electromagnetic n → (1232) transition shin nan yang department of physics national taiwan...
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Electromagnetic N → (1232) Transition
Shin Nan YangDepartment of Physics
National Taiwan University
Lattice QCD Journal Club, NTU, April 20, 2007
Pascalutsa, Vanderhaeghen, SNY,
Physic.Reports 437 (2007) 125, hep-ph/0609004.
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Motivation
low energies ─ ChPT high energies, high momentum transfer─ pQCD medium energies ․LQCD ․Phenomenology : hadron models, reaction theory
QCD Hadronic phenomena
Δ(1232) physics
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1232
1st, most prominent and non-overlapping resonance
2
Discovered by Fermi in 1952 in πp scatterings
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Properties of
M = 1232 MeV, = 120 MeV
I(JP) =
Electromagnetic properties of the ?
++ + 0 -3 3 3 3, . , spin = , isospin = , , ,
2 2 2 2i e
N (branching ratio > 99%)
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lectromagnetic properties of the
1. , Q ….. of the
E.g., + p → + 0 + p + p → + + p
( A2/TAPS)
1980’s(A2/TAPS, MAMI)
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GM1, GE2
|GE2| << |GM1|
photo- and electro-production of p
ion
*
(
' )
N N
e N NN e N
2. , in the transitionN NQ N
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Parity and angular momentum of multipole radiationelectric 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 = +
Multipole transition
i( , )1 3
2 2( , )i f fN J P J P
1 1 : 1 S( 1) ( 1) , ( ) ( 1)
2 : ( ) , ( 2)
S
2 S D
l ll P E P
l P
M
E P M
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S S
S D (deformed)
(S=1/2, L=2) J=3/2
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helicity conserving
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Jones-Scadron f.f’s
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(3/ 2) 1/ 2 3/ 21
(3/ 2)1 1/ 2 3/ 2
(3/ 2)1
(
*
1
*
3
Multipole amplitudes : , ,
orbital angular momentum of final N
1/ 2, total angular moment
1
3
um
3,em
sm
l l
E
M
M E
l
j l
G
G
A AE
R REMM A A
SR RSM
M
1/ 2/ 2)
1/ 2 2
2
/
2
*
2 *3
,4
2
3
Q ( )
C
M
N
S
A
G
M
M
A
Q
G
Q Q
M
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2 N → ,Q N → in the * N → transition
E.g., + N → + N , e + N → e + N +
For electroproduction, Coulomb quadrupole transition C2 is allowed, in addition to magnetic dipole M1 and electric quadrupole E2 transitions.
Q N → = Q, > 0
1.13 > > 0.4 (Dillon and Morpurgo)
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* N → transition In a symmetric SU(6) quark model the electromagnetic excitation of the could proceed only via M1 transition.
If the is deformed, then the photon can excite a nucleon into a through electric E2 and Coulomb C2 quadrupole transitions.
At Q2 = 0, recent experiments give, Rem = E2/M1 -2.5 %, ( indication of a deformed
pQCD predicts that, as Q2 → ∞
hadronic helicity conservation: A1/2 A3/2
scaling: A1/2 Q-3, A3/2 Q-5, S1+ Q-3
Rem = E1+(3/2)/M1+
(3/2) → 1, Rsm = S1+(3/2)/M1+
(3/2) → const.
What region of Q2 correspond to the transition from nonperturbative to pQCD descriptions?
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Two aspects of the problem
1) Theoretical predictions QCD-motivated models, e.g., constituent
quark models, bag models, skyrmion lattice QCD, large-Nc
2) Extraction from experiments dispersion relation dynamical model effective field theory
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SU(6) constituent quark model
Both N and ∆ are members of the [56]-plet and the three quarks are in the (1s)3 states
In a symmetric SU(6) quark model the e.m. excitation of the could proceed only via M1 transition
large-Nc QCD has an exact SU(6) spin-flavor symmetry
If the is deformed, then the photon can excite a nucleon into a through electric E2 and Coulomb C2 quardrupole transitions.
At Q2 =0, recent experiments give, REM = E2/M1 ≈ -2.5 %, (MAMI, LEGS) ( indication of a deformed )
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In constituent quark model,
(3)3
. .
,
2 8 13( ,
2 3)
conf
sij iji j i j i jij
i
OGEP
Oj ij
conf
P
H O
GE
VH T V
r S S S r S r S Sm m r
V V
V ij
��������������������������������������������������������������������������������������������������
Fermi contact term
Tensor force (2) (2) (0)[ ]ij ijR S
D-state component
PD(%) Q(fm2)
N(938) 0.4 0
1.9 -0.089
Too small !!
-0.8% < REM < -0.3%
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SU ( 6 ): 0.0MIT bag model : 0.0Large Nc : 0.0Non. rel. quark model : -0.8% ~ -0.3%Relativized quark model : -0.1%
Cloudy bag model -2.0 to -3.0%Chiral constituent quark model -1.0 to -4.0%Skyrme model : -2.5 to -6.0%
PQCD : -100%LQCD
pion cloud models
EMR : E2/M1 RATIO (Theory)
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QCD: hadron helicity conservation at high Q2 and scaling
3 * 41/2
5 * *3/ 2
3 * 61/ 2
2
, ,
,
,
,
. .
M
E M
C
A Q G Q
A Q G G
S Q G Q
Q
+1,
.
,
em smR R
Q
const
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Alexandrou et al , PR D 66,094503 (2002)
Lattice QCD
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22Alexandrou et al., PR D 94, 021601 (2005)
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Pascalutsa and Vanderhaeghen,
PR D 73, 034003 (2006)
2 20.1 Q GeV
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Extraction from experiments
dispersion relation (analyticity, crossing symmetry)
dynamical model (SL, DMT, DUO)
effective field theory (QCD symmetry, perturbative)
SL: Sato-Lee
DMT: Dubna-Mainz-Taipei
DUO: dynamical Utrecht-Ohio
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Both on- & off-shell
v , t N
two ingredients
Dynamical model for * N → N
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In resonant channel like (3,3), resonance excitation plays an important role. If a bare is assumed such that the transition potential v consists of two terms
v (E)=vB + v(E),
where
vB = background transition potential
v(E) =
(0) (0)
0
N Nf f
E m
•
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DMT Model (Dubna-Mainz-Taipei)
PV only
Bv
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N Model (Taipei-Argonne) Three-dimensional Bethe-Salpeter formulation with driving term, with pseudovector NN coupling, given by
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Chiral effective theory in the Δ-resonance region
1. Chiral relativistic Lagrangian of π, N, and Δ2. The Lagrangian is organized in powers of electromagntic coupling e, plus the number of derivatives of pion and photon field3. Power counting for the γπamplitude: δ-expansion scheme.
4. Dressed Δ propagator = (p-Δ-Σ)-1 .
2( ) / / , /N QCD QCDM M m
13 3
In the resonance region
(
,
) 1/, p
p
p
(D. Phillips, V. Pascalutsa, M. Vanderhaeghen)
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Only electric eNN coupling contributes in NLO
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MAID
DMT
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Threshold electromagnetic productionπ0
Photoproduction
HBChPT O ( ) Dispersion relation Exp. ( )
-1.1 -1.22 -1.33±0.88±0.03
-0.43 -0.56 -0.45±0.06±0.02
4p
0 π nE
00 π pΕ
π3 m/10
• LET (Gauge Inv. + PCAC) : 0 30 π( p) 2.3 x 10 /m
30
0π
2.3 x 10( p) (1 ( ))
mO
π NChPT The above expansion in μ m /m converges slowly:
Electroproduction
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HBChPT : a low energy effective field theory
respecting the symmetries of QCD, in
particular, chiral symmetry
perturbative calculation - crossing symmetric
DMT : Lippman-Schwinger type formulation with
potential constructed from chiral effective
lagrangian
unitarity - loops to all orders
What are the predictions of DMT?
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Cooper-Jennings reduction scheme
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0
,( ) (
2
0
( ),( )
) ( )
( )
( , ; ) exp(
' ( , '; ) ( ', )( , ) '
(
) c
'
s
)
o
B B BN
BE
EE
N
NB q q q E q kq k P dq
t v v g
vv
R
t
t k E
q
q i i
E E
Pion cloud effects
bareexcitation
K-matrix
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(K-matrix) ,
---------,
B
B
t
t
full
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Experimentally, it is only possible to extract the contribution of the following process,
= +
dressed vertex bare
vertex
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A1/2
(10-3GeV-1/2)A3/2
QN →
(fm2)N→Δ
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 N → with experiments and Sato-Lee’s prediction. The numbers within the parenthesis in red correspond to the bare values.
Q N→ = Q > 0, 1.13 > > 0.4 (Dillon and Morpurgo) is oblate !!!
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For electroproduction :
2( , )v E Q
Q2-dependent2( ), ( = , , )F Q M E C
0 2 2fit Jlab data for ( , ' ) at 2.8 and 4.0 (GeV/c)p e e p Q
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2 24.03 ( / )
1232
Q GeV c
W MeV
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Hadronic helicity conservation A1/2 >> A3/2?
Not yet!
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scaling:
A1/2 ~ Q-3 A3/2 ~ Q-5 S1+ ~ Q-3
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Summary Abundant precision data are now available from Bates (MIT), MAMI (Mai
nz), and Jlab on e.m. production of pion for Q2 ranging from 0.0 to 6.0 (GeV/c)2.
Existing data give clear indication of a deformed Δ.
DMT dynamical model describes well the existing data on pion photo- and electroproduction data from threshold up to 1 GeV photon lab. energy.
it predicts N → = 3.516 N , QN → = -0.081 fm2 , and REM = -2.4%, all in close agreement with experiments. is oblate
bare is almost spherical. The oblate deformation of the arises almost exclusively from the pion cloud.
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Existing data between Q2 = 0-6 (GeV/c)2 indicate
hadronic helicity conservation and scaling are still not yet observed in this region of Q2 .
REM still remains negative. | RSM | strongly increases with Q2.
Impressive progress have been made in the lattice QCD calculation for N → Δ e.m. transition form factors
More data at higher Q2 will be available from Jlab upgrade
Other developments: N →Δ generalized parton distributions (GPDs), two-photon exchange effects, chiral effective field theory approach. extension of dynamical model to higher energies
.
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The end
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To order e, the t-matrix for * N → N is written as
t(E) = v + v g0(E) t N (E), (1) where, v = transition potential, two ingredients
t N (E) = N t-matrix,
g0 (E) = .
Multipole decomposition of (1) gives the physical amplitude in channel =( , l , j)
where(), R() : N scattering phase shift and reaction matrix in channel k=| k|, qE : photon and pion on-shell momentum
Dynamical model for * N → N
0
1
HE
( ) ( ) ( )
( ( )2( )
0
)
( , ; ) exp( )cos
' ( , '; ) ( ', )( , ) '
( ')N
E
EE
N
t q k E i i
q q q E q kq k P dq
v
E
R
E qv
v , t N
pion cloud effects
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Electromagnetic N → (1232) Transition
Shin Nan YangDepartment of Physics
National Taiwan University
Motivations
Model for * N → N DMT (Dubna-Mainz-Taipei) dynamical model Effective field theory
Results
Summary
University of Maryland, College Park, MD, USA, March 12, 2007
Pascalutsa, Vanderhaeghen, SNY, Physic.Reports 437 (2007) 125, hep-ph/0609004.