EIC2006 & Hot QCD 19th July 2006

Towards Three-Dimensional Imaging of the Proton Towards Three-Dimensional Imaging of the Proton

Dieter Müller

Arizona State UniversityArizona State University

OutlineOutline• Introductory remarks:Introductory remarks:

• A short look back in historyA short look back in history

• How to resolve the proton?How to resolve the proton?

• Factorization: How to work with Quantum Chromodynamics?Factorization: How to work with Quantum Chromodynamics?

• Exploring the proton contentExploring the proton content

• Form factorsForm factors

• Parton densitiesParton densities

• An unifying concept: generalized parton distributionsAn unifying concept: generalized parton distributions

• Present and future experimentsPresent and future experiments

• SummarySummary

• Hadron mass spectraHadron mass spectra• Magnetic moments, e.g., Magnetic moments, e.g., • etc. etc. • Proton spin solely built from the quark spins!Proton spin solely built from the quark spins!

Tremendously successful model in description ofTremendously successful model in description of

What is the proton made of?What is the proton made of?What is the proton made of?What is the proton made of?The variety of hadrons is explained by an underlying symmetry “eightfold way”:

M. Gell-Mann, G. Zweig, 1964

0

p

n

)3/2(u )3/1(d

)3/1(s

qp mm 3

S 12

12

12

• Proton mass:Proton mass:

• Proton spin:Proton spin:

u

u

d

The proton is build from three quarks of The proton is build from three quarks of masses masses ~ 300 MeV andand spin spin s = 1/2::qm

cm

e

cm

e

ppp )3(22

79.2

mE

eV

p

h 610

m1010

Quantum mechanical duality of particle and waves

• Electron microscope E ~ 100 KeV resolution of

allows for a deeper look into matter:

• Particle accelerator: SLAC 20 GeV electron beam (1966)

exploring the femto universe, i.e., a resolution of

mr 1510fm1

How to resolve the proton?How to resolve the proton?• Experiments with highly energetic electromagnetic probe acting Experiments with highly energetic electromagnetic probe acting as a micro-scopeas a micro-scope

• Virtual photon resolves the proton on the distanceVirtual photon resolves the proton on the distance:GeV

m102.1 15

QQ

hcr

11 ~ Qhcr

e

21 QQ

e

m10~ 15pd

22 ~ Qhcr

• The change with the resolution scale is a QCD prediction, The change with the resolution scale is a QCD prediction,

calculable within perturbation theory. calculable within perturbation theory.

rQ /1~

virtual photon mass (=virtuality) virtual photon mass (=virtuality)

22 )'( kkQ

electronelectron

k

k '

p Q

How to study the proton content?How to study the proton content?

elastic, exclusive deeply inelastic, inclusive

e

ep

p

Q

High energetic scattering experiments on a proton target or beam with

p hadr

oniz

atio

n( )Q

e

xp

• hadron beam, e.g., Tevatron@Fermilab (1TeV proton + antiproton beams), LHC

etc.

• lepton (electron, muon, or neutrino ) beam e.g., JLab@6GeV, DESY (27 GeV electron + 820 GeV proton beam)

inelastic, exclusive

Q

e

p p p B

Q

e

M,

FactorizationFactorization

QxqQxdxQ longs

short ,)(,

• Precise measurements at the few percent level of (inclusive) observables

0020.01187.0GeV91 Zs M

• The scattering process of high energy particles appear at short distances.

• However, in the asymptotic (initial and final) states hadrons are observed.

• The basic concept for the application of QCD is factorization:

Form factor in quantum mechanicsForm factor in quantum mechanics

ei k r

rki 'e

Elastic scattering of fast electrons on atoms.Elastic scattering of fast electrons on atoms.

2)(e)( rrdqF rqi

Atomic form factor:Atomic form factor:

( ) ~ ( ) q F q2

is the Fourier transform of theis the Fourier transform of thecharge density.charge density.

The cross section:The cross section:

E.g., the hydrogen atom in the ground state:E.g., the hydrogen atom in the ground state:

2

2

2201)(

qaqF

30

2/

8

e)(

0

ar

ar

2)()( rr

charge densitycharge density

m105.04 10

20

ecma

with Bohr radius

The electric and The electric and magnetic charge distributions inside the proton are measured in elastic electron-proton scattering elastic electron-proton scattering epe’p’:

quarkquark

Form factor in QCDForm factor in QCD

),,(

ME GGd

d

d

d

electronelectron

virtual photonvirtual photonmass (= virtuality)mass (= virtuality)

22 )'( kkQ

k

k '

Q

p p

• electric form factor

• magnetic form factor

10 pE eG 2QGE

2QGM 79.20 pMG

22

71.01

QQGQG DE

Proton is not point-like!Proton is not point-like!

R.Hofstadter, 1955(1961 Nobel Prize)

m108.0 15r

Interpretation of form factorsInterpretation of form factors

pz

Lorentz trans.

proton at restproton at rest

zy

x

momentum frame of momentum frame of a fast moving protona fast moving proton

r

x pi z

no spatial extentno spatial extent

x pz1

( )r

0 r

Form factors might be interpreted asForm factors might be interpreted astransverse distributiontransverse distribution of quarks of quarksirrespective of their longitudinal motion.irrespective of their longitudinal motion.

Q

e

p

““Magnetic charge distribution”Magnetic charge distribution”

00~ LLEG •

01~ LLMG •

The QCD calculation of form factors remains challenging.

r

l

j

s

• Form factors might be represented by wave functions:

• Sensitivity to orbital momentum of quarks!Sensitivity to orbital momentum of quarks!

• Confronting model calculations with data leads to new insights into the proton (orbital momentum, wave function shape)(orbital momentum, wave function shape)

Parton densities (PDs) in QCDParton densities (PDs) in QCD

x

),( 2Qxq

1

0

y

xp

xz

p

Qr 1~

Deeply inelastic electron-proton scattering Deeply inelastic electron-proton scattering epe’X : :

Proton has point-like constituents!Proton has point-like constituents!

D.Taylor, H.Kendall, J.Friedman, 1969(1990 Nobel Prize)

R.P.Feynman, 1972

is the is the parton densityparton density, depending on , depending on longitudinal momentum fractionlongitudinal momentum fraction x=k||/p and transversal resolution scaletransversal resolution scaleNo information on their transverse position!No information on their transverse position!

),( 2Qxq

Qr 1~

p

)(Q

e

xp

2

X

Qx 2, mp p

xp

q q

PD

““Spin crisis”Spin crisis”

A polarized lepton scatters differently A polarized lepton scatters differently off quarks polarized along oroff quarks polarized along oropposite to the nucleon’s spin providingopposite to the nucleon’s spin providing

The quark polarization inside the proton is measured within polarized scattering The quark polarization inside the proton is measured within polarized scattering European Muon Collaboration (EMC) at CERN (1987):European Muon Collaboration (EMC) at CERN (1987):

The fraction of the proton spin carried by quarks is:The fraction of the proton spin carried by quarks is:

1.02.0~)( xqdx

… … the result implies that a rather small fraction of the result implies that a rather small fraction of thethespin of the proton is carried by the spin of the quarks. spin of the proton is carried by the spin of the quarks.

EMC Coll., 1987

““SPIN CRISIS”: SPIN CRISIS”: Where is the rest? How to define it? How to measure it?Where is the rest? How to define it? How to measure it?

qqq

1 (quark model prediction)

p

The spin of a composite particle is build from The spin of a composite particle is build from

Building up the nucleon spinBuilding up the nucleon spin

L r p

• spin of its constituentsspin of its constituents

• orbital motion of constituentsorbital motion of constituents

r

p

s

L

s

The sum rule for the proton The sum rule for the proton spinspin

gqz JLpJp 2

1

2

z

zz

BErDirrd

rrrdJ

)()(2

1

)(

3

03

0iThe angular momentum is given by the energy momentum densityThe angular momentum is given by the energy momentum density

X. Ji, 1996

Probing the proton with two Probing the proton with two photonsphotons

)(q

p'pBjorken limit

Bjorken limit:Bjorken limit:

fixed

~2

22

qpQ

qpqQ

time

spacez / 2

z / 2

p'n

p

“Handbag”

x p1 x p2

GPDGPD

Non-invasiveNon-invasive exploration of the proton!exploration of the proton!

quantum mechanical incoherence of quantum mechanical incoherence of physical processes at short and large physical processes at short and large distances scales ensures factorizationdistances scales ensures factorization

D. Müller (PhD), 1992 et al. 1994

DVCS

x

),( 2xq

1

0

z

Generalized parton distributions (GPDs)Generalized parton distributions (GPDs)y

xp

x

r

p

r Q ~ 1

GPDs simultaneously carry information GPDs simultaneously carry information on both on both longitudinallongitudinal and and transversetransverse distribution of partons in a protondistribution of partons in a proton

D. Müller (PhD) 1992 et al. 1994X. Ji; A. Radyushkin, 1996

GPDs contain also information onGPDs contain also information onquark (orbital) angular momentumquark (orbital) angular momentum

),(lim 2

0

xqxdxJ zq

p

x p2

GPD GPD

px1

p pp

X. Ji, 1996

GPDs as a unifying conceptGPDs as a unifying conceptGPDs are reducible to form factors and parton densities!GPDs are reducible to form factors and parton densities!

orbital angular momentumorbital angular momentum

p

x p2

GPDGPD

px1

p pp

p p FF FF

pp

p

xp

PD PD

xp

p0

p p pp

femto holography femto holography ((3D picture of the proton)

calculable in lattice QCDcalculable in lattice QCD

duality, etc.duality, etc.

mass and gravitomagnetic mass and gravitomagnetic charges (matrix element of charges (matrix element of energy-momentum tensor)energy-momentum tensor)

““Holography” with photo leptoproductionHolography” with photo leptoproduction

GPDGPD

FFFF

Bethe-Heitler

DVCS

2reference source

beam diffracted off a parton

lepton beam

detector

‘‘sp

litt

er’’

‘‘mirror’’

‘‘mirr

or’’

NOTE:NOTE: objects displayed in yellow are not present in real experiment! objects displayed in yellow are not present in real experiment!

'' peep

Geometric picture of DVCSGeometric picture of DVCS

x

y

Initial stateInitial state

Lq

z

p

r

( )Q2

r Q ~ 1

x

y

z

Final stateFinal state

azimuthalasymmetry

( ) cos( ) sin( ) a n b nn nn

Cross section:Cross section:

Extracting interferenceExtracting interference

A

)sin()1()1( aA

Model AModel A

Model BModel B

Jq 0 3.

Jq 01.

A. Belitsky, D. Müller, A. Kirchner, 2001

Lepton-beam charge asymmetryLepton-beam charge asymmetry

Proton spin asymmetryProton spin asymmetry

Lepton-beam spin asymmetryLepton-beam spin asymmetry

Lepton-beam spin Lepton-beam spin asymmetryasymmetry

, rad , rad

CLASCLASHERMESHERMES

The quark distribution in the protonThe quark distribution in the proton

• Theoretical constraints together with plausible assumptions give already a rough

idea about the average squared distance in dependence of x and

),,(2

,, 2222

22 Qxqe

dQbx bi

q

b

2b

2Q

b

no spatial extentno spatial extent

pxQ/1

• The probability to find a quark in transversal direction from the proton center with momentum fraction x is

2GeV100

2GeV10

22 GeV1Q

The proton image at large WThe proton image at large W The proton image at large WThe proton image at large W • Photon leptoproduction measured at H1 & ZEUS (DESY) Photon leptoproduction measured at H1 & ZEUS (DESY)

allows to extract the deeply virtual Compton cross section allows to extract the deeply virtual Compton cross section

D. Müller 2006

22

22

112

2

22smallor largefor

QW

QxqpW Bj

HCtQQdt

tQWds

QW

Q

,

222

2

224

22

,,4,,

FFGPDGPD + FF+d + interference

2 2

subtracted DVCS Bethe-Heitler

• A new representation for GPDs allows to make contact with A new representation for GPDs allows to make contact with Regge phenomenology Regge phenomenology [D. Müller, A. Schäfer (05)] (see also talk M. Kirch)

2

2

,,2

2cot

22/3

2/3

2Qt

ni

n

ndn

i

Qn

nic

ic

s

• Generalization of Mellin representation for DIS structure function Generalization of Mellin representation for DIS structure function

• Moments are labeled by complex angular momentum Moments are labeled by complex angular momentum n n

• These moments contain spin & orbital momentum couplingThese moments contain spin & orbital momentum coupling

n

n

dn LSn

GPD HGPD H

dx px1 x p2

2,, Qtn

• Near the `pomeron’ pole evolution is driven by gluonsNear the `pomeron’ pole evolution is driven by gluons

1,,

22

nGGdQ

dQ s

nG

nGG

n

n

nGG

nG

nG

n

n

n

• Assuming gluonic `pomeron’ dominance at low input scale, we Assuming gluonic `pomeron’ dominance at low input scale, we arrive to the arrive to the Aligned Jet Model/dipole-quarkAligned Jet Model/dipole-quark picture for DVCS: picture for DVCS:

GPD HGPD HGPD HGPD H

Q0~ 0.5 GeV

Q 2 GeV

evolution

Although, analyze can be performed in next-to-next-to-leading order [K. Kumerički, D.M., K. Passek- Kumerički, A. Schäfer (2006)]

we will rely in the following on the leading order approximation

0,)(

1

3/1 3

n

G

Gn tntB

NG

• Small -behavior of arises from pomeron poles:

• -independent pure gluonic input:

`pomeron’ poles

non-leadingsingularities

-2 -1 1 2

n

DVCS data are described within three parameters: NG, BG , and Q0

1

2ln

/ln

/lnln

220

22

Q

QPomeron dominance yields double log approx., i.e.,

tt 25.01)(

• fit yield NG=1.97, BG=3.68 GeV-2 and Q0 =0.7 GeV

in particular, parton distribution in impact parameter space 0

mean squared value in transversal directionh~b2i

100 GeV2

10 GeV2

2 GeV2

gluons quarks

gluon distrib

ution

NOTE: J/ production yield a ~25% smaller value

Strikman &Weiss (05)

fm63.02 b

322 10,GeV3 xQ

quark and gluon GPDs at low x

How one can measure GPDs?How one can measure GPDs?How one can measure GPDs?How one can measure GPDs?• Deeply virtual Compton scattering (clean probe)Deeply virtual Compton scattering (clean probe)

eepp

peep

'

''

*

p'

e e'

• Hard exclusive meson production (flavor filter)Hard exclusive meson production (flavor filter)

ep e p

ep e p

ep e p

' '

' '

' '

M

p'p

e e'

• etc.etc.

x

scanned area of the surface as scanned area of the surface as a functions of lepton energya functions of lepton energy

'' peep

'' peep

A. Belitsky, D. Müller 2003

Current and future facilitiesCurrent and future facilities

• Jefferson Lab @ 6 GeV: Jefferson Lab @ 6 GeV: • Hall A: recoil detector*Hall A: recoil detector*

* For full exclusivity of the scattering event!* For full exclusivity of the scattering event!

• Hall B: near beam calorimeterHall B: near beam calorimeter

• Jefferson Lab @ 12 GeVJefferson Lab @ 12 GeV

• DESYDESY

• HERMES: recoil detector*HERMES: recoil detector*

• H1 and ZEUS: polarized protonH1 and ZEUS: polarized proton

• COMPASS @ CERN: recoil detector*COMPASS @ CERN: recoil detector*

• EIC @ BNL? EIC @ BNL? • ELFE?ELFE?

ConclusionsConclusions

• Experimentally accessible: Experimentally accessible: (see parallel session Exclusive Physics)(see parallel session Exclusive Physics)

• hard exclusive electroproduction of photon or lepton pairhard exclusive electroproduction of photon or lepton pair

• hard meson electroproduction, etc. hard meson electroproduction, etc.

• Generalized parton distributions are a new theoretical concept: Generalized parton distributions are a new theoretical concept:

• unified description of form factors and parton densitiesunified description of form factors and parton densities

• containing mass and gravitational form factors, etc.containing mass and gravitational form factors, etc.

• messuarable in QCD lattice simulations messuarable in QCD lattice simulations

• The internal structure of the proton (hadrons) can be explored with The internal structure of the proton (hadrons) can be explored with generalized parton distributions from a new perspective:generalized parton distributions from a new perspective:

• 3D3D partonic content of the protonpartonic content of the proton

• decomposition of the proton spindecomposition of the proton spin

• Generalized parton distributions allow also to explore nuclei Generalized parton distributions allow also to explore nuclei in terms of partonic degrees of freedomin terms of partonic degrees of freedom