The Transition from soft to hard physics through Meson Electroproduction at Jlab and beyond Tanja Horn Jefferson Lab UMd Seminar College Park, MD 26 March 2008

Outline The dual nature of QCD: physics interest Exclusive processes Observables for the fundamental degrees of freedom Experiments to access information about the reaction mechanism Cross section data and conclusions at current energies Work in progress and future plans

Hadrons Atom (atomic number A): Z electrons Z protons, (A-Z) neutrons Protons and neutrons are two examples of a larger category of strongly-interacting particles called hadrons Two families of hadrons: Baryons: valence qqq Mesons: valence

Quarks and Leptons The ground state of matter

QED vs. QCD QED The theory of electricity and magnetism The theory of the strong force QED Slide from: Jlab Open House 2007

The Dual Nature of QCD At short distances, we have a good understanding of strong interactions with perturbative QCD (pQCD) Proton is not point like – elastic electron scattering [Hofstadter, 1961] Quarks and gluons are the constituents – Deep Inelastic Scattering [Friedmann, Kendall and Taylor, 1990] Asymptotic freedom [Gross, Politzer, Wilczek, 2004] Long distance properties are understood in terms of chiral perturbation theory Color confinement From: W. Melnitchouk et al., Phys.Rept.406:127-301,2005

The Fundamental Issue Confinement occurs at an intermediate distance scale Lattice QCD and phenomenological models give insight into the hadron structure at the confinement scale Need experimental observables of the fundamental degrees of freedom of QCD in coordinate space Forward parton distributions do not resolve partons in space Form Factors measure spatial distributions, but the resolution cannot be selected independent of momentum transfer Need a combination of both!

Generalized Parton Distributions Generalized Parton Distributions (GPDs) are a generalization of Parton Distribution Functions (PDFs), where initial and final quark-gluon momenta are not identical x, momentum fraction variables t=2.  Fourier Conjugate to impact parameter of quark or gluon. Q2 = resolution of the probe

Exclusive Processes and GPDs Increasing the virtuality of the photon (Q2) allows one to probe short distances Sensitivity to partonic degrees of freedom At sufficiently high Q2, the process should be understandable in terms of the “handbag” diagram Incoming virtual photon scatters off one quark interaction can be calculated in perturbative QCD The non-perturbative (soft) physics is represented by the GPDs Shown to factorize from QCD perturbative processes for longitudinal photons [Collins, Frankfurt, Strikman, 1997] t-channel process handbag

Experimental Access to GPDs: DVCS q = k-k’ Q2 = q2>0 =q-q’ t=2 s = (k+p)2 xBj = Q2/(2p·q) W2 = (q+p)2 Using a polarized beam on an unpolarized target, two observables can be measured:

GPDs from Exclusive Meson Production From: Diehl, Kugler, Schaefer, CW 2005 Interest: spin/flavor structure of GPDs – mesons select spin Vector mesons (r,w,f) sensitive to H and E Pseudo scalar mesons sensitive to and Detection of final states easier – but interpretation is complicated by convolution with meson distribution amplitude (DA) ~ H ~ E

GPD Program at JLab DVCS Beam-spin asymmetry [Stepanyan et al, PRL 87, 182002, 2001] E00-110, DVCS at 6 GeV (Hall A) E01-113, DVCS at 6 GeV with CLAS Meson Production: many studies of exclusive cross sections exist, but contribution of σT unknown at higher energies Hall B: E99-105 (ρ, ω) Q2: 1.5-3.5 GeV2, -t<1.5 (GeV/c)2 Hall C: Fpi-1, E91-003, Fpi-2, pionCT (π±) Q2 range for precision L/T to 2.45 GeV2 Hall A, Hall B: DVCS, e1-6 (π° - unseparated) A major motivation for the 12 GeV upgrade is a program of Deep Exclusive Measurements to constrain GPDs

Tests of the Handbag Dominance To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies No single criterion for the applicability, but tests of necessary conditions can provide evidence that the Q2 scaling regime (partonic picture) has been reached One of the most stringent tests of factorization is the Q2 dependence of the π electroproduction cross section σL scales to leading order as Q-6 σT scales as Q-8 As Q2 becomes large: σL >> σT Factorization Q2 ? Factorization theorems for meson electroproduction have been proven rigorously only for longitudinal photons [Collins, Frankfurt, Strikman, 1997]

Designing a pion electroproduction experiment Precision measurement of kinematics Precision knowledge of the acceptance Detect scattered electron and π Need to know about the neutron as well Q2= |q|2 – ω2 t=(q - pπ)2 W=√-Q2 + M2 + 2Mω scattering plane reaction plane Can isolate L/T/LT/TT if one knows azimuthal angle (φ) and virtual photon polarization (ε) are known For a given Q2, higher W allows for smaller tmin

Pion Electroproduction in Hall C Three experiments took data to the highest possible value of Q2 with 6 GeV beam at Jlab: Fpi-1 (1997), Fpi-2 (2003), pionCT(2004) Full separation of the L/T/TT/LT terms in the cross section Ancillary measurements of the separated π+/π- ratio to test the reaction mechanism Exp Q2 (GeV2) W (GeV) |t| (Gev)2 Ee Fpi-1 0.6-1.6 1.95 0.03-0.150 2.445-4.045 Fpi-2 1.6,2.45 2.22 0.093,0.189 3.779-5.246 πCT 2.15, 4.0 2.2 0.16-0.44 4.021-5.012

Experimental Setup Short Orbit Spectrometer (SOS) detects e- HMS: 6 GeV SOS: 1.7 GeV Short Orbit Spectrometer (SOS) detects e- High Momentum Spectrometer (HMS) detects π+ Relatively small acceptance – well understood Kinematics well constrained, angles well reproducible Cryogenic targets at high currents - relatively short experiments

Analysis: p(e,e’π+)n Event Selection Coincidence measurement between charged pions in HMS and electrons in SOS ±1ns Continous wave (CW) beam minimizes “accidental” coincidences Excellent particle identification: Protons in HMS rejected using coincidence time and aerogel Cerenkov Electrons in SOS identified by gas Cerenkov and Calorimeter 17

p(e,e’π+)n Exclusivity Easy to isolate the exclusive channel Missing mass resolution easily excludes 2π contributions Q2, x t, φ e e’ p n π Missing mass cut assures exclusivity 18

Analysis: Extraction of Observables Radial coordinate: -t, azimuthal coordinate: φ Θπ=0 Θπ=+4 Θπ=-3 -t=0.1 -t=0.3 Q2=1.60, High ε Measure σTT and σLT by taking data at three angles: θπ=0, +4, -3 degrees W/Q2 cuts define a common phase space at both epsilon points Q2=2.45 GeV2 Q2=1.60 GeV2 Extract σL by a simultaneous fit of L, T, LT, TT using the measured azimuthal angle (φ) and knowledge of the photon polarization (ε) 19

Cross section W-dependence σπ depends on W, -t, Q2 Cross section W-dependence given by: (W2-M2)n Fpi-1/Fpi-2 data suggest that a n~2 is appropriate πCT data were taken at central W=2.2 GeV Relatively small sensitivity to variations in W, ~1% at Q2=2.15 GeV2 Fit: n=1.8 Fπ1 Fπ2 W-dependence of σπ makes sense – but what about –t and Q2?

Cross section t-dependence T. Horn et al., Phys. Rev. Lett. 97, 192001 (2006) σL decreases with –t as expected due to the pion pole The magnitude decreases at constant W with increasing Q2 as tmin increases with Q2 σT is largely flat in t Magnitude decreases with increasing Q2 Still a large contribution at Q2=2.45 GeV2 VGL σL VGL σT

Global t-dependence of σL VGL σL VGL σT Scaled to W=2.19 GeV, Q2=0.7 GeV2 σL is dominated by the pion pole An exponential t dependence describes the data from Jlab and earlier data from DESY quite well t-dependence of σπ as expected – what about Q2?

Q2 dependence of σL and σT Hall C data at 6 GeV The Q-6 QCD scaling prediction is consistent with the JLab σL data Limited Q2 coverage and large uncertainties make it difficult to draw a conclusion The two additional factorization predictions that σL>>σT and σT~Q-8 are not consistent with the data Q2=2.7-3.9 GeV2 Q2=1.4-2.2 GeV2 σL σT T. Horn et al., arXiv:0707.1794 (2007)

Fπ - a factorization puzzle? T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001. Fπ has a simple prediction in perturbative QCD Q2>1 GeV2: Q2 dependence of Fπ is consistent with hard-soft factorization prediction (Q-2) But globally Fπ data still far from hard QCD calculations Not in QCD factorization regime? Or additional soft contribution from the pion wave function? T. Horn et al., arXiv:0707.1794 (2007). A.P. Bakulev et al, Phys. Rev. D70 (2004)] H.J. Kwee and R.F. Lebed, arXiv:0708:4054 (2007) H.R.Grigoryan and A.V.Radyushkin, arXiv:0709.0500 (2007)

Compton Scattering and Soft Contributions Soft contributions can result in deviations from expected scaling behavior [A. Radyushkin, Phys. Rev. D58 (1998) 114008.] Fixed θ*: dσ/dt ~ s-n(θ), nhard(θ) =6 If similar soft effects are important in π+ production, then the observed scaling would be accidental θ ndata nsoft 60 5.9±0.3 6.1 90 7.1±0.4 6.7 105 6.2±1.4 7.0 M. A. Shupe et al., Phys. Rev. D19, 1921 (1979) dσ/dt ~ A s-n

Conclusions at 6 GeV σL data consistent with hard-soft factorization prediction relatively large uncertainties Limited Q2 range Fπ data consistent with hard-soft factorization prediction, but overall normalization is not right soft contributions still important Compton scattering experiments suggest that higher order effects dominate the Compton cross section

Factorization Tests at 12 GeV Measurements with large kinematic coverage and improved precision L/T separated π+ cross sections at fixed xB and –t Factorization studies without L/T separation - studies of π-cross sections Higher Q2 Fπ studies Extension to strange channels

Hall C Factorization @ 12 GeV: Experiment approved for 42 days in Hall C E12-07-105 (T. Horn et al.) Super High Momentum Spectrometer (SHMS) detects pions Small angles, large momenta HMS detects electrons SHMS HMS x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.31 1.5-4.0 2.0-3.1 0.1 0.40 2.1-5.5 2.0-3.0 0.2 0.55 4.0-9.1 2.0-2.9 0.5

E12-07-105 Kinematics Overview The Q2 coverage is a factor of 3-4 larger compared to 6 GeV Facilitates tests of the Q2 dependence even if L/T is less favorable than predicted Cross section becomes small as Q2 increases High luminosity important (typical Jlab: 1038 cm-2 s-1) Phase space for L/T separations with SHMS+HMS x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.31 1.5-4.0 2.0-3.1 0.1 0.40 2.1-5.5 2.0-3.0 0.2 0.55 4.0-9.1 2.0-2.9 0.5 The kinematics for the LD2 π- measurement

Q-n scaling after the Jlab Upgrade Fit: 1/Qn QCD scaling predicts σL~Q-6 and σT~Q-8 Projected uncertainties for σL are improved by a factor of more than two compared to 6 GeV xB dnL dnT dnLT dnTT 0.31 0.3 0.2 0.5 0.6 0.40 0.4 0.7 0.8 0.55 2.5 1.0 - Data will provide important information about feasibility of GPD experiments at JLab 12 GeV kinematics

π- cross section – measure σL without explicit L/T? Fpi-1 and Fpi-2 saw σL/σT larger for π- than for π+ If σT is small, one may extract σL from the unseparated cross sections Scaling prediction for σT/σL is Q-2 Measure L/T from π- production to an absolute precision of 0.1-0.3 Uncertainties assume R= σL/σT for π+: π- is at least 1:2 (based on Fpi-1 and Fpi-2 results)

Fπ after the JLab Upgrade Experiment (E12-06-101) approved for 55 days in Hall C The 11 GeV electron beam and the SHMS in Hall C with θ=5.5º allows for precision data up to Q2=6 GeV2 May expect to see the onset of perturbative regime

Fπ Background Studies at 12 GeV –tmin<0.2 GeV2 constraint limits Q2 reach of Fp measurements Measurement of σL for p0 could help constrain pQCD backgrounds JLab 6 GeV PAC31 proposal (T. Horn et al.) In a GPD framework, p+ and p0 cross sections involve different combinations of same GPDs – but p0 has no pole contribution VGG GPD-based calculation pole non-pole p+ p0 33

Strangeness in GPDs and exclusive processes Kaon production probes polarized GPDs analogous to pions Pole term is prominent in K form factor measurements New information about SU(3) in meson wave function High –t meson production to learn about the reaction mechanism QCD factorization ~ E

Hall C Kaon Electroproduction Unseparated kaon cross sections from E93-018 Limited Q2 range Difficult to draw a conclusion about the reaction mechanism

K+ Form Factor at 6 GeV JLAB experiment E93-018 extracted –t dependence of σLK+ near Q2=1 GeV2 Trial Kaon FF extraction was attempted using a simple Chew-Low extrapolation technique gKLN poorly known Q2=1.0 GeV2 Q2=0.75 GeV2 -t dependence shows some “pole-like” behavior

Kaon electroproduction at 11 GeV Planned proposal for PAC34 T. Horn, P. Markowitz et al. Measure form factor to Q2=3 GeV2 with good overlap with elastic scattering data Measure kaon electroproduction cross section to Q2=5 GeV2 Additional information about the reaction mechanism Kinematics allow for comparison of the π+/K+ ratio for factorization studies

Factorization at 11 GeV Summary L/T separated π+ cross sections will be essential for understanding the reaction mechanism at 12 GeV Relative contribution of σL and σT in π+ production - interpretation of asymmetry and ratios π- data will check the possibility of measuring σL without explicit L/T separation Are energies sufficiently large to access GPDs with these data? For DVCS: likely yes For deep exclusive processes: probably not Higher order contributions may contribute up to relatively large values of Q2 – Fpi prediction even at Q2=6 GeV2

GPD studies beyond JLab: EIC Studies of exclusive processes is a new territory for colliders Demanding in luminosity requirements Particle detection not easy Physics interest closely related to JLab 6 GeV and 12 GeV program Feasibility studies at JLab (A. Bruell, T. Horn, C. Weiss, V. Guzey) in progress π+n, π0p, K Λ channels

π+n at EIC: first estimates Cross section parameterization from Ch. Weiss Seems feasible at not too small values of x

π+n at EIC: angle and momentum p e Neutron is the largest momentum particle Neutron at <1° from beam line Emitted at relatively small angle with respect to proton beam Not in acceptance of main detector - need separate neutron detection (similar to HERA/LHC)

Summary GPDs may provide the most complete information on the structure of the nucleon Tests of hard-soft factorization are essential for our understanding of the dominant reaction mechanism L/T separated π+ cross sections at 6 GeV lack precision L/T separated π+ data over a wide kinematic range at 12 GeV will have a significant impact on our understanding of hard exclusive reactions Relative contribution of σL and σT in π+ production - interpretation of asymmetry and ratios Experimental access to GPDs may require the additional energy range of an electron ion collider

Extraction of Fπ from p(e,e’π+)n data π+ electroproduction can only access t<0 (away from pole) Early experiments used “Chew- Low” technique measured –t dependence Extrapolate to physical pole This method is unreliable – different fit forms consistent with data yet yield very different FF A more reliable approach is to use a model incorporating the + production mechanism and the `spectator’ nucleon to extract F(Q2) from L.  t-pole “extrapolation” is implicit, but one is only fitting data in the physical region

Check of the pion electroproduction technique Does electroproduction really measure the physical form-factor since we are starting with an off- shell pion? This can be tested making p(e,e’+)n measurements at same kinematics as +e elastics Looks good so far: Ackermann electroproduction data at Q2 = 0.35 GeV2 consistent with extrapolation of SPS elastic data.

Fπ and Factorization Tests Hard Scattering Fπ provides another test of the validity of QCD factorization If one replaces the GPD in the handbag mechanism by the Nπ vertex and the pion DA, one obtains Fπ Naively expect a correlation between pQCD calculations of Fπ and experimental data where factorization applies Fπ scales to leading order as Q-2 Hard Scattering

K+ Form Factor Extraction At low Q2 measure charged kaon form factor similar to p+ using elastic K+ scattering from electrons [Amendolia et al, PLB 178, 435 (1986)] Can “kaon cloud” of the proton be used in the same way as the pion to extract kaon form factor via σL from p(e,e’K+)Λ ? Kaon pole pion pole H(e,e’K+) This can be tested making p(e,e’K+)n measurements at same kinematics as K+e elastics H(e,e’π+)

σT global t-dependence Scaled to W=2.19 GeV, Q2=0.7 GeV2 An exponential t dependence describes the data from Jlab and earlier data from DESY quite well Slope is less steep then for sigL, but clearly sigT is not independent of t and Q2 t-dependence of σπ as expected – what about Q2?