May 22-26, Italy1

Nucleon form factors and N-Δ transitions in a hypercentral constitue

nt quark model

D. Y. Chen, Y. B. Dong,Institute of High Energy Physics, Beijing 10049, P. R. China

M. M. Giannini and E. SantopintoDepartimento di Fisica dell’ Universita di Genova and

INFN, Sezione di Genova, Italy

May 22-26, Italy2

ContentsRecent problemsHypercentral potenial modelMeson cloud effectResults and DiscussionsConclusions

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Recent problems

1), μpGEp(q2)/GM

p(q2) is monotonically decreasing Electron-to proton polarization transfer

Traditional Rosenbluth separation:

GM=F1+F2 ; GE=F1-τF2 (Space-like Q2 >0)

Sensitive to uncertain radiative corrections(RS) (two-photon)

pepe

M

E

l

tGG

pp

)1(2

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GEp(q2) falls faster than GM

p(q2)

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2), Quark-hadron Duality Strong interaction: Two end points

Two languages1), nQCD, Confinements : Resonance 2), pQCD, Asympototic freedom

Connection of pQCD and nQCD

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Duality for the structure functions

Observable can be explained by two different kinds of Languages (R, S)

Bloom-Gilman Duality( F2 ,1970): Resonance region data oscillate around the s

caling curve. smooth scaling curve seen at high Q2 was

an accurate average over the resonance bumps at a low:Q2(4GeV2)

Q2(4GeV2)Q2(4GeV2)

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By I. Niculescu et al. Phys. Rev. Lett. 85, 1182, 1186 (2000),

New data of JLab.

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Hyper central potential model

Conventional two-body interaction (Cornell Potential) (Isgur-Karl, Chiral model), Three-body force can play an important role in hadrons (Y-type interaction) (non-abelian nature of QCD leads to g-g coupling, which can produce three-body forces) Hyper-central potential model, which amounts to average any two-body potential for the baryon over the hyperangle ζ

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Previous works on Hyper-central model

J. –M. Richard, Phys. Rept. C212 (1992) M. Fabre de la Ripelle and J. Navarro, Ann. Phys. 123 (1979), 18

5. Application to the nucleon resonance properties By Genova Group (M. M. Giannini, E. Santopinot, M.

Aillo, M. Ferraris, A. Vassallo et al.) EPJ A1, 187; EPJ A1, 307; EPJ A2, 403; EPJ A12, 447 PRC62, 025208; PLB387, 215

Spectroscopy of non-strange baryons Electromagnetic form factors of nucleon Electromagnetic transition amplitudes

May 22-26, Italy11

Frame-work of Hypercentral potential model

The potential is assumed to be the function of hyper-radius x

Jacobi coordinates Hyper-spherical coordinates:x and

For a baryon, the Hamiltonian is

)2(6

1)(

21

32121 rrrrr

),(),(

)(22

arctgx

)(22

22xV

mP

mPH

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Frame work of HCPM

The kinetic energy is

The quadratic Casimir operator of the six dim. Rotation group O(6)

With the grant-angular quantum number The hyper-radial wave function

,...1,02 ll

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Potentials and wave functions

Tow typical examples which can be solved analytically

(six-dimensional harmonic oscillator, Coulomb potentials)

The principal quantum number n=ω+5/2 (ω =γ+n’)

An interesting property is the degeneracy of the first exciting L=0 and the L=1

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Hyperfine interactions

Confinement:

Other interactions:

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Spectrum of the model

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Transition amplitudes S

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Form factors

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A short summary

1), The simple hyper-central potential model simple 3-body quark model

2), The spectrum of the non-strange nucleon resonances

3), Transition amplitudes S11(1535), D13(1520)

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Meson cloud effect

To include the meson cloud, the total Lagrangian densitiy with πqq coupling,

The total electromagnetic current is

where

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Electromagnetic interaction

Pion meson coupling, a baryon state is written as

The interaction for the process of emission and absorption of pions is

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Parameters and calculations

a), then b), wave functions (HC, and HO potentials)

, ; , . c), Nucleon form factors

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Transition amplitudes(1)

For nucleon resonance, the electro-production amplitudes are

To calculate in the Breit frame,

The form factors are defined as

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Transition amplitudes (2)

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Individual contribution

α1 τ2

τ2α1

GM

p(Q2

)/μp GM

p(Q2

)/μp

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Low energy region

High energy region

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Magnetic form factor of proton Two sets of parameters; H O: α1=0.410GeV,α2=0.229 GeV HYC: τ1=6.39 ,τ2=4.59

α1

α2

τ1

τ2

GM

p(Q2

)/μp GM

p(Q2)/μp

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Charge form factors of proton ：

！

α2

α1

τ2τ1

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α1 τ1

Electromagnetic form factors of neutron ：

GM

p(Q2

)/μp GM

p(Q2

)/μp

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Individual contributions to the transition amplitude of Δ(1232)

α1τ2

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ΔγN Amplitudes

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Other results ：

-250 ± 8

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Conclusions 1), Meson cloud effect is considered.

2), Its effect on the EM transition of nucleon and its resonances is stressed.

3), The size is enlarged (for the helicity amplitude and E2/M1)

Relativistic version +configuration mixing effect

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Rujula, Georgi and Politzer

The resonance strengths average to a global scaling curve resembling the curve of DIS, as the higher-twist effect is not large, if averaged over a large kinematics region.

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GEp(q2) falls faster than GM

p(q2)

(spacelike Q2=-q2 )F2/F1 falls more slowly than 1/Q2 (1/Q) PQCD and dimension counting

rulesF1(1/Q4 ,Dirac), F2(Pauli)/F1(Dirac)1/Q2