Transcript Pion cloud and the deformation of the \Delta

Chiral symmetry and Δ(1232) deformation
in pion electromagnetic production
Shin Nan Yang
Department of Physics
National Taiwan University
“11th International Workshop on Meson Production, Properties and
Interaction”, KRAKÓW, POLAND, 10 - 15 June, 2010
 threshold π0 em production
 Δ(1232)-excitation and its
deformation
2
LQCD  L0  Lm ,
1 a  a
L0   F F  qi  D q, exact chiral symmetry
4
Lm  mq qq, explicity chiral symmetry breaking
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)
3
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.
LQCD  Leff (U , U ,  2U ,....)
= L2eff  L4eff  L6eff  .....,
where n in Lneff represents the number of derivative.
The predictions of ChPT are given by expansions
in the Nambu-Goldstone masses and momentum.
4
Threshold π0 electromagnetic production
Photoproduction
• LET (Gauge Inv. + PCAC) gives
0 ( 0p)  2.3 x 103/mπ
3
2.3
x
10
0 ( 0 p)  
(1  O(  )), exp. -1.33  0.088  0.03
mπ
ChPT：The above expansion in μ  mπ /mN converges slowly
Ε0
π0 p

HBChPT (p4) : -1.1
dispersion relation: -1.22
x 103 / mπ
What are the predictions of dynamical models?
5
Dynamical model for * N →  N
Both on- & off-shell
two ingredients
v , t N
6
DMT Model (Dubna-Mainz-Taipei)
vB 

 PV only 
Collaborators: S. S. Kamalov (Dubna)
D. Drechsel, L. Tiator (Mainz)
Guan Yeu Chen (Taipei)
7
t N :Taipei-Argonne meson-exchange πN model
Three-dimensional Bethe-Salpeter formulation obtained with
Cooper-Jennings reduction scheme, and with the following driving
terms, in pseudovector  NN coupling, given by
chiral
couplin
g
8
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?
9
Results for π0 photoproduction
near threshold,
tree
approx.
10
Photon Beam Asymmetry near Threshold
Data: A. Schmidt et al., PRL 87 (2001) @ MAMI
DMT: S. Kamalov et al., PLB 522 (2001)
11
D. Hornidge (CB@MAMI)
private communication
12
D. Hornidge (CB@MAMI)
private communication
13
D. Hornidge (CB@MAMI)
private communication
14
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.
15
M. Weis et al., Eur. Phys. J. A 38 (2008) 27
16
Δ(1232) deformation
17
* 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  )
18
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

v (E)  vB  v
(E),
where
v = background •transition potential
B

v ( E ) 
†(0) (0)
 N  N
0
N
f
f
E m
19
bare 
excitation
20
photoproduction
, tB (K-matrix)
---------, tB
full
almost no bare Δ
E2 transition
21
Experimentally, it is only possible to extract the
contribution of the following process,
=
dressed
vertex
+
bare
vertex
22
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 !!!
23
For electroproduction :

v ( E, Q ) 
2
Q2-dependent
F (Q2 ), ( =M , E, C)
fit Jlab data for p(e, e ' 0 ) p at Q2  2.8 and 4.0 (GeV/c)2
24
25
NΔ Transition form factors
Magnetic Dipole Form Factor
Pion
cloud
Quadrupole Ratios
CLAS
Hall A
Hall C
MAMI
REM
QM
Pascalutsa,
Vanderhaeghen
Sato, Lee
CLAS
Hall A
Hall C
MAMI
RSM
0.2
 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
26
2015年7月16日
26
Pascalutsa and Vanderhaeghen,
PR D 73, 034003 (2006)
Q2  0.1 GeV 2
27
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.
28
Summary
 Existing data give clear indication of a
deformed 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.
29
The end
30
 threshold π photo- and
electro-production
▪ threshold charged pion photoproduction is well
described by Kroll-Ruderman term
E0 ( n) 

E0 (  p) 
eg N
4 2(1   )3/ 2
eg N
4 2(1   )1/ 2
 27.6 103 / m , (exp. 28.1)
 31.7 103 / m , (exp. -31.7)
31
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.,
♠ s-wave π-hadron scattering length
I I h
a ( , h)  
m
2
4 F
I
♠ πN interaction
V N  g N  q
 (1232) resonance
Results of lowest chiral perturbation theory
32
tB  vB  vB g 0t N
tB ,( ) (qE , k ; E  i )  exp(i ( ) ) cos  ( )

 B ,( )
q '2 R(N) (qE , q '; E ) v( ) (q ', k ) 
 v (qE , k )  P  dq '

E  E N (q ')


0
K-matrix
Pion
cloud
effects
33
34
Threshold values of Ε0 (in units of 10-3/mπ ) for
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
27.72
28.62
(3.2%)
28.82
(0.7%)
28.85
28.2±0.6
28.3±0.3
35
DMT
HBChPT
chiral symmetry
yes
yes
crossing symmetry
no
yes
unitarity
yes
no
counting
Loop( gπN )
chiral power
36
37
38
Multipole amplitudes : M l  , El  ,
l  orbital angular momentum of final  N
j  l  1/ 2, total angular momentum
2)
E1(3/
Rem  REM  (3/ 2)
M 1
1
A1/ 2 
A3/ 2
*
G
3

  *E ,
GM
A1/ 2  3 A3/ 2
*
2)
2
S
G
S1(3/
Q
Q
1/ 2
Rsm  RSM  (3 / 2) 
   2 *C ,
M 1
4M  GM
A1/ 2  3 A3 / 2
Q  (M   M N )2  Q 2
39
40
Alexandrou et al., PR D 94, 021601 (2005)
41
 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.
2
 | RSM | strongly increases with Q .

 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
42