 2.0ltQ2lt6.0 GeV2 for g around 1.4.

• Prediction of g2 is based on helicity
  conservation for massless quarks.
• Constituent quark masses are too large to be
  considered zero, especially the strange-quark
  mass (ms660 MeV).

21
Outline

• Introduction
• Baryons quarks
• Strange baryons or hyperons
• Kaon electroproduction p(e,eK)Y
• Tree-level isobar model
• Bonn constituent quark model
• Computed electromagnetic properties
• Form factors for the octet hyperons
• Helicity amplitudes for the electromagnetic
  transitions L?L, L?S0, S0?L and S0,?S0,.
• Conclusions

22
Baryons
Nucleus
Atom
Baryon

• Baryons interact strongly.
• Baryons are fermions.
• The number of baryons is conserved.
• The most known baryons are the proton and
  neutron, the main constituents of nuclei.
• Baryons are made up of quarks and gluons.

23
Quarks

• Quarks come in six different flavours with
  different masses.
• For the baryons considered in this work, only the
  three lightest quarks (u,d,s) play a role.
• Non-exotic baryons are composites of three
  valence quarks, gluons, and quark/antiquark pairs
  (sea quarks).

24
The Baryon Octet

• The valence quarks are responsible for the
  ordering of the lightest baryons with spin ½
  according to two quantum numbers Y and T3.
• Strange baryons, or hyperons, have at least one
  strange (s) valence quark.
• The lightest hyperons are the L, the S-triplet
  and the X-doublet.

25
The Tree-Level Isobar Model (1)

• The reaction dynamics of the p(g,K)Y process can
  be described with isobar (hadronic) degrees of
  freedom.
• The formalism is that of perturbative
  relativistic quantum field theory for point-like
  particles ? Feynman diagrams.
• At tree-level (lowest order), the dynamics
  involve
• An electromagnetic vertex (g-hadron coupling).
• A strong vertex.
• A propagating hadron (baryon, kaon or one of
  their resonances).

26
The Tree-Level Isobar Model (2)
s-channel
u-channel
t-channel

• The sum of the Born terms (upper row) is gauge
  invariant.
• The terms corresponding to exchanged resonances
  are separately gauge in variant.

27
Baryon Resonances

• In Quantum Physics, a system of (interacting)
  particles induces a spectrum.
• Due to confinement, one has a bound-state
  spectrum.
• The excited states of the baryon spectrum are
  called baryon resonances.
• If the (non-exotic) baryon resonance contains at
  least one strange valence quark, one speaks of a
  hyperon resonance.
• The kaon electroproduction reaction p(e,eK)Y is
  well-suited to study both nonstrange and strange
  baryon resonances.

28
Form Factors

• Both the hadronic and the electromagnetic (EM)
  vertex can be modified with form factors to
  parameterize the finite extension of the
  particles involved.
• These form factors serve as input for isobar
  models.
• Not all form factors are measured experimentally.
  This effects the quality of the isobar-model
  results for the p(e,eK)Y process.

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Constituent Quark Model (CQM)

• Degrees of freedom are constituent quarks
  (CQs) ? valence quarks surrounded by cloud of
  gluons and quark-antiquark pairs.
• Quantum numbers of the hyperon (generally hadron)
  are determined by the CQ quantum numbers and the
  interactions between them.
• Baryons contain three CQs. Mesons contain one CQ
  and one anti-CQ.
• Effective interactions between CQs.

30
Form Factors

• F1 and F2 are the Dirac and Pauli form factors.
• Related to the Sachs form factors GE and GM.

31
L, S0, S, S-

• Dot-dashed lines from H.-Ch. Kim et al., Phys.
  Rev. D53, 4013 (1996).
• Dotted lines from A. Silva, private
  communication.
• (chiral quark/soliton model)

32
X0, X-
33
S ? L
34
Helicity Asymmetries (1)
35
Helicity Asymmetries (2)

• At higher Q2, the photon preferentially couples
  to the CQs.
• For resonances in a predominantly S1/2 SUsf(6)
  state
• Process (a) gives the main contribution to the
  A1/2. The photon couples to the CQ.
• Process (b) gives the main contribution to the
  A3/2. The photon couples to the baryon.
• For resonances in a predominantly S3/2 SUsf(6)
  state
• Process (a) still gives the main contribution to
  the A1/2. The photon couples to the CQ.
• Process (c) now gives the main contribution to
  the A3/2. The photon couples to the CQ.

36
Helicity Asymmetries (3)
37
Static Properties
Magnetic moments (mN)
Magnetic ms radii (fm2)
Electric ms radii (fm2)
exp
calc
calc
calc
Adamovich et al. 0.91 0.32 (stat.) 0.40
(syst.) fm2 Eschrich et al. 0.61 0.12
(stat.) 0.09 (syst.) fm2
38
Octet Hyperons

• The magnetic form factors are dipole-like with
  cutoff masses ranging from 0.79 GeV for the S to
  1.14 GeV for the L.
• The electric form factors of the neutral hyperons
  differ substantially from the neutron electric
  form factor.
• Computed magnetic moments are in excellent
  agreement with experimental values.
• Also the electric radius of the S- hyperon is
  well-reproduced.