chiral symmetry and Δ(1232) deformation in pion electromagnetic production
DESCRIPTION
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 π 0 em production - PowerPoint PPT PresentationTRANSCRIPT
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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
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threshold π0 em production
Δ(1232)-excitation and its deformation
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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)
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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.
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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?
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Both on- & off-shell
v , t N
two ingredients
Dynamical model for * N → N
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DMT Model (Dubna-Mainz-Taipei)
PV only
Bv
Collaborators: S. S. Kamalov (Dubna) D. Drechsel, L. Tiator (Main
z) Guan Yeu Chen (Taipei)
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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
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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?
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1010
Results for π0 photoproductionnear threshold,
tree approx.
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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)
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D. Hornidge (CB@MAMI)private communication
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D. Hornidge (CB@MAMI)private communication
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D. Hornidge (CB@MAMI)private communication
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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.
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1616M. Weis et al., Eur. Phys. J. A 38 (2008) 27
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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 )
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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
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bareexcitation
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(K-matrix) ,
---------,
B
B
t
t
full
photoproduction
almost no bare Δ
E2 transition
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Experimentally, it is only possible to extract the contribution of the following process,
= +
dressed vertex bare
vertex
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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 !!!
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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
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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
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Pascalutsa and Vanderhaeghen,
PR D 73, 034003 (2006)
2 20.1 Q GeV
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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.
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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.
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The end
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▪ 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
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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
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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
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-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
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DMT HBChPT
chiral symmetry yes yes
crossing symmetry no yes
unitarity yes no
counting chiral power)( Loop πNg
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(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
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41Alexandrou et al., PR D 94, 021601 (2005)
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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
.