some recent developments in the nucleon structure studycolloquium/05112005.pdf · 2005. 5. 13. ·...
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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
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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.
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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
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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⇒
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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
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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
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Little bag of Brownand Rho
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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
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(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
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(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
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Polarization transfer experiments from Jlab
.....
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22
2 2 202
0
( ) 1 , 0.71 ( / )dQG Q Q GeV cQ
−⎡ ⎤⎛ ⎞
= + =⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
Proton form factors
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Neutron form factors
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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 !
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TwoTwo--photon exchange calculation : photon exchange calculation : elastic contributionelastic contribution
N
world Rosenbluth data
Polarization Transfer
Blunden, Tjon, Melnitchouk (2003, 2005)
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TwoTwo--photon exchange : photon exchange : partonicpartonic calculationcalculation
GPDs
Chen, Afanasev, Brodsky, Carlson, Vdh
(2004)
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1232
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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
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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?
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* 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
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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
+ → +
+ → + + + → +
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Tree diagrams
Bvγπ
⎧ ⎫⎪ ⎪⎪ ⎪⎪ ⎪= ⎨ ⎬⎪ ⎪⎪ ⎪⎪ ⎪⎩ ⎭
and rescatterings
tπNVγπ
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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+
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Dynamical approach
Both on- & off-shell
Dubna-Mainz-Taipei (DMT)
Sato-Lee
MAID – K-matrix approximation
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MAID
DMT
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MAID
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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.
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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
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Theory² significantly improved nucleon model is urgently needed
² better reaction description of is needed
² lattice QCD calculations
'e p e Nπ+ → + +
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The End
Thanks you for your attention!
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Dubna-Mainz-Taipei (DMT)
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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)
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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%
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Tree diagrams
ρ, ω
and rescatterings
tπNVγπ