Tomography of the Proton Volker D. Burkert Jefferson Lab University of South Carolina, March 30, 2006

Outline  Brief historical overview  Generalized Parton Distributions - a unifying framework of hadron structure  Experiments to access GPDs  3D Imaging of the Proton Quark Structure  12 GeV – A GPD factory  Wrap Up

Some well known facts about the proton Charge: Q p = +1 –It has a neutral partner, the neutron, Q n = 0 Mass: M p ~ 940 MeV/c 2 –Proton + neutron make up 99.9% of the mass of the visible universe Spin: s = ½ћ –Magnetic moment  p  N –Anomalous magnetic moment  a = 1.79  N The exploration of the internal structure of the proton began in the 1950’s with Hofstadter’s experiments. 1950’s: Does the proton have internal structure?

Electron Scattering as a probe of the Proton Structure e’e’ p e Q p’ elastic vv e’e’ p e Q X inclusive vv e’e’ p e Q p’  exclusive vv Q 2 = -(e-e’) 2 = E e – E e’ x B = Q 2 /2M t = -(p-p’) 2 x B = 1 (for elastic scattering) 1/  Q 2 is spatial sensitivity of virtual 

Elastic electron-proton scattering  the proton is not a point-like particle, it has finite size Physics Nobel Prize 1961 R. Hofstadter Proton form factors, transverse charge & current densities Does the Proton have finite size? 1955 d  d  d  /d  n.s. |F(q)| e-e- p e-e- Q p R. Hofstadter

Elastic Electron Proton Scattering JLab/Hall A Q 2 (GeV 2 ) Ratio of Pauli F 2 and Dirac F 1 form factors Elastic form factor experiments continue to this day, and with very high precision.

Constituent Quark model M. Gell-Mann, 1964 G. Zweig, 1964 The proton is build from three quarks of spin s = 1/2 moving in the s-state (L = 0) and having masses m q ~ 300 MeV. Solely built from the quark spins! Proton mass: Proton spin: !!! Proton spin content: a mystery long thought to be solved !!! Tremendously successful model in description of Hadron mass spectra Magnetic moments e.g., u u d

Determine quark momentum distribution f(x). Quarks carry ~ 50% of the proton momentum. What is the internal structure of the proton? => Deep inelastic electron-proton scattering d  /d  dE’ = d  /d  Mott [W 2 (Q 2, )] ep→e ’ X e’e’ p e Q X Nobel prize 1990 J. Friedman H. Kendall R. Taylor Scaling => Quarks are point-like objects! 1968 = 1/x B

SMC experiment at CERN finds that the total quark helicity  s q =  u +  d +  s constitutes only ~20% of proton spin. “Spin crisis” or crisis of over simplified thinking? Where is the Proton Spin? The “spin” of the sun & the planets contributes only 2% to the total angular momentum of the solar system, 98% are the result of the orbital motion of the planets. Angular momentum sum rule for proton: J = ½·(  s q +  L q +  G) => Need to measure  L q and  G !

Proton form factors, transverse charge & current densities D. Mueller, X. Ji, A. Radyushkin, A. Belitsky, … M. Burkardt, … Interpretation in impact parameter space Structure functions, quark longitudinal momentum & helicity distributions How is the proton charge density related to its quark momentum distribution? ? Correlated quark momentum and helicity distributions in transverse space - GPDs

2-D Scotty z x z y 3-D Scotty x GPDs & PDFs 1-D Scotty x probablity Calcium Water Carbon Deep Inelastic Scattering & PDFs Deeply Virtual Exclusive Processes & GPDs

From Holography to Tomography An Apple A. Belitsky, B. Mueller, NPA711 (2002) 118 detector A Proton By varying the energy and momentum transfer to the proton we probe its interior and generate images of the proton’s quark content (“proton tomography”).

Inclusive ScatteringCompton Scattering  = 0 ppp From Inclusive to Exclusive Scattering Deeply Virtual Compton Scattering (DVCS) GPDs depend on 3 variables, e.g. H(x, , t). They probe the quark structure at the amplitude level. t Handbag mechanism  – longitudinal momentum transfer x B 2-x B  = real  pp

Link to DIS and Elastic Form Factors ),,( ~, ~,,txEHEH qqqq  DIS at  =t=0 )()0,0,( ~ )()0,0,( xqx H xqxH q q   Form factors (sum rules)  )(),,( ~, )(),,( ~ ) Dirac f.f.(),,(, 1 1, tGtxEdxtGtxH tF1F1 txH qP q qA q q q          ) Pauli f.f.(),,( 1 tF2F2 txEdx q q          J G =  1 1 )0,, q(q()0,, q(q( xE xHxdxJ q X. Ji, Phy.Rev.Lett.78,610(1997) Angular Momentum Sum Rule

Link to Quark Structure of the Proton dxxH q (x, ,t) = H q (t) +  2 D q (t) ∫ 1 dxxE q (x, ,t) = E q (t) -  2 D q (t) ∫ 1 Quark distributions in transverse space, and orbital angular momentum distribution. Distribution of the forces on quarks in transverse space. finite t

Universality of GPDs Parton momentum distributions Elastic form factors Real Compton scattering at high t Single Spin Asymmetries Deeply Virtual Meson production Deeply Virtual Compton Scattering GPDs

Proton’s gravitational form factors GPDs Quark angular momentum Quark-quark correlations Quark tomography Universality of GPDs

How can we determine the GPDs?

Accessing GPDs in exclusive processes Deeply virtual Compton scattering (clean probe, flavor blind)Deeply virtual Compton scattering (clean probe, flavor blind) Hard exclusive meson production (quark flavor filter)Hard exclusive meson production (quark flavor filter) 4 GPDs in leading order, 2 flavors (u, d) → 8 measurements4 GPDs in leading order, 2 flavors (u, d) → 8 measurements Sensitive to all GPDs. Insensitive to quark flavor Sensitive to H, E ~~ } epep  '' epLL   ''  

e’e’     p  e y x z ** plane ee’  * plane Deeply Virtual Compton Scattering  *p ep ep  Kinematics

Accessing GPDs through DVCS d4d4 dQ 2 dx B dtd  ~ | T DVCS + T BH | 2 E o = 11 GeV E o = 6 GeV E o = 4 GeV BH DVCS T BH : given by elastic form factors F 1, F 2 T DVCS : determined by GPDs I  ~ ( T BH ) Im (T DVCS ) BH-DVCS interference generates beam and target polarization asymmetries that carry the proton structure information. DVCS BH pp e e

Model representation of GPD H(x, ,0) Accessed by cross sections Accessed by beam/target spin asymmetry t=0 Quark distribution q(x) -q(-x) DIS measures at  =0

A =           = Measuring GPDs through polarization  LU  ~ sin  Im{F 1 H +  (F 1 +F 2 ) H +kF 2 E }d  ~ Polarized beam, unpolarized target: Unpolarized beam, longitudinal target:  UL  ~ sin  Im{F 1 H +  (F 1 +F 2 )( H +  /(1+  ) E ) -.. }d  ~ Unpolarized beam, transverse target:  UT  ~ sin  Im{k(F 2 H – F 1 E ) + ….  }d   = x B /(2-x B ) k = t/4M 2 H ( ,t ) Kinematically suppressed H ( ,t ) ~ Kinematically suppressed H (  t ), E (  t)

Pioneering experiments observe interference First GPD analyses of HERA/CLAS/HERMES data in LO/NLO consistent with  ~ A. Freund (2003), A. Belitsky et al. (2003) twist-3twist-2 A UL =  sin  +  sin2  2001 e - p  e - p  e + p  e + p 

CLAS JLab Site: The 6 GeV CW Electron Accelerator

C EBAF L arge A cceptance S pectrometer

- Polarized electrons, E = 5.75 GeV - Q 2 up to 5.5 GeV 2 - x B from 0.2 to Hadronic invariant mass W < 2.8 GeV W = GeV First JLab experiment with GPDs in mind.

A first view at kinematical dependencies A LU CLAS preliminary Model with GPD parametrization and quark k T corrections describes data. ~ B  LU  ~ sin  Im{F 1 H +  (F 1 +F 2 ) H – t/4m 2 F 2 E }d  ~ A UL =  sin  +  sin2  

=> These measurements are much harder, as a typical polarized target NH 3 contains only 3 out of 17 nucleons that have their spins aligned. beam Helmholtz coils liquid He final state particle to CLAS Magnetic field ~ 5 Tesla Temperature ~ 1 K target cell 1m Dynamically polarized proton target

Installation of the Polarized in CLAS

First DVCS measurement with spin-aligned target Unpolarized beam, longitudinally spin-aligned target:  UL  ~ sin  Im{F 1 H +  (F 1 +F 2 ) H +… }d  ~  = ±  = ± H=0 ~ ~ A UL shows sensitivity to and strongly depends on x B (  ). H=0 ~ Planned experiment in 2008 will improve accuracy dramatically. CLAS preliminary

DVCS DVMP GPDs – Flavor separation hard vertices hard gluon Photons cannot separate u/d quark contributions. longitudinal photons only M =       select H, E, for u/d quarks M = , K select H, E High Q 2

Cross section  L  (  * L p  p  L 0 ) GPD formalism works well for all Q 2 > 1.7GeV 2 and x B =

GPD model parameterization by Guidal, Polyakov, Radyushkin, Vanderhaeghen (2005) x b (fm) y x z First model-extraction of GPD H u (x,b ) T  u-quarks carrying a large momentum fraction x of the proton are concentrated at small transverse distances from the proton center.  slow u-quarks can be as far as several fm away from the proton center.

In the past few years, we have made a start in the quest to unravel the Structure of the Proton. What does the future hold?

JLab Upgrade to 12 GeVCHL-2 Enhance equipment in existing halls Add new hall At 12 GeV, CEBAF will be an ideal for GPD studies.

Deeply Virtual Exclusive Processes - Kinematics Coverage of the 12 GeV Upgrade H1, ZEUS JLab Upgrade 11 GeV H1, ZEUS 12 GeV 11 GeV 27 GeV 200 GeV W = 2 GeV Study of high x B domain requires high luminosity 0.7 HERMES COMPASS

CLAS12 EC TOF Cerenkov Torus Drift Chambers Cerenkov Central Detector Beamline Increase luminosity to tenfold to cm -2 s -1 1m

CLAS12 Forward Detector Single Sector (exploded view) University of SC NP Group

Hall B 12 GeV Upgrade - CLAS12 Proton Tomography Spin Structure of the Proton Excited Baryons and Mesons QCD and Nuclei

 GPD’s and 3D-Imaging of the Nucleon  Valence Quark Distributions  Form Factors and Resonance Excitations  Hadron Spectroscopy with quasi-real Photons Initial Physics Program in Hall B at 12 GeV  Hadrons in the Nuclear Medium

DVCS/BH- Beam Asymmetry With large acceptance, measure large Q 2, x B, t ranges simultaneously. A(Q 2,x B,t)  (Q 2,x B,t)  (Q 2,x B,t) E e = 11 GeV A LU

CLAS12 - DVCS/BH- Beam Asymmetry Luminosity = 720fb -1 E e = 11 GeV Q 2 =5.5GeV 2 x B = t = 0.25 GeV 2

CLAS12 - DVCS/BH Beam Asymmetry L = 1x10 35 T = 2000 hrs  Q 2 = 1 GeV 2  x = 0.05 E = 11 GeV Selected Kinematics  LU ~sin  Im{F 1 H +.  }d  e p ep 

GPD H from expected DVCS A LU data b val =b sea =1 MRST02 NNLO distribution Q 2 =3.5 GeV 2  Other kinematics measured concurrently 

CLAS12 - DVCS/BH Target Asymmetry e p ep  Longitudinally polarized target  ~sin  Im{F 1 H +  (F 1 +F 2 ) H... }d  ~ E = 11 GeV L = 2x10 35 cm -2 s -1 T = 1000 hrs  Q 2 = 1GeV 2  x = 0.05

CLAS12 - DVCS/BH Target Asymmetry  Asymmetries highly sensitive to the u-quark contributions to the proton spin. Transverse polarized target e p ep   ~ sin  Im{k 1 (F 2 H – F 1 E ) +…}d  Q 2 =2.2 GeV 2, x B = 0.25, -t = 0.5GeV 2 E = 11 GeV Sample kinematics A UTx Target polarization in the scattering plane A UTy Target polarization perpendicular to the scattering plane

Exclusive   production on transverse target 2  (Im(AB*)) T  UT  A ~ 2H u + H d B ~ 2E u + E d 00 K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001 Q 2 =5 GeV 2 E u, E d allow to map the orbital motion of quarks. 00 B A ~ H u - H d B ~ E u - E d ++

Double DVCS (DDVCS) Cross section DVCS asymmetry DDVCS DDVC rates reduced by more than factor 200 e - p e - pe + e -

d X ( x,b ) T E d (x,t) M. Burkardt Tomographic Images of the Proton I E u (x,t) u X ( x,b ) T CAT scan slice of human abdomen flavor polarization ∫ d2td2t (2  ) 2 e -i·t·b E(x,0,t) T q(x,b ) = T Target polarization

X. Ji and F. Yuan, D image is obtained by rotation around the z-axis Charge density distributions for u-quarks y z Tomographic Images of the Proton II x= fm fm x= fm fm x= fm -220fm interference pattern 10

Wrap - Up We have come a long way in studying the structure of the proton since Hofstadter’s first experiments 50 years ago. QCD is the theoretical framework, and GPDs and the handbag mechanism the tool to study the proton structure in a consistent way. With the JLab energy upgrade and CLAS12, we will have the equipment needed to study the proton structure at a much deeper level.

To me, the study of the proton structure using the GPDs is one of the most exciting applications of QCD Nobel prize for “Asymptotic Freedom in Strong Interaction” D. Gross D. Politzer F. Wilczek “QCD is our most perfect physical theory”, F. Wilczek, PANIC Conference, Uppsala, 1999