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.

2

Motivation

low energies ─ ChPT high energies, high momentum transfer─ pQCD medium energies ․LQCD ․Phenomenology : hadron models, reaction theory

QCD Hadronic phenomena

Δ(1232) physics

3

1232

1st, most prominent and non-overlapping resonance

2

Discovered by Fermi in 1952 in πp scatterings

4

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%)

lectromagnetic properties of the

1. , Q ….. of the

E.g., + p → + 0 + p + p → + + p

( A2/TAPS)

1980’s(A2/TAPS, MAMI)

6

GM1, GE2

|GE2| << |GM1|

photo- and electro-production of p

ion

*

(

' )

N N

e N NN e N

2. , in the transitionN NQ N

7

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

8

S S

S D (deformed)

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

9

helicity conserving

10

Jones-Scadron f.f’s

11

(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

12

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)

13

* 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?

15

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 )

17

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)

19

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

20

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

Lattice QCD

21

22Alexandrou et al., PR D 94, 021601 (2005)

23

Pascalutsa and Vanderhaeghen,

PR D 73, 034003 (2006)

2 20.1 Q GeV

24

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

25

Both on- & off-shell

v , t N

two ingredients

Dynamical model for * N → N

26

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

•

27

DMT Model (Dubna-Mainz-Taipei)

PV only

Bv

28

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

29

30

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

33

34

35

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

36

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?

37

Cooper-Jennings reduction scheme

38

39

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

40

(K-matrix) ,

---------,

B

B

t

t

full

41

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

= +

dressed vertex bare

vertex

42

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

44

2 24.03 ( / )

1232

Q GeV c

W MeV

45

46

47

48

49

50

51

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

Not yet!

52

scaling:

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

53

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

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

57

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.