Dynamical study of N- transition with N(e,e')

Shin Nan Yang

Department of Physics

National Taiwan University

Collaborators: G.Y. Chen, J.C. Chen (NTU) S.S. Kamalov (Dubna) D. Drechsel, L. Tiator (Mainz)

Motivations

Model for * N ! N

² DMT (Dubna-Mainz-Taipei) dynamical model

Results

Summary

International Conference on QCD and Hadronic Physics, Beijing, June 16-20, 2005

lectromagnetic properties of the ² , Q ….. of the

E.g., + p ! + 0 + p + p ! + + p

( A2/TAPS)

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)

* 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 quardrupole transitions.

At Q2 =0, recent experiments give, REM = E2/M1 ' -2.5 %, ( indication of a deformed

pQCD predicts that, as Q2 ! 1

¦ hadronic helicity conservation: A1/2 À 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?

Two aspects of the problem

1) Theoretical prediction lattice QCD QCD-motivated models, e.g., constituent

quark models, bag models, skyrmion

2) Extraction from experiments dispersion relation effective Lagrangian approach dynamical model

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) = . vand t N

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

Both on- & off-shell

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) =

then we obtain

t= tB + t

with

tB(E) = vB + vB g0(E) t N (E)

t(E) = v + v g0(E) t N (E)

0

)0()0(

mE

ff NN

t= ei33 |t|

tB(E) = ei33 |tB(E)|

t(E) = ei33 |t(E)|

Fermi-Watson theorem

Gauge invariance is maintained by the following substitution

where is the electromagnetic current corresponding to the background contribution vB

With R N (qE, q’;E) obtained from a meson-exchange model

, ( ) ( )

2 ( ) ,, 2

0

( ) exp( )cos

' ( , '; ) ( ', )( , ) '

( ')

B

BN EB

N

t DM i

q R q q E v q kv W Q P dq

E E q

2

BB B k J

J J kk

( ) 2 ( ) 2 ( ) 21 1 1( , ), ( , ), ( , )B B BM W Q E W Q S W Q

BJ

In resonant channels, the total multipole amplitude is the sum of the background and resonant contributions

A(W,Q2) = AB(W,Q2) + AR

(W,Q2).

If a bare resonance like is assumed in the dynamical model, AR(W,Q2)

is given by

AR(W,Q2) = ,

where

f N = f 0 N + f 0

N g0 tB N = dressed N ! vertex,

f0 N = bare N vertex

† 2 0

0

( , )

( )N Nf W Q f

E m W

2 2

2 2 2 2, ( 450 )PV PSm

NN NN NN mm m

qL L L MeV

q q

, ( ) ( ) , 2( ) exp( )cos ( , )B Bt MAID i v W Q

2 ( ) ,, 2

, ( ) ( ) 0

, 2

' ( , '; ) ( ', )( , ) ' ,

exp( )cos ( ')

( , ),

BN EB

BN

B

q R q qDM

E v q kv W Q P dq

t i E

MA

E

W Iv D

q

Q

Bv

DMT Model

PV only

N Model Three-dimensional Bethe-Salpeter formulation with driving term, with pseudovector NN coupling, given by

MAID

DMT

In DMT, we approximate the resonance contribution AR(W,Q2) by the follo

wing Breit-Winger form

with

f R = Breit-Winger factor describing the decay of the resonance R

R (W) = total width

MR = physical mass

(W) = to adjust the phase of the total multipole to be equal to the corresponding N phase shift ().

Note that

2 22 2

( ) ( )( , ) ,( ) R R R RR i

R

R

R R

f W M f WA W Q e

M W iA

MQ

2 bare, DM( )

dressed, MAID

RA Q

Born term in K-matrix

approximation

A1/2

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

QN !

(fm2)N !

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.

For electric ( =E) and Coulomb ( = S) multipoles,

with X (0) = 1.

XE and XS : to be determined by the experiments. X

1 violation of the scaling law

For N*(1440) resonance: two parameters XP11

M and XP11S

No Scaling (electroproduction)

2 2 2( ) ( ) (0) ( ),W

kA Q X Q A F Q

k

Parameters determined from global fit to:Recent Jlab differential cross section data on p(e, e’0)p in1.1 < W < 1.4 GeV

751 points at Q2 = 2.8867 points at Q2 = 4.0 (GeV/c)2

Violation of the scaling assumption:

XE (MAID00) = 1 - Q2/3.7 X

E (DM) = 1 + Q4/2.4X

S (MAID00) = 1 + Q6/61 XS (DM) = 1 - Q2/0.1

Hadronic helicity conservation A1/2 >> A3/2 ??

scaling: A1/2 ~ Q-3 A3/2 ~ Q-5 S1/2 ~ Q-3

Summary

DMT dynamical model describes well the existing data on pion photo- and electroproduction data from threshold up to 1 GeV photon lab. energy.

The DMT model predicts N ! = 3.516 N , QN ! = -0.081 fm2 , and REM = -2.4%, all in close agreement with experiments.

dressed is oblate

The bare is almost spherical. The oblate deformation of the dressed arises almost exclusively from the pion cloud.

The recent Jlab data for the electroproduction of the (1232) resonance via p(e,e’p)0 have been re-analyzed with DMT model. In contrast to previous finding, we find

At Q2 = 4.0 (GeV/c)2, A3/2 is still as large as A

1/2, implying that hadronic helicity conservation is still not yet observed in this region of Q2 .

REM , starting from a small and negative values at the real photon point, actually exhibits a clear tendency to cross zero and change sign as Q2 increases.

| REM | is strongly increases with Q2. S1/2 and A

1/2, but not A3/2, start exhibiting scaling behavior at

about Q2 ≥ 2.5(GeV)2. It appears likely that the onset of scaling behavior might take place at a lower momentum transfer than that of hadron helicity conservation.

The End

Model dependence of v and t N should be further studied

vB : PV or PV + PS ?

form factors, gauge invariance consistency between N and coupling constants, e.g, = 6.5 (DMT), 2.2 (SL)

off-shell behaviors of v and t N

Hadronic helicity conservation A1/2 >> A3/2

Model dependence in v, t N

Model dependence in v, t N