Chiral symmetry and Δ(1232) deformation in pion electromagnetic production

Shin Nan YangDepartment of Physics

National Taiwan University

“11th International Workshop on Meson Production, Properties and Interaction”, KRAKÓW, POLAND, 10 - 15 June, 2010

2

threshold π0 em production

Δ(1232)-excitation and its deformation

3

0

0 exact chiral symmetry

explicity chiral symmetry breaking

,

1,

4

,

QCD m

a a

m q

L L L

L F F qi D q

L m qq

Consequence of exact chiral symmtry: parity doubling of all hadronic states

(Wigner-Weyl mode) ? spontaneously broken (Nambu-Goldstone mode)

→ massless pseudoscalar (0-) boson

(Goldstone theorem)

4

Chiral perturbation theory (ChPT)• An effetctive field theory which utilizes the concepts of

spontaneously broken chiral symmetry to replace 1. quark and gluon fields by a set of fields U(x)

describing the d.o.f. of the observed hadrons. For the

Nambu-Goldstone boson sector, U(x)=exp[iψ(x)/Fπ],

where ψ represents the Nambu-Goldstone fields.

2. 2

2 4 6

( , , ,....)

= .....,

where in represents the number of derivative.

QCD eff

eff eff eff

effnn

L L U U U

L L L

L

The predictions of ChPT are given by expansions in the Nambu-Goldstone masses and momentum.

5

Threshold electromagnetic productionπ0

Photoproduction

00 π pΕ 3

πx 10 / m

• LET (Gauge Inv. + PCAC) gives 0 30 π( p) 2.3 x 10 /m

30

0π

2.3 x 10( p) (1 ( )), e -1.33 0.088 0.03 xp.

mO

π NChPT The above expansion in μ m /m converges slowly：

HBChPT (p4) : -1.1

dispersion relation: -1.22

What are the predictions of dynamical models?

6

Both on- & off-shell

v , t N

two ingredients

Dynamical model for * N → N

7

DMT Model (Dubna-Mainz-Taipei)

PV only

Bv

Collaborators: S. S. Kamalov (Dubna) D. Drechsel, L. Tiator (Main

z) Guan Yeu Chen (Taipei)

8

Three-dimensional Bethe-Salpeter formulation obtained with Cooper-Jennings reduction scheme, and with the following drivingterms, in pseudovector NN coupling, given by

chiral coupling

:Taipei-Argonne meson-exchange πN modelNt

9

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?

1010

Results for π0 photoproductionnear threshold,

tree approx.

1111

Photon Beam Asymmetry near ThresholdPhoton Beam Asymmetry near Threshold

Data: A. Schmidt et al., PRL 87 (2001) @ MAMIDMT: S. Kamalov et al., PLB 522 (2001)

12

D. Hornidge (CB@MAMI)private communication

13

D. Hornidge (CB@MAMI)private communication

14

D. Hornidge (CB@MAMI)private communication

15

How about electroproduction?

HBChPT calculations have only been performed up to O(p3) by V. Bernard, N. Kaiser, and u.-G. Meissner, Nucl. Phys. A 607, 379 (1996), 695 (1998) E.

1616M. Weis et al., Eur. Phys. J. A 38 (2008) 27

17

Δ(1232) deformation

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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 %, (MAMI & LEGS) ( indication of a deformed )

19

In DMT, in a 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

where

= background transition potential

•

( ) ( ),Bv E v v E

Bv†(0) (0)

0( ) N N

N

f fv E

E m

20

bareexcitation

21

(K-matrix) ,

---------,

B

B

t

t

full

photoproduction

almost no bare Δ

E2 transition

22

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

= +

dressed vertex bare

vertex

23

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, is oblate !!!

24

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

25

26

NΔ Transition form factorsQuadrupole RatiosMagnetic Dipole Form Factor

No sign for onset of asymptotic behavior, REM→+100%, RSM→ const. REM remains negative and small, RSM increases in magnitude with Q2. Large meson-baryon contributions needed to describe multipole amplitudes

REM

RSM

CLASHall AHall CMAMI

CLASHall AHall CMAMI

QM

Pion cloud

0.2

Pascalutsa, Vanderhaeghen

Sato, Lee

26二〇二三年四月二十一日 星期五

27

Pascalutsa and Vanderhaeghen,

PR D 73, 034003 (2006)

2 20.1 Q GeV

28

Summary

DMT dynamical model, which starts from a chiral invariant Lagrangian, describes well the existing data on pion photo- and electroproduction data from threshold up to 1 GeV photon lab. energy. Predictions of DMT near threshold are in excellent agreement with the most recent data from MAMI while existing HBChPT have problems.

29

Summary Existing data give clear indication of a deform

ed Δ and confirmed by the LQCD calculations. 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.

30

The end

31

▪ threshold charged pion photoproduction is well described by Kroll-Ruderman term

threshold π photo- and electro-production

30 3/ 2

30 1/ 2

28.1( ) 27.6 10 / , (exp. )4 2(1 )

( ) 31.7 10 / , (exp -. )4 2(1 )

31.7

N

N

egE n m

egE p m

32

Weinberg: (1966) interaction between Goldstone boson and other hadrons ~ q at low energies, where q is the relative momentum between boson and target, e.g.,

2 ( ) ,

4I hI I

a h mF

♠ s-wave π-hadron scattering length

♠ πN interaction

(1232) res onanceN NV g q

::::::::::::::::::::::::::::

Results of lowest chiral perturbation theory

33

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

K-matrix

34

35

-30 πΕ (in unitThreshold valu s of 10 /mes ) of r fo

different channels predicted by DMT

Tree 1-loop 2-loop Full ChPT Exp

π⁰p -2.26-1.06

(53.1%)

-1.01

(2.2%)-1.00 -1.1 -1.33±0.11

π⁺n 27.7228.62

(3.2%)

28.82

(0.7%)28.85 28.2±0.6 28.3±0.3

36

DMT HBChPT

chiral symmetry yes yes

crossing symmetry no yes

unitarity yes no

counting chiral power)( Loop πNg

37

38

39

(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

40

41Alexandrou et al., PR D 94, 021601 (2005)

42

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

.