Some recent developments in Some recent developments in the nucleon structure studythe nucleon structure study

Shin Nan YangShin Nan YangNational Taiwan UniversityNational Taiwan University

IntroductionIntroductionElectromagnetic form factorsElectromagnetic form factorsN N !! ∆∆ transition form factorstransition form factors²² deformation of the deformation of the ∆∆ (1232)(1232)Outlook and conclusionOutlook and conclusion

Colloquium at National Tsing-Hua University, May 11, 2005

History of Nuclear Physics1932 Chadwick discovered neutronmarked the birth of nuclear physics

Nuclei with A=1-292, Z=1-116 havebeen discovered A= 1: nuclear matter, e.g., neutron stars

nuclear astrophysics (Bethe)

AZ Name

Spectroscopy, electron scatterings (Hofstadter), nuclear reactions (fission, fusion, β−decay, fragmentation…..), high-spin states, super-deformed nuclei, super-heavy nuclei etc.

Standard model of nuclear physicsNon-relativistic quantum mechanicswith

2

( ) ( )2

iij ijk

i ij ijki

pH V NN W NNNm < > < >

= + +∑ ∑ ∑uur Three-body force

Bethe-Salpeter equation

Faddeev equation, Faddeev-Yacubovsky equation

Green’s function Monte Carlo method etc.

Quantum many-body theory

Modelsshell model -- Mayer and Jensen

collective model – Bohr and Mottelson

interacting boson model – Iachello and Arima

Developments of QCD

1964 Gell-Mann and Zweig proposedquark model

1969 Friedman, Kendall, and Taylordiscovered partons in deep inelastic scattering of electronsfrom nucleon

1973 formulation of QCD by Gross, Politzer, and Wilczekt’Hooft

Hadron physics⇒

Hadron physics

Structure of hadrons ( baryons and mesons )experiments mostly performed with electron accelerators like MAMI (Mainz), Bates (MIT),Jlab etc.

Quark-gluon plasma (QGP)experiments mostly performed with heavy-ion accelerators like SPS, GSI, RHIC, and LHC

Nucleon structure

Bjorken SR

Structure functions

N* form factors

Duality

Hybrid baryons

Missing states

Elastic form factorsElastic form factors NΔNΔ

GDH SRGDH SR GPD’sGPD’s

You name itYou name itSU(6) symmetrySU(6) symmetry

Little bag of Brownand Rho

Electromagnetic form factorsRutherford scattering

(1) Electron (spin-1/2) scattered by a spin-0 charged particle with mass M(Mott scattering)

(2) Mott scattering from a spin-0 particle with extended structure

2 22

2 24

2

(1 sin )24( ) ,2( )

v 1 n

=si

2cMott

d EZe Ed qcM

θβσθ β

−⎛ ⎞ =⎜ ⎟Ω⎝ ⎠ +

2 322

, exp (iq r ) ( () ( ) )Mott

F q F rd d d rqd d

ρσ σ⎛ ⎞ ⎛ ⎞= = ⋅⎜ ⎟ ⎜ ⎟Ω Ω⎝ ⎠ ⎝ ⎠ ∫r r uurrr

form factor charge density

(3) Electron scattering from proton (Dirac particle) with finite extension and anomalous magnetic moment, in one-photon-exchange approximation,

( ) ( ) ( )

( ) ( )

2 2 2 22 2 2

2

2 tan ,1 2

0 1, 0 1 2.79 , 4

E MM

Mott

p pE M p p

N

G Q bG Qd d bG Qd d b

QG G bm

σ σ θ

κ µ

⎡ ⎤+⎛ ⎞ ⎛ ⎞⎢ ⎥= +⎜ ⎟ ⎜ ⎟Ω Ω +⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦

= = + = = =

Rosenbluthformular

(4) In elastic scattering of longitudinally polarized electrons from unpolarized protons,in one-photon-exchange approximation,

' tan ,2 2

ptE

pM l N

PG E EG P m

θ+ ⎛ ⎞= − ⎜ ⎟⎝ ⎠

polarization components of the recoiling proton perpendicularand parallel to its momentum in the scattering plane

, :t lP P

proton

Pl

Pt

The one-photon-exchange diagram for the polarized electron-nucleon scatteringThe one-photon-exchange polarized electron-photon elastic scattering

Polarization transfer experiments from Jlab

.....

22

2 2 202

0

( ) 1 , 0.71 ( / )dQG Q Q GeV cQ

−⎡ ⎤⎛ ⎞

= + =⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

Proton form factors

Neutron form factors

Rosenbluth vs polarization transfer measurements of GE/GM of proton

Jlab/Hall A Polarization data

Jones et al. (2000)Gayou et al. (2002)

SLAC

Rosenbluth data

Two methods, two different results !

TwoTwo--photon exchange calculation : photon exchange calculation : elastic contributionelastic contribution

N

world Rosenbluth data

Polarization Transfer

Blunden, Tjon, Melnitchouk (2003, 2005)

TwoTwo--photon exchange : photon exchange : partonicpartonic calculationcalculation

GPDs

Chen, Afanasev, Brodsky, Carlson, Vdh

(2004)

1232

Properties of ∆M∆ = 1232 MeV, Γ∆ = 120 MeVI(JP) =

Is ∆ spherical? Namely, does it have a D-state?

( )++ + 0 -3 3 3 3, . , spin = , isospin = , , , 2 2 2 2

i e+⎛ ⎞

∆ ∆ ∆ ∆⎜ ⎟⎝ ⎠

N (branching ratio > 99%)π∆ →

Alexandrou et al Lattice QCD calculationNucl-th/0311007

In constituent quark model,

( ) ( )( 3 )3

. .

,

2 8 1( ) 3 ,2 3

con f O G EP

sij iji j i j i jO G EP ij

i j ij

con f H O

H T V V

V ij r S S S r S r S Sm m r

V V

α π δ

= + +

⎧ ⎫⎪ ⎪= ⋅ + ⋅ ⋅ − ⋅⎨ ⎬⎪ ⎪⎩ ⎭

=

ur ur ur ur ur ur ur$ $

Fermi contact term

Tensor force(2) (2) (0)[ ]ij ijR S×

D-state component

PD(%) Q(fm2)N(938) 0.4 0∆(1232) 1.9 -0.089

Small effect !!

How to measure it?

* transitionNγ ↔ ∆Parity and angular momentum of multipole radiation

electric multipole of order (l,m), parity = (-1)l

magnetic multipole of order (l,m), parity = (-1)l+1

Allowed multipole orders are l=1 and 2, with parity = +

N(J=1/2) ∆=(J=3/2)

i1( , ) ( , )2i f fN J P J Pγ + = = + → ∆ = +

11: ( 1) ( 1) , ( 1) ( 1) =+2 : ( 2) ,

S( 2)

SS D

l ll P E P Ml P E P M

+= = − = − = −= + −

→= →=

γ

N

γ

∆

GM1, GE2

|GE2| << |GM1|

γ

∆

N

π

N

photo- and electro-production

of pion

*' ) (N N

e N e NN Nγ π

γ π

π

+ → +

+ → + + + → +

Tree diagrams

Bvγπ

⎧ ⎫⎪ ⎪⎪ ⎪⎪ ⎪= ⎨ ⎬⎪ ⎪⎪ ⎪⎪ ⎪⎩ ⎭

and rescatterings

tπNVγπ

Experimentally, it is only possible to extract the contribution of the following process,

= +

In particular, interests have been focused on the extraction of EMR and CMR from experiments

E2

M1

EMR =C2

M1

CMR=

NEED A GOOD THEORY OFELECTROMAGNETIC PRODUCTION OF PION

M1+=

E1+ S1+= M1+

Dynamical approach

Both on- & off-shell

Dubna-Mainz-Taipei (DMT)

Sato-Lee

MAID – K-matrix approximation

MAID

DMT

MAID

A1/2

(10-3GeV-1/2)A3/2

QN ! ∆

(fm2)µN ! ∆

PDG -135 -255 -0.072 3.512

LEGS -135 -267 -0.108 3.642

MAINZ -131 -251 -0.0846 3.46

DMT-134(-80)

-256(-136)

-0.081(0.009)

3.516(1.922)

SL-121(-90)

-226(-155)

-0.051(0.001)

3.132(2.188)

Comparison of our predictions for the helicity amplitudes, QN ! ∆, and µ N ! ∆with experiments and Sato-Lee’s prediction. The numbers within the parenthesis in red correspond to the bare values.

OUTLOOK and ConclusionNucleon form factors

² Jlab 12 GeV upgrade will extend the proton GE/GM measurement to Q2=14 (GeV/c)2

² will be extended to Q2=4 (GeV/c)2 via and to Q2=10 (GeV/c)2

via ratio technique of

² new analyses for the form factors, including the two-photon-exchange correctionsneeded to be carried out

N-∆ transition form factors² Jlab 12 GeV upgrade will extend the EMR and CMR measurements to Q2=14 (GeV/c)2

² several precision measurements at low Q2 are still being analyzed

² ∆ is deformed and oblate

EGn 3( , ' )He e e n

uuur rMG n

D( , ' ) / D( , ' )e e n e e p

Theory² significantly improved nucleon model is urgently needed

² better reaction description of is needed

² lattice QCD calculations

'e p e Nπ+ → + +

The End

Thanks you for your attention!

Dubna-Mainz-Taipei (DMT)

SU(6):0.0MIT bag model:0.0Non. rel. quark model:0 to -2.0%

Konuik, Isgur Phys. Rev. D21（1980）1868Gershteyn Sov. J. Phys. 34（1981）870Drechsel, Giannini Phys. Lett. 143 B（1992）2864

Relativized quark model:-0.1%

Capstick, Karl Phys. Rev. D41（1990）2767Capstick Phys. Rev. D46（1992）2864

Cloudy bag model:-2.0 to -3.0%

Kalbermann Phys. Rev. D28（1983）71Bermuth Phys. Rev. D37（1988）89

Chiral constituent quark model: -1.0 to -4.0%

Glozman, Riska Phys. Report 268（1996）263Sato, Lee Phys. Rev. C56（1997）1246

EMR: E2/M1 Ratio (Theory)

Skyrme model: -2.5 to -6.0%Adkins, Witten Nucl. Phys. B228（1983）552Weise Phys. Lett. B188（1987）6

Lattice QCD: - 6.0 to -12.0%Leinweber Baryon 1992

PQCD: -100%

Tree diagrams

ρ, ω

and rescatterings

tπNVγπ