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