marc vanderhaeghen johannes gutenberg universität, mainz college of william & mary
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Marc Vanderhaeghen
Johannes Gutenberg Universität, Mainz College of William & Mary
Lattice 2008 Williamsburg, July 14-19, 2008
Overview of nucleon Overview of nucleon structure studiesstructure studies
nucleonform
factors
(generalized) parton distributions spin, tomography
nucleon resonancesΔ(1232),…
proton proton e.m. form factor : statuse.m. form factor : status
green : Rosenbluth data (SLAC, JLab)
Pun05Gay02
JLab/HallA
recoil pol. data
new JLab/HallC recoil pol. exp. (spring 2008) : extension up to Q2 ≈ 8.5 GeV2 new MAMI/A1 data up to Q2 ≈ 0.7
GeV2
neutron neutron e.m. form factor : statuse.m. form factor : status
JLab/CLASJLab/HallA
MAMIJLab/HallC
new JLab/HallA double pol. exp. (spring 07) : extension up to Q2 ≈ 3.5 GeV2
completed
new MIT-Bates (BLAST) data for both p and n at low Q2
Rosenbluth vs polarization transfer measurements of GE/GM of proton
Jlab/Hall A Polarization
data
Jones et al. (2000)
Gayou et al. (2002)
SLAC, Jlab
Rosenbluth data
Two methods, two different results ! 2γ exchange proposed as
explanation
Two-photon Two-photon exchange effectsexchange effects
Guichon, Vdh (2003)
Observables including two-photon exchangeObservables including two-photon exchange
Real parts Real parts of two-photon amplitudesof two-photon amplitudes
Normal spin asymmetries in Normal spin asymmetries in elastic eN scatteringelastic eN scattering
on-shell intermediate state
spin of beam OR target
NORMAL to scattering
plane
directly proportional to the imaginary part of 2-photon exchange amplitudes
OR
order of magnitude estimates :
target :
beam :
Beam Beam normal spin normal spin asymmetryasymmetry
EEee = 0.300 GeV = 0.300 GeV
ΘΘe e = 145 deg= 145 deg
EEee = 0.570 GeV = 0.570 GeV
ΘΘe e = 35 deg= 35 deg
EEee = 0.855 GeV = 0.855 GeV
ΘΘe e = 35 deg= 35 degdata : MAMI A4
theory : Pasquini & Vdh (2004)
also : SAMPLE, Happex, G0, E-158
New MAMI A4 data at
backward angles
Two-photon exchange calculations Two-photon exchange calculations
Blunden, Melnitchouk, Tjon (2003, 2005)
N
elastic contribution
Chen, Afanasev, Brodsky, Carlson, Vdh (2003)
partonic calculation
GPDs
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 polarization5) single-spin target
asymmetry
eande
Hall C 04-019, completed
Hall B 07-005; Olympus/Doriswith refurbished BLAST detector
Hall C 05-017; being analyzed
by-product of 04-019/04-108?
Hall A 05-015 (3He )
whether two-photon exchange is entirely responsible for the
discrepancy in the FF extraction is to be determined experimentally
The preliminary data for Q2=2.5 GeV2 show no ε-dependence of
GEp/GMp at the 0.01 level
PRELIMINARY, not
to be quoted
test oftest of εε-dependence of P-dependence of Ptt / P / Pll
new JLab/Hall C data (2008)
1γ result for Pt / Pl
nucleon FF :nucleon FF : lattice lattice
prospectsprospectsstate of art :
connected diagrams
-> OK for isovector quantities
Pion masses down to less than 300 MeV chiral extrapolation to physical mass
LHPColl.
√(r2)1V
F1V
next step :
inclusion of disconnected diagrams
full QCD lattice calculations
Leinweber, Thomas, Young (2001)
LHPC results see talk : Meifeng Lin
valence DWF on Asqtad staggered sea
new mπ = 293 MeV
modest mπ dependence
factor 4 reduction in error
GEV
<r12>V
mπ = 0.493 GeV mπ = 0.607 GeV mπ = 0.695 GeV
RBC results
2 degenerate dynamical flavors of DWF
arXiv:0802.0863 [hep-lat] see talk : T. Yamazaki
see also talks : J. Zanotti,
Ph. Haegler, T. Korzec, H.-W. Lin, …
F1V
F2V
Puzzle : no strong chiral behavior expected at Q2 ≈ 1 GeV2 , however more than factor 2 deviation with data !
quark quark transversetransverse charge charge densities densities in in
nucleon (I)nucleon (I)
unpolarized nucleon
q+ = q0 + q3 = 0
photon only couples to forward moving quarks
quark charge density operator
transversely polarized nucleon
transverse spin
e.g. along x-axis :
dipole field pattern
quark quark transversetransverse charge charge densities densities in in
nucleon (II)nucleon (II)
empirical quark empirical quark transverse densitiestransverse densities
inin proton proton
data : Arrington, Melnitchouk, Tjon (2007)
densities : Miller (2007); Carlson, Vdh (2007)
ρTρ0
induced EDM : dy = - F2p (0) . e / (2 MN)
empirical quark empirical quark transverse densitiestransverse densities
inin neutron neutron
data : Bradford, Bodek, Budd, Arrington (2006)
densities : Miller (2007); Carlson, Vdh (2007)
ρT
ρ0
induced EDM : dy = - F2n (0) . e / (2 MN)
empirical transverseempirical transverse transition densitiestransition densities
forfor N -> N -> ΔΔ excitationexcitation
data : MAID 2007 , Drechsel, Kamalov, Tiator (2007)
densities : Carlson, Vdh (2007)
combination of M1, E2, C2 FFs
dipole
monopole
quadrupole
Elastic Scattering
transverse quark distribution in
coordinate space
DISlongitudinal
quark distributionin momentum space
DES (GPDs)fully-correlated
quark distribution in both coordinate and
momentum space
GGeneralizedeneralized P Partonarton DDistributions : yield 3-dim istributions : yield 3-dim quark structure of nucleonquark structure of nucleon
Burkardt (2000,2003)
Belitsky,Ji,Yuan (2004)
GPDs :GPDs :
Fourier transform of GPDs : simultaneous distributions of quarks w.r.t. longitudinal momentum x P and transverse position b
P + Δ/2
*Q2 >>
x + ξ
x - ξP - Δ/2
t = Δ2
GPD (x, ξ ,t)
ξ = 0
Handbag (bilocal) operatorHandbag (bilocal) operator : : new way to probe the new way to probe the
nucleonnucleon
y3
y0
generalized probe
y 0
( W±, Z0 ) probe spin 2 (graviton) probe
Y-
energy-momentum form factors
electroweak form factors
( Y ≈ 0 )
Why Why GPDs GPDs are interesting 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 GPDs : : transverse transverse image of the image of the nucleon (tomography) nucleon (tomography) Hu(x, b? )
Guidal, Polyakov, Radyushkin, Vdh (2005)
x
b? (fm)
PROTON M2q 2 Jq
valence model
(GPV 01, GPRV 04)
2 Jq
Lattice
(QCDSF)
u 0.37
0.58 0.66 ± 0.04
d 0.20 -0.06 -0.04 ± 0.04
s 0.04 0.04
u + d + s 0.61 0.56 0.62 ± 0.08
quark contribution to quark contribution to proton proton spinspin
with
parametrizations for E q :
X. Ji
(1997)
μ2 = 2 GeV2
GPD : based on
MRST2002
lattice : full QCD,
no disconnected diagrams so far
see talks on Fri : hadron structure
Difference of polarized cross sectionsDifference of polarized cross sections
Unpolarized cross sectionsUnpolarized cross sections
also JLab/CLAS, HERMES, H1 / ZEUS
DVCS Bethe-Heitler
GPDs
DVCS DVCS onon protonproton
JLab/Hall A @ 6 JLab/Hall A @ 6 GeVGeV
Q2 ≈ 2 GeV2 xB =
0.36
DVCS DVCS onon neutron neutron EHHF )(
4
~)()()()( 22211 tF
M
ttFtFtFC 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 /JLab / Hall A (E03-106) : Hall A (E03-106) :
preliminary data
electromagnetic electromagnetic N -> N -> ΔΔ(1232)(1232) transitiontransition
Role of quark core (quark spin flip) versus pion cloud
non-zero values for E2 and C2 : measure of non-spherical distribution of charges
Sphere: Q20=0 Oblate:
Q20/R2 < 0 Prolate: Q20/R2 > 0
spin 3/2
J P=3/2+ (P33),
M ' 1232 MeV, ' 115 MeV
N ! transition:
N ! (99%), N ! (<1%)
QQ22 dependence of dependence of E2/M1 E2/M1 andand C2/M1 C2/M1 ratiosratios
EFT calculation predicts the Q2 dependence
data points : MIT-Bates (Sparveris et al., 2005)
MAMI :
Q2 = 0 (Beck et al., 2000)
Q2 = 0.06 (Stave et al., 2006)
Q2 = 0.2 (Elsner et al., 2005, Sparveris et al., 2006)
no pion loops
pion loops included
Pascalutsa, Vdh (2005)also Gail, Hemmert
M1
C2/M1
E2/M1
mmππ dependence of dependence of E2/M1 E2/M1 andand C2/M1 C2/M1 ratiosratios
Q2 = 0.1 GeV2
linear extrapolatio
n in mq ~ mπ
2
discrepancy with lattice explained by chiral
loops (pion cloud) ! data points : MAMI, MIT-Bates
quenched lattice QCD results :
at mπ = 0.37, 0.45, 0.51 GeV
Nicosia – MIT group :
Alexandrou et al. (2005)
EFT calculation
Pascalutsa, Vdh (2005)
full QCD results available
Alexandrou et al.
MMagnetic agnetic DDipole ipole MMoment of oment of (1232) (1232) - -
resonanceresonance
J P = 3/2+, M = 1232 MeV, = 115 MeV
N -> transition: N -> (99%), N -> (<1%)
p! (+! ’ + ) ! 0 p
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 ?
μΔ Δ++ Δ+ Δ0 Δ-
Experiment 5.6 ± 1.9
[PDG 02]
2.7 ± 1.2 ± 1.5 ± 3
[Kotulla (TAPS) 02]
- -
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[Butler et
al.,94]
4.0 ± 0.4 2.1 ± 0.2 -0.17 ± 0.04 -2.25 ± 0.25
ChQSM[Kim et al.,
04]
5.4 2.66 -0.08 -2.82
Status of Status of μμΔΔ
for Δ+ : high precision exp.
underway using Crystal Ball @ MAMI
p! (+! ’+ ) ! 0 p
Chiral behavior of the Chiral behavior of the --resonance magnetic momentresonance magnetic moment
quenched lattice points : Leinweber (1992) Cloet,Leinweber,Thomas (2003)
Lee et.al. (2004) – revised (2006)
Pascalutsa, Vdh (2004)
chiral calculations Real parts
Imag. parts
full lattice QCD full lattice QCD calculations : calculations : ΩΩ--
anisotropic clover dynamical lattices (JLab)
C. Aubin
background field method
μΩ
in physical nuclear
magnetons
mΩ = 1.65 GeV
NERSC
Kyklades @ WM
JLab
EXP.
-2.02 ± 0.05
Periodic b.c. : magnetic flux continuous over boundary B = n . 2 π / L2 : Damgaard, Heller
(1988)
full lattice QCD full lattice QCD calculations : calculations : ΔΔanisotropic clover dynamical lattices : 243 x 128, aS = 0.1, at =
0.036 fm
C. Aubin
background field method (patched)
μΔ
in physical nuclear
magnetons
mπ = 366 MeV
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)
SummarySummary
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