Electromagnetic N → (1232) Transition

Shin Nan Yang

Department of Physic, National Taiwan University

Motivations

Model for * N → N

DMT (Dubna-Mainz-Taipei) dynamical model

Results

Summary

“NEW TRENDS IN HEP”, Yalta, Crimea, Ukraine, September 16-23, 20061

Pascalutsa, Vanderhaeghen, SNY, hep-ph/0609004, Phys. Report

1232

1st, most prominent and non-overlapping resonance

2

Discovered by Fermi in 1952 in πp scatterings

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%)

3

lectromagnetic properties of the 1 , 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)

4

* 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 → ∞

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? 5

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( , ) ( , )

2i f fN J P J P

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

2 : ( ) ,

1 S S

2 ( 2) S

D

l lM

E

l P E P

l P P M

6

S S

S D (deformed)

(S=1/2, L=2) J=3/2

7

Two aspects of the problem

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

quark models, bag models, skyrmion lattice QCD

2) Extraction from experiments dispersion relation dynamical model effective field theory

8

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

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 )

9

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%

10

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)

11

Jones-Scadron f.f’s

12

13

helicity conserving

(3/ 2) 1/ 2 3/ 21

(3/ 2)1 1/ 2 3/ 2

(3/ 2)1/ 21

(3/ 2)

*

2 2

*

*

2 *1 1/ 2 3/ 2

,

,4

Q (

1

33

2

3

)

em

s

E

M

E

Mm

N

A AE

R REMM A A

SSR RSM

M A A

Q Q

G

M

M

G

M

G

G

Q

14

QCD: hadron helicity conservation at high Q2 and scaling

5 * 41/2

3 * *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 co s

Q

n t

15

Alexandrou et al , PR D 66,094503 (2002)

Lattice QCD

16

17

Alexandrou et al., PR D 94, 021601 (2005)

18

Pascalutsa and Vanderhaeghen,

PR D 73, 034003 (2006)

19

Extraction from experiments

dispersion relation (analyticity, crossing symmetry)

dynamical model (SL, DMT, DUO)

effective field theory (QCD symmetry, perturbative)

20

To order e, the t-matrix for * N → N is written as

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

21

pion cloud effects

Both on- & off-shell

22

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

23

•

DMT Model (Dubna-Mainz-Taipei)

PV only

Bv

24

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

25

26

MAID

DMT

27

28

29

30

31

….. .……..

tBγπ K-matrix approx.

_ _ _ _ tBγπ

full

32

For electroproduction :

2( , )v E Q

Q2-dependent2( ), ( = , , )F Q M E C

33

0 2 2fit Jlab data for ( , ' ) at 2.8 and 4.0 (GeV/c)p e e p Q

34

35

36

37

38

39

40

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

41

scaling:

A1/2 ~ Q-3 A3/2 ~ Q-5 S1+ ~ Q-3

42

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.

43

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. | REM | 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.

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