Helicity amplitudes and electromagnetic decays of strange baryon

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

Outline • Motivation. • Bonn constituent-quark model. • Helicity amplitudes. Results for: – (J=1/2, 3/2) L* L and L* S 0 – (J=1/2, 3/2) S 0* L and S 0, ±* S 0, ± • Conclusions and outlook.

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 ?

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 Ge. V. • Uncertainties up to 50%. • Can we reduce these uncertainties ? S. Janssen et al. , Phys. Rev. C 67, R 052201 (2003). R. M. Mohring et al. (Hall C, JLab), Phys. Rev. C 67, 055205 (2003).

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 3 q confining interaction and a 2 q residual interaction, the ‘t Hooft instanton induced interaction.

Current Matrix Elements

Helicity Amplitudes (HA’s) Definitions

L* (J = 1/2) L* L(1116) Resonance S 01(1405) Gcalc 0. 912 (Me. V) Gexp 0. 027± 0. 008 (Me. V) L* S 0(1193) Resonance Gcalc Gexp S 01(1405) 0. 233 0. 010± 0. 004/ 0. 023± 0. 007 S 01(1670) 3. 827 ----

L* L(1116) Resonance D 03(1520) Gcalc 0. 258 L* (J = 3/2) Gexp 0. 125+0. 042 -0. 038 L* S 0(1193) Resonance D 03(1520) Gcalc 0. 157 Gexp 0. 304+0. 076 -0. 070

Isospin Asymmetries

L* : Conclusions • The first excited state of a certain spin and parity couples considerably stronger to a photon with intermediate virtuality Q 2 than to a real photon. • The lowest-lying L*‘s with certain quantum numbers decay preferably the L(1116); the 2 nd and 3 rd excited states decay preferentially to the S 0(1193). • The computed widths for the S 01(1405) L(1116) and S 01(1405) S 0(1193) EM decays are larger than the experimentally known values. This lends support to the special structure of this resonance. • The width for the S 01(1670) S 0(1193) EM decay turns out to be rather large.

S 0* (J = 1/2) S 0* L(1116) Resonance S 0* S 0(1193) Resonance P 11(1660) Gcalc 0. 451 P 11(1660) 0. 0578 S 11(1620) 1. 551 S 11(1620) 0. 688 Gcalc

S±* (J = 1/2) S+* S+(1193) Resonance S-* S-(1193) Resonance P 11(1660) Gcalc 0. 733 P 11(1660) 0. 141 S 11(1620) 5. 955 S 11(1620) 0. 631 Gcalc

S 0* (J = 3/2) S 0* L(1116) S 0* S 0(1193)

S±* (J = 3/2) S+* S+(1193) S-* S-(1193)

S* : Conclusions • The first excited state of a certain spin and parity can couple considerably stronger to a photon with intermediate virtuality Q 2 than to a real photon. • The EM decay width of a S±* to the S± ground state can be considerably larger for the S 0* to the S 0(1193), e. g. for the P 11(1660). • Very large widths are reported for the S 11(1620), decaying electromagnetically to the L and S ground states.

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 Q 2 up to 6. 0 Ge. V 2. • Some S* resonances can contribute significantly to the p(e, e’K 0)S+, but not to the p(e, e’K+)S 0 process. • Further work: implementation of helicity amplitudes into an isobar model; GPD’s.

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.

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.

Qg F 2/F 1 • 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<Q 2<6. 0 Ge. V 2 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 Me. V).

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* S 0, S 0* L and S 0, ±* S 0, ±. • Conclusions

Baryons Nucleus Atom • • 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.

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).

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 T 3. • 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.

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).

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.

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.

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.

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.

Form Factors • F 1 and F 2 are the Dirac and Pauli form factors. • Related to the Sachs form factors GE and GM.

L, S 0, S+, S- Dot-dashed lines from: H. -Ch. Kim et al. , Phys. Rev. D 53, 4013 (1996). Dotted lines from: A. Silva, private communication. (chiral quark/soliton model)

X 0, X -

S→L

Helicity Asymmetries (1)

Helicity Asymmetries (2) • At higher Q 2, 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 A 1/2. The photon couples to the CQ. – Process (b) gives the main contribution to the A 3/2. 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 A 1/2. The photon couples to the CQ. – Process (c) now gives the main contribution to the A 3/2. The photon couples to the CQ.

Helicity Asymmetries (3)

Static Properties Magnetic moments (m. N) L S+ S 0 S|S 0→L| X 0 X- Magnetic ms radii (fm 2) Electric ms radii (fm 2) -0. 613 -0. 61 0. 40 0. 038 2. 458 2. 47 0. 69 0. 79 (0. 649) 0. 73 0. 69 0. 150 -1. 160 -0. 99 0. 81 0. 49 1. 61 1. 52 1. 96 -0. 120 -1. 25 -1. 33 0. 47 0. 140 -0. 65 -0. 57 0. 38 0. 47 exp calc Adamovich et al. : 0. 91 ± 0. 32 (stat. ) ± 0. 40 (syst. ) fm 2 Eschrich et al. : 0. 61 ± 0. 12 (stat. ) ± 0. 09 (syst. ) fm 2 calc

Octet Hyperons • The magnetic form factors are dipole-like with cutoff masses ranging from 0. 79 Ge. V for the S+ to 1. 14 Ge. V 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.