Outline. Generalized Parton Distributions. Elastic Form Factors and Charge Distributions in Space. From Form Factors to Quark Spin Distributions

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1 Outline Generalized Parton Distributions in lepton scattering and antiproton annihilation experiments Michael DürenD Universität Gießen en The structure of the proton: From form factors to uark spin distributions Hard exclusive reactions: Quantum phase-space space tomography of the nucleon Experiments with lepton probes (HERMES) Experiments with hadron probes (PANDA) Conclusions Kollouium an der Univ. Freiburg, Feb. 08, 006 (By the way: some of my transparencies are stolen e.g. from X. Ji) From Form Factors to Quark Spin Distributions Elastic Form Factors and Charge Distributions in Space In studying the microscopic structure of matter, the form factor F( ) is one of the most fundamental observables The Fourier Transformation (FT) of the form factor is related to the spatial charge (matter) distributions! The proton form factor is measured by elastic electron scattering (exclusive reaction) y (fm) Up-uark charge distribution k k P P 4 x (fm)

2 Momentum Distributions Feynman Quark Distributions The form factors provide the static picture; no information about the dynamical motion of the constituents. The momentum space distributions of the particles can be measured through single-particle knock-out out experiment Measurable in inclusive and semi-inclusive inclusive deep-inelastic scattering Our knowledge on unpolarized uark distributions The Feynman x distributions are the density of uarks with longitudinal momentum xp (with transverse momentum integrated over) 5 x-distribution from fit to experimental data (GRV, CTEQ, MRS parameterization ) Q²-evolution agrees with QCD calculation (over 4 orders of magnitude) Great test of pertubative QCD 6 Spin Structure of the Proton The spin ½ of the proton is composed in a complicated way: = ( d s) { G u L LG 3 uarks gluons Measurement of (x,q²) and G(x,Q²) in inclusive and semi-inclusive inclusive polarized deep inelastic scattering orbital angular momentum Access by hard exclusive reactions Hard exclusive reactions Quantum phase-space space tomography of the nucleon Quark flavor tagging Photon-gluon fusion 7

3 Quantum phase-space space Wigner distribution A classical particle is defined by its coordinate and momentum (x,p): phase-space space A state of classical identical particle system can be described by a phase-space space distribution f(x,p). The time evolution of f(x,p) obeys the Boltzmann euation. In uantum mechanics, because of the uncertainty principle, the phase-space space distributions seem useless, but Wigner introduced the first phase-space space distribution in uantum mechanics (93) Wigner function: Wigner function When integrated over x, one gets the momentum density. When integrated over p, one gets the probability density. Any dynamical variable can be calculated from it! The Wigner function contains the most complete (one-body) info about a uantum system.! Example: Wigner function of uantum light 9 0 Can we measure the complete uantum information of uarks in the nucleon? Wigner operator Wigner distribution: density for uarks having position r and 4-momentum 4 k µ (off-shell) From the Wigner distribution to Generalized Parton Distributions (GPDs) The reduced Wigner distribution is a function of six variables [r,k=( r,k=(k k )]. After integrating over r, one gets transverse-momentum dependent parton distributions Alternatively, after integrating over k, one gets a spatial distribution of uarks with fixed Feynman momentum k =(k 0 k z )=xm xm: Proton tomography: For every choice of x, one can use the Wigner distribution to picture the nucleon The reduced Wigner distribution is related to the Generalized parton distributions (GPDs) 7-dimensional distribution No known experiment can measure this!

4 What is a GPD? A proton matrix element which is a hybrid of elastic form factor and Feynman distribution Depends on x: fraction of the longitudinal momentum carried by parton t= : t-channel momentum transfer suared ξ: skewness parameter 3-D D contours of uark distributions for various Feynman x values There are 4 important GPDs (among others): ~ ~ H ( x, ξ, t), E ( x, ξ, t), H ( x, ξ, t), E ( x, ξ, t) Limiting cases: t 0: Ignoring the impact parameters leads to ordinary parton distributions ( x) = H ( x,0,0) ~ ( x) = H ( x,0,0) Integrating over x: Parton momentum information is lost, spatial distributions = form factors remain F F ( t) = ( t) = H ( x, ξ, t) dx E ( x, ξ, t) dx 3 b y b x Fits to the known form factors and parton distributions 4 with additional theoretical constraints (e.g. polynomiality) and model assumptions z Conclusions: Quarks in the uantum mechanical phase-space space Elastic form factors charge distribution (space coordinates) Parton distributions momentum distribution of uarks (momentum space) Generalized parton distributions (GPDs( GPDs) ) are reduced Wigner functions correlation in phase-space space e.g. the orbital momentum of uarks: L = r p Experiments with lepton probes Angular momentum of uarks can be extracted from GPDs: Ji sum rule: J = [ H ( x, ξ,0) E ( x, ξ,0 ] xdx ) GPDs provide a unified theoretical framework for various experimental processes 5

5 The HERMES Experiment at DESY Positrons New recoil detector in Jan. 006 The HERMES experiment at HERA Detectors... Storage cell Spectrometer magnet GeV e and e - polarized <P>~55% r r Internal gas target: He, D, H, H unpol: : H,D,He,N,Ne,Kr,Xe Reconstruction: δp/p < %, δθ < 0.6 mrad 8 Particle ID: TRD, preshower, calorimeter; since 998: RICH muon-id The HERMES recoil detector The HERMES recoil detector Measure complete final states of exclusive reactions including the recoil proton e.g. ep e pγ Improved kinematic resolution Improved background suppression of non-exclusive events High statistics on unpolarized targets (~fb -, proton and nuclear targets) SciFi detector A test run with the complete recoil detector was done using cosmic rays Silicon strip detector Scintillating fiber detector Photon detector Silicon detector Photon detector 9 Super conducting 0 solenoid

6 HERMES recoil detector (Jan 006) 80 x 64-channel-PMTs Experimental Access to GPDs QCD handbag diagram Recoil detector (hidden) 80 x 64-fibrelightguide bundles Deeply virtual Compton scattering (DVCS) Hard exclusive meson production (HEMP) Deeply virtual Compton scattering (DVCS) DVCS is the cleanest way to access GPDs: γ * N γn DVCS and BH Interference (ep( ep e γp) xξ: longitudinal momentum fraction of the uark ξ: exchanged longitudinal momentum fraction t :suared momentum transfer Factorization theorem is proven! Handbag diagram separates hard scattering process (QED & QCD) and non-pertubative structure of the nucleon (GPDs) ξ = x x B B / dσ τ DVCS (τ * BH τ τ DVCS BH τ FF Bethe-Heitler (BH) * DVCS τ BH ) Kinematics: DVCS x [-,] ξ x B /(- x B ) t=(- ) Q =- GPDs = probability amplitude for N to emit a parton (xξ)( and for N N to absorb it (x-ξ)( 3 DVCS-BH interference I gives non-zero azimuthal asymmetry Use BH as a vehicle to study DVCS. 4

7 Azimuthal asymmetries in beam spin and beam charge Fourier decomposition of interference term: 3 I I I I ± c0 cn cos( nφ) λ sn sin( nφ) n= n= A Results: BSA and BCA on proton LU r s N( φ) N( φ) ( φ) = r s < P > N( φ) N( φ) B A C N ( φ) = N ( φ) N ( φ) N ( φ) ( φ) charge spin Access to real and imaginary part of helicity conserving amplitude M, (GPDs enter in linear combinations in amplitudes) beam spin asymmetry (BSA) r dσ s, ( ep) dσ( ep) s I sinφ sinφ Im M beam charge asymmetry (BCA) dσ -, ( e p) dσ( e p) c I cosφ cosφ Re M HERMES is the only experiment which measures BCA 5 BSA: Significant sin(φ) ) dependence r dσ s, ( ep) dσ( ep) s I sinφ sinφ Im M BCA: Significant cos(φ) ) dependence dσ -, ( e p) dσ( e p) c I cosφ cosφ Re M 6 Projected error-bars of the recoil running σ L First results for Hard Exclusive Meson Production (HEMP) from HERMES: Pseudoscalar Mesons sinφ [ S σ S σ ] A sinφ L LT UL σ S sinφ E ~ H ~ T Pion form factor BSA and BCA on proton 7 HEMP cross section ep e n π GPD Model: 8 Vanderhaeghen, Guichon, Guidal

8 First results for HEMP from HERMES: Vector Mesons (ρ 0,φ,ω) -Clean signal without background subtraction; -DIS-background well described by MC; Present and Future Lepton Scattering Experiments HERMES Coll. in DESY and CLAS Coll. in Jefferson Lab and COMPASS at CERN have made measurements of DVCS and related processes. HERMES is uniue in beam charge asymmetries First results of DVCS on nuclei (HERMES) Large acceptance recoil detector will run Future: COMPASS recoil upgrade? Jefferson Lab GeV upgrade?? Electron-ion collider (EIC) 00?? HEMP target spin asymmetry ep e p ρ Are hadron probes as good as lepton probes? Experiments with hadron probes For exclusive processes, crossing allows to measure the same matrix elements with completely different experiments and probes Instead of having an initial electromagnetic process, a final state electromagnetic process is selected Example: Compton scattering Annihilation γ p γ p Mandelstam t is replaced by s GPDs=General Parton Distributions become General Distribution Amplitudes 3

9 Are hadron probes as good as lepton probes? Experimental difficulty: the total cross section of a hadronic beam is typically much larger than the one of the exclusive electro- magnetic process The experiment needs a huge background suppression factor as the majority of events have a hadronic final state Example: Compton scattering Annihilation γ p γ p Turning Matter into Light: pp γγ annihilation at large energies and angles What is the dominant mechanism? Large p T in this exclusive reaction defines hard scale: parton picture Emission of a single photon from one (uasi-free) parton is suppressed Emission of two photons from the same parton is allowed At intermediate energies (s~0 GeV) the hard interaction of one parton can be separated from the soft part which is parameterized by General Distribution Amplitudes: handbag diagram Quasi-free partons cannot emit single photons (suppressed) Handbag diagram: one uark emits both photons (allowed) 33 Soft part of annihilation 34 Further processes of interest: Reactions with the QCD handbag diagram Further processes of interest: Another distribution amplitude hard gluon π, ρ, φ,... Hard exclusive meson production (large p T ) Q small: like Crossedchannel wide angle Compton scattering (large p T ) Q large: additional degrees of freedom e -, µ e, µ No handbag diagram Here the photons and the pion are produced in forward direction! Measure Transition distribution amplitudes 35 pp γ * π explores the pion cloud pp γ * ρ explores the ρ cloud pp γ * γ explores the photon cloud (Study next to lowest Fock state of the proton) B. Pire and L. Szymanowski 36

10 The experimentalist s s point of view:.: Reject all events with more than primary final state particles 3.: Observe second particle which balances momentum and total energy.:tag one real photon with with large large p T (for p T GDA) (or virtual photon with in forward direction) (TDA)) γ, γ * π, ρ, ω, φ,... 4.: Compare the differential production x-sections of real of real photons, virtual photons and and all kind all kind of neutral of neutral mesons mesons (and in in case of of a a deuteron target also also charged mesons) Ask theoreticians for predictions (γ*,ρ even give polarization 37 observables) Trivial -body kinematics p beam =5 GeV/c, s=5.5 GeV p T θ Eγ Photon kinematics: Eγ = Photon angle in CMS and transverse momentum are large for wide angle Compton: p T = few 00 MeV....7 GeV Interesting range in LAB around Eγ = 8 θ=0 4π calorimeter needed! Background suppression by Large acceptance charged particle detector veto Good resolution calorimeter for check of exclusivity (momentum balance) Possibly large acceptance neutral particle veto (neutrons) 38 First estimate of cross section axial vector vector dσ πα = d cosθ s Assumptions : p beam s = 0 GeV L = 0 Result : = 5 GeV/c 3 cm σ = Rate em RV - s fm -3 - ( s)cos θ R sin θ /s = few 0 3 A /month ( s) e Turning light into matter... Compare with the time inverted process γγ pp Available at e e - machines: uasi real photons e e e γ * γ * e e pp Comparison of the model with e e - data Simple model by Freund, Radyushkin, Schäfer, Weiss,... PRL 90, 0900 (003) Data from e e - suggest that the model 39 underestimates the real rate by a large factor (status of ~003) 40

11 Latest results from Belle Asymmetric e e - collider High luminosity machine Latest results from Belle γγ pp s = 0.6 GeV L = 0 34 /cm s 4 Energy dependence Angular dependence (GPD curve from Kroll/Schäfer) 4 Measured cross section in Fermilab experiment E760 has already some first measurements of this channel! Feed down background The cross section at 3.6 GeV is - ππ: : ~0 000 pb - πγ: : ~ 00 pb - γγ: : ~ 5 pb - γγ feed-down: down: ~5 pb (similar contribution from ππ and πγ) Necessary selections: no charged tracks exactly neutral clusters Each cluster has * E s / Two clusters are collinear in E760 detector: * CMS θ γγ 80 Non-magnetic spectrometer * Minimal angle cut θ γ > lead glass counter Additional hits in calorimeter E>0 MeV threshold below threshold may not match 6- mrad resolution to asymmetric π 0 decay δe / E = 6% / E.4 % 43 Fermilab data are all background dominated!... 44

12 Cross section comparison Belle γγ pp Fermilab First Results of Panda Simulation by G. Serbanut PANDA 0. pb E760 feed down limit from ππ and πγ (upper limit of γγ signal) Panda limits: W= s = 5.5 GeV and σ = 0. pb (for 00 *0 3 /cm²s) 45 Reconstructed invariant mass of 5.5 GeV γγ events Feed-down of 5.5 GeV πγ events are strongly suppressed; ππ is zero in this simulation of 0000 ev. 46 hard gluon Processes of interest: πγ-process is not only background but also signal! π, ρ, φ,... Hard exclusive meson production (large p T ) Much larger cross section (compared to γγ) makes it easier to access! 3-γ final state The PANDA detector E760 results 47 (curve from Kroll/Schäfer) 48

13 PANDA HESR: High Energy Storage Ring Beam Momentum.5-5 GeV/c High Intensity Mode: Luminosity x0 3 cm - s - (x0 7 Hz) dp/p (stoch. cooling)~0-4 High Resolution Mode: Luminosity x0 3 cm - s - dp/p(e- cooling) ~0-5 HESR at GSI Outlook: Are GPDs useful for ATLAS? Future forward detectors at LHC can measure exclusive diffractive reactions which can be described by GPDs diffractive Higgs production Exclusive annihilation reactions related to the handbag and similar QCD diagrams can be measured at HERMES and PANDA These reactions tell us something about the uark structure of the proton, about QCD and about the reaction mechanisms Conclusions Is the GPD concept universal for all reaction types? γ p γ Special thanks to X. Ji, M. Diehl, R. Jakob, P. Kroll, B. Pire, A. Schäfer, C. Weiss, H. Stenzel M. Düren, Univ. Giessen 5