Transcript Overview of nucleon structure studies Marc Vanderhaeghen Johannes Gutenberg Universität, Mainz College of William & Mary Lattice 2008 Williamsburg, July 14-19, 2008

Overview of nucleon
structure studies
Marc Vanderhaeghen
Johannes Gutenberg Universität, Mainz
College of William & Mary
Lattice 2008
Williamsburg, July 14-19, 2008
nucleon
form
factors
(generalized)
parton distributions
spin, tomography
nucleon
resonances
Δ(1232),…
proton e.m. form factor : status
green : Rosenbluth data (SLAC, JLab)
Pun05
Gay02
new MAMI/A1 data up to Q2 ≈ 0.7 GeV2
JLab/HallA
recoil pol. data
new JLab/HallC recoil pol. exp. (spring 2008) :
extension up to Q2 ≈ 8.5 GeV2
neutron e.m. form factor : status
MAMI
JLab/HallC
JLab/CLAS
JLab/HallA
new MIT-Bates (BLAST) data
for both p and n at low Q2
new JLab/HallA double pol. exp. (spring 07) :
extension up to Q2 ≈ 3.5 GeV2 completed
Two-photon exchange effects
Rosenbluth vs polarization transfer measurements of GE/GM of proton
SLAC, Jlab
Rosenbluth data
Jlab/Hall A
Polarization data
Jones et al. (2000)
Gayou et al. (2002)
Two methods, two different results ! 2γ
exchange proposed as explanation
Guichon, Vdh (2003)
Observables including two-photon exchange
Real parts of two-photon amplitudes
Normal spin asymmetries in elastic
eN scattering
directly proportional to the imaginary part of 2-photon
exchange amplitudes
spin of beam OR target
NORMAL to scattering
plane
OR
on-shell intermediate state
order of magnitude estimates :
target :
beam :
Beam normal spin asymmetry
New MAMI A4
data at backward
angles
Ee = 0.300 GeV
Θe = 145 deg
Ee = 0.570 GeV
Θe = 35 deg
Ee = 0.855 GeV
Θe = 35 deg
data : MAMI A4
theory : Pasquini & Vdh (2004)
also : SAMPLE, Happex, G0, E-158
Two-photon exchange calculations
elastic contribution
partonic calculation
N
GPDs
Blunden, Melnitchouk, Tjon (2003, 2005)
Chen, Afanasev, Brodsky, Carlson, Vdh (2003)
whether two-photon exchange is entirely
responsible for the discrepancy in the
FF extraction is to be determined
experimentally
Real part of Y2γ
1)
ε-independence of GEp/GMp in
recoil polarization
2)
cross section difference in
e+ and e- proton scattering
3)
non-linearity of Rosenbluth
plot
Also imaginary part
4)
from induced out-of-plane
polarization
5)
single-spin target
asymmetry
Hall C 04-019, completed
e and e
Hall B 07-005; Olympus/Doris
with refurbished BLAST detector
Hall C 05-017; being analyzed
by-product of 04-019/04-108?
Hall A 05-015 (3He )
test of ε-dependence of Pt / Pl
new JLab/Hall C
data (2008)
1γ result for Pt / Pl
The preliminary data for
Q2=2.5 GeV2 show
no ε-dependence of GEp/GMp
at the 0.01 level
nucleon FF :
lattice prospects
F1V
state of art :
connected diagrams
-> OK for isovector
quantities
LHPColl.
full QCD lattice calculations
√(r2)1V
Pion masses down to less than 300 MeV
chiral extrapolation to physical mass
Leinweber, Thomas, Young (2001)
next step :
inclusion of disconnected
diagrams
LHPC results
see talk : Meifeng Lin
valence DWF on Asqtad
staggered sea
GEV
new mπ = 293 MeV
factor 4 reduction in error
modest mπ dependence
<r12>V
RBC results
see talk : T. Yamazaki
arXiv:0802.0863 [hep-lat]
F1V
2 degenerate dynamical
flavors of DWF
mπ = 0.493 GeV
mπ = 0.607 GeV
mπ = 0.695 GeV
Puzzle : no strong chiral behavior
expected at Q2 ≈ 1 GeV2 ,
however more than factor 2
deviation with data !
F2V
see also talks : J. Zanotti,
Ph. Haegler, T. Korzec,
H.-W. Lin, …
quark transverse charge
densities in nucleon (I)
q + = q 0 + q3 = 0
photon only couples to
forward moving quarks
quark charge density operator
unpolarized nucleon
quark transverse charge
densities in nucleon (II)
transversely polarized nucleon
transverse spin
e.g. along x-axis :
dipole field pattern
empirical quark
transverse densities
in proton
ρT
ρ0
induced EDM : dy = - F2p (0) . e / (2 MN)
data : Arrington, Melnitchouk, Tjon (2007)
densities : Miller (2007); Carlson, Vdh (2007)
empirical quark
transverse densities
in neutron
ρT
ρ0
induced EDM : dy = - F2n (0) . e / (2 MN)
data : Bradford, Bodek, Budd, Arrington (2006)
densities : Miller (2007); Carlson, Vdh (2007)
empirical transverse
transition densities
for N -> Δ excitation
combination of M1, E2, C2 FFs
data : MAID 2007 , Drechsel, Kamalov, Tiator (2007)
densities : Carlson, Vdh (2007)
monopole
dipole
quadrupole
Generalized Parton Distributions :
yield 3-dim quark structure of
nucleon
Elastic Scattering
transverse quark
distribution in
coordinate space
DIS
longitudinal
quark distribution
in momentum space
Burkardt (2000,2003)
Belitsky,Ji,Yuan (2004)
DES (GPDs)
fully-correlated
quark distribution in
both coordinate and
momentum space
Q2 >>
GPDs :
P - Δ/2
*
t = Δ2
x+
ξ
x-ξ
P + Δ/2
GPD (x, ξ ,t)
ξ=0
Fourier transform of GPDs : simultaneous distributions of quarks
w.r.t. longitudinal momentum x P and transverse position b
Handbag (bilocal) operator :
new way to probe the nucleon
Y-
y0
y
y3
(Y ≈ 0
)
0
generalized probe
( W±, Z0 ) probe
spin 2 (graviton) probe
electroweak
form factors
energy-momentum
form factors
Why GPDs are interesting
Unique tool to explore the internal landscape of the nucleon :
3D quark/gluon imaging of nucleon
Access to static properties :
constrained (sum rules) by precision measurements of
charge/magnetization
orbital angular momentum carried by quarks
GPDs : transverse image of the nucleon
Hu(x, b? )
(tomography)
x
Guidal, Polyakov,
Radyushkin, Vdh
(2005)
b? (fm)
quark contribution to proton spin
X. Ji
with
(1997)
parametrizations for E q :
PROTON
u
d
s
u+d+s
M2q
GPD : based on
MRST2002
μ2 = 2 GeV2
2 Jq
2 Jq
valence model
Lattice
(GPV 01, GPRV 04)
(QCDSF)
0.37
0.58
0.66 ± 0.04
0.20
-0.06
-0.04 ± 0.04
no disconnected
diagrams so far
0.04
0.04
0.61
0.56
0.62 ± 0.08
see talks on Fri :
hadron structure
lattice : full QCD,
DVCS on proton
JLab/Hall A @ 6 GeV
Q2 ≈ 2 GeV2
xB = 0.36
DVCS
GPDs
Difference of polarized cross sections
Unpolarized cross sections
also JLab/CLAS, HERMES, H1 / ZEUS
Bethe-Heitler
DVCS on neutron
~
t
C ( F )  F1 (t ) H   F1 (t )  F2 (t )  H 
F2 (t ) E
4M 2
I
n
0 because F1(t) is small
0 because of cancelation of u and d quarks
n-DVCS gives access to the least known and constrained GPD, E
JLab / Hall A (E03-106) :
preliminary data
electromagnetic N -> Δ(1232) transition
J P=3/2+ (P33),
M ' 1232 MeV,  ' 115 MeV
N !  transition:
 N !  (99%),  N !  (<1%)
non-zero values for E2 and C2 : measure of
non-spherical distribution of charges
Sphere: Q20=0
Oblate Q20/R2 < 0
:
spin 3/2
Prolate:
Role of quark core (quark spin flip) versus pion cloud
Q20/R2 > 0
Q2 dependence of E2/M1 and C2/M1 ratios
M1
data points :
MIT-Bates (Sparveris et al., 2005)
MAMI :
Q2 = 0 (Beck et al., 2000)
E2/M1
Q2 = 0.06 (Stave et al., 2006)
Q2 = 0.2 (Elsner et al., 2005,
Sparveris et al., 2006)
EFT calculation predicts the
Q2 dependence
C2/M1
no pion loops
pion loops included
Pascalutsa, Vdh (2005)
also Gail, Hemmert
mπ dependence of E2/M1 and C2/M1 ratios
Q2 = 0.1 GeV2
quenched lattice
QCD results :
at mπ = 0.37, 0.45,
0.51 GeV
linear
extrapolation
in mq ~ mπ2
Nicosia – MIT group :
Alexandrou et al.
(2005)
EFT calculation
discrepancy
with lattice
explained by
chiral loops
(pion cloud) !
Pascalutsa, Vdh
(2005)
data points : MAMI, MIT-Bates
full QCD results
available
Alexandrou et al.
Magnetic Dipole Moment
of (1232) - resonance
octet baryon MDMs : precession in
external magnetic fied
decuplet baryon MDMs :
only Ω- lives long enough (weak decay)
to be measurable by precession method
how about other – strongly decaying decuplet baryons ?

J P = 3/2+, M = 1232 MeV,  = 115 MeV

N ->  transition:  N ->  (99%),  N ->  (<1%)
+
 p! ( ! ’ + ) ! 0 p
Status of μΔ
μΔ
Δ++
Experiment
Δ+
5.6 ± 1.9 2.7 ± 1.2 ± 1.5 ± 3
[PDG 02] [Kotulla (TAPS) 02]
Δ0
Δ-
-
-
SU(6)
5.58
2.79
0
-2.79
lattice (quenched)
[Leinweber 92]
4.9 ± 0.6
2.5 ± 0.3
0
-2.5 ± 0.3
HBChPT
4.0 ± 0.4
2.1 ± 0.2
-0.17 ± 0.04
-2.25 ± 0.25
5.4
2.66
-0.08
-2.82
[Butler et al.,94]
ChQSM
[Kim et al., 04]
for
Δ+ :
high precision exp.
+
p! ( ! ’+ ) ! 0 p
underway using Crystal Ball @ MAMI
Chiral behavior of the -resonance
magnetic moment
quenched lattice points :
Leinweber (1992)
Cloet,Leinweber,Thomas (2003)
Lee et.al. (2004) – revised (2006
chiral calculations
Real parts
Imag. parts
Pascalutsa, Vdh (2004)
full lattice QCD calculations : Ω-
anisotropic clover dynamical lattices (JLab)
background field method
Periodic b.c. : magnetic flux continuous over boundary
B = n . 2 π / L2 : Damgaard, Heller (1988)
μΩ
in physical
nuclear
magnetons
EXP.
NERSC
mΩ = 1.65 GeV
Kyklades @ WM
-2.02 ± 0.05
C. Aubin
JLab
full lattice QCD calculations : Δ
anisotropic clover dynamical lattices : 243 x 128, aS = 0.1, at = 0.036 fm
background field method (patched)
m = 366 MeV
μΔ
in physical
nuclear
magnetons
C. Aubin
π
Summary
Nucleon form factors :
-> high precision data at low Q2 : map out transverse quark densities in nucleon
-> difference Rosenbluth vs polarization data GEp /GMp :
mainly understood as due to two-photon exchange effects (new expt. planned)
-> PV e-scattering : strangeness contributions to E and M distributions very small
-> lattice QCD : state-of-art full QCD calculations go down to mπ ~ 300 MeV,
some puzzles
GPDs :
-> unifying theme in hadron physics (form factors, parton distributions)
-> provide a tomographic image of nucleon
-> access to angular momentum of quarks/gluons in nucleon
-> encouraging experimental results coming out of HERMES, H1/ZEUS, JLab@6 GeV
indicating twist-2 dominance
-> future programs : COMPASS, dedictated JLab@12 GeV, EIC…
Nucleon excitation spectrum :
-> precision data on NΔ form factors : shape of hadrons
-> chiral EFT is used in dual role :
describe both observables and use in lattice extrapolations
strong non-analytic behavior in quark mass due to opening of πN decay channel
(interplay of scales)