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 Arxiv:nucl-th/0509047

2. Outline • Motivation. • Bonn constituent-quark model. • Helicity amplitudes. Results for: • (J=1/2, 3/2) L*L and L*S0 • (J=1/2, 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,e’K+)L • Usual ansatz for the unmeasured EM form factors: dipoles with cutoffs 0.4 < L < 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 (HA’s) 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 L*‘s 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,e’K)L and which to the p(e,e’K)S process, and this for Q2 up to 6.0 GeV2. • Some S* resonances can contribute significantly to the p(e,e’K0)S+, but not to the p(e,e’K+)S0 process. • Further work: implementation of helicity amplitudes into an isobar model; GPD’s.

18. Kaon Electroproduction p(e,e’K)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,e’K)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 g=2 for the proton, yet measurements show that g is around 1. • For the L hyperon, the computed ratio is constant in the interval 2.0<Q2<6.0 GeV2 for g around 1.4. • Prediction of g=2 is based on helicity conservation for massless quarks. • Constituent quark masses are too large to be considered zero, especially the strange-quark mass (ms=660 MeV).

21. Outline • Introduction • Baryons & quarks • Strange baryons or hyperons • Kaon electroproduction p(e,e’K)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 • 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. Atom Baryon

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,e’K)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,e’K)Y process.

29. Constituent Quark Model (CQM) • Degrees of freedom are ‘constituent quarks’ (CQ’s)  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 CQ’s. Mesons contain one CQ and one anti-CQ. • Effective interactions between CQ’s.

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 CQ’s. • For resonances in a predominantly S=1/2 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 S=3/2 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.