Scaling Study of the L-T Separated p(e,e’π+)n Cross Section at Large Q2 Tanja Horn Jefferson Lab GW Seminar Washington, DC November 2007

DIS and Parton Distribution Functions Deep Inelastic Scattering (DIS) can be factorized into short and long distance physics in the limit of large Q2 and at fixed values of xB Hard scattering can be calculated in perturbative QCD (pQCD) Soft physics is described by Parton Distribution Functions (PDFs) Forward Compton amplitude can be directly related to DIS cross section via optical theorem 2 ~

Generalized Parton Distributions Deep Virtual Compton Scattering Deep Virtual Meson Production x-ξ x+ξ A similar factorization of scales is expected for hard exclusive processes – DVCS is simplest Generalized Parton Distributions (GPDs) are a generalization of PDFs, where initial and final quark-gluon momenta are not identical Unified concepts of quark parton density and elastic form factors Transverse spatial distribution of quarks Spin decomposition of the nucleon

Leading Twist GPDs At leading twist, there are four independent GPDs for each quark, gluon type x is the light cone momentum fraction of struck parton (x ≠ xB) ξ defined by Δ+ = -2ξ(p+Δ/2)+ Longitudinal fraction of the momentum transfer, t Parameterizes the skewedness t=Δ2, momentum transfer to nucleon

GPDs and DIS ~ H In the limit of ξ → 0 and t → 0, H and reduce to ordinary parton distributions E and not accessible in DIS – parton helicity flip is forbidden ~ E

GPDs and Elastic Scattering First moments of GPDs yield usual elastic form factors F1,F2 = Dirac and Pauli form factors GA, GP = axial vector and pseudo scalar form factors Common formalism can describe DIS and elastic scattering

GPDs and Quark Imaging t x+ξ x-ξ “take out” “put back” GPDs contain more information than parton densities and form factors alone GPDs describe the probability to probe a parton of momentum fraction x, at a transverse distance b^ transverse spatial distribution of quark Access to dynamic properties

GPDs and Total Angular Momentum Second moments of GPDs at t=0 give expectation value of nucleon spin Nucleon spin can be inferred from (from GPDs) and (from DIS) X. Ji, PRL 78, 610

Experimental Access to GPDs DVCS Deeply Virtual Compton Scattering sensitive to a combination of all 4 GPDs → Large background from Bethe-Heitler Azimuthal asymmetries can access DVCS and BH interference terms ~ ~ H,E, H,E

GPDs and Exclusive Meson Production Vector mesons (r,w,f) sensitive to H and E Pseudo scalar mesons sensitive to and Detection of final states easier – but interpretation complicated by convolution with meson wave function (additional soft object) ~ H ~ E

GPD “Measurements” GPDs are not observables – they are a framework that allows us to describe a wide variety of processes DIS, elastic scattering, exclusive reactions We already have constraints on GPDs from: DIS: H(x,0,0) = q(x) and H(x,0,0) = Dq(x) Elastic scattering: ∫dx x H(x,x,t) = F1(t) To fully understand GPDs, we need a program to measure: a variety of exclusive processes vector mesons, DVCS, pseudo scalar mesons a broad range of phase space (t, xB) ~

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: Fpi1, E91-003, Fpi2, 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

Hard-Soft Factorization 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 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

Pion Electroproduction Kinematics Q2= |q|2 – ω2 t=(q - pπ)2 W=√-Q2 + M2 + 2Mω scattering plane reaction plane The lab cross section can be expressed in terms of virtual photon flux, Jacobian and virtual photon cross section. The virtual photon cross section can be written in terms of contributions from transversely and longitudinally polarized photons.

Jefferson Lab Two superconducting Linacs Three experimental Halls operating concurrently E<~ 5.7 GeV Hadron-parton transition region C.W. beam with currents of up to 100 uA Luminosity ~1038 Fπ measurements 15

Pion Electroproduction in Hall C Three experiments took data to the highest possible value of Q2 with 6 GeV beam at JLab Full L/T/TT/LT separation in π+ production Measurement of separated π+/π- ratio to test the reaction mechanism HMS: 6 GeV SOS: 1.7 GeV Exp Q2 (GeV2) W (GeV) |t| (Gev)2 Ee (GeV) Fpi1 0.6-1.6 1.95 0.03-0.150 2.445-4.045 Fpi2 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 Configuration Hall C spectrometers Coincidence measurement SOS detects e- HMS detects π+ Targets Liquid 4-cm H/D cells Al (dummy) target for background measurement 12C solid targets for optics calibration HMS Aerogel Cerenkov Improves p/π+/K+ PID at large momenta, first use in 2003 Built by Yerevan group [Nucl. Instrum. Meth. A548(2005)364] 17

p(e,e’π+)n Event Selection Coincidence measurement between charged pions in HMS and electrons in SOS Coincidence time resolution ~200-230 ps Cut: ± 1ns Protons in HMS rejected using coincidence time and aerogel Cerenkov Electrons in SOS identified by gas Cerenkov and Calorimeter Exclusive neutron final state selected with missing mass cut 0.92 ‹ MM ‹ 0.98 GeV After PID cuts almost no random coincidences 18

Fpi2 Kinematic Coverage Have full coverage in φ BUT acceptance not uniform Measure σTT and σLT by taking data at three angles: θπ=0, +4, -3 degrees W/Q2 phase space covered at low and high ε is different For L/T separation use cuts to define common W/Q2 phase space Radial coordinate: -t, azimuthal coordinate: φ Θπ=0 Θπ=+4 Θπ=-3 -t=0.1 -t=0.3 Q2=1.60, High ε Q2=2.45 GeV2 Q2=1.60 GeV2 19

Determination of σL σL is isolated using the Rosenbluth separation technique Measure the cross section at two beam energies and fixed W, Q2, -t Simultaneous fit using the measured azimuthal angle (φπ) allows for extracting L, T, LT, and TT Careful evaluation of the systematic uncertainties is important due to the 1/ε amplification in the σL extraction Spectrometer acceptance, kinematics, and efficiencies 20

Cross section W-dependence σπ depends on W, -t, Q2 Cross section W-dependence given by: (W2-M2)n Fpi1/Fpi2 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?

t-dependence of separated cross sections T. Horn et al., arXiv:0707.1794 (2007) VGL/Regge describes σL reasonably well Fit to the t-dependence allows for extracting Fπ σT contributes significantly at Q2=4.0 GeV2 Interference terms →0 as Q2 increases Λπ2=0.518 GeV2

Q2 dependence of σL and σT Hall C data at 6 GeV: 3 different experiments 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 Testing the applicability of factorization requires larger kinematic coverage and improved precision Q2=2.7-3.9 GeV2 Q2=1.4-2.2 GeV2 σL σT T. Horn et al., arXiv:0707.1794 (2007)

Q2 Scaling of the Interference Terms Preliminary from Fpi1, Fpi2 Scaling prediction based on transverse content to the amplitude σLT ~ Q-7 σTT ~Q-8 Limited Q2 coverage complicates the interpretation Interference terms decrease in magnitude as Q2 increases Q2 range is small T. Horn, Ph.D. thesis, University of Maryland (2006)

Transverse Contributions T. Horn et al., Phys. Rev. Lett. 97, 192001 (2006) VGL σL VGL σT Note: -tmin is different Even at Q2=2.45 GeV2, σT is not small But electroproduction is a multi-variable phase space At fixed W, tmin increases with Q2 and σL decreases more rapidly than σT Scaling tests need high precision separated cross sections at fixed xB and -t

Regge Exchange Contributions Calculation by A.P. Szczepaniak et al. [arXiv:0707.1239v2] suggest significant scaling violations at small –t and independent of Q2 Expect Q2 behavior characteristic for hadronic Regge amplitudes σL,T ~ (Q-n) 2α(t)-1 x αL αT 0.31 0.46 ± 0.50 1.90 ± 0.36 0.45 0.92 ± 2.00 0.99 ± 0.51 HERMES π+ fit: α=0.31 ± 0.2 (0.26 < xB < 0.80), BUT not separated

Fπ and Factorization Tests 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 The modified mechanism is also characterized by a single hard gluon exchange 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 Hard Scattering

Fπ in 2007 T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001. Q2>1 GeV2: Q2 dependence of Fπ is consistent with the power law behavior expected from the hard scattering mechanism (Q-2) Fπ data still far from hard QCD calculations Not in QCD factorization regime Or additional soft contribution from the pion wave function Additional soft contribution would be inconsistent with Q-6 scaling for the cross section AdS/CFT describes Q2-dependence, and provides a reasonable description of the magnitude 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 Scaling Predictions Expected scaling behavior Fixed θ*: dσ/dt ~ s-n(θ), nhard(θ) =6 Experimental fits are consistent with the prediction within the uncertainty But is this sufficient? θ ndata 60 5.9±0.3 90 7.1±0.4 105 6.2±1.4 M. A. Shupe et al., Phys. Rev. D19, 1921 (1979)

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

Factorization at 12 GeV? L/T separated cross sections will play a large role in guiding the 12 GeV GPD program If transverse contributions are larger than anticipated, the accessible phase space for GPD studies may be limited Extraction of GPDs from unseparated observables relies on the dominance of σL – but are transverse contributions really small? Effect from σT may cancel in asymmetries and ratios – need to know the relative contribution of L and T Precision separated L/T data from JLab suggest that transverse contributions to the π+ cross section are larger than predicted by Regge calculations and the constituent quark model Limited knowledge of L/T ratio at higher energies limits the interpretability of unseparated cross sections in π± production

Scaling Test at 12 GeV Experiment approved for 42 days in Hall C SHMS E12-07-105 (T. Horn*, G. Huber et al.) Measure the Q2 dependence of the p(e,e’π+)n cross section at fixed xB and –t to search for evidence of hard-soft factorization Separate the cross section components: L, T, LT, TT The highest Q2 for any L/T separation in π electroproduction Also determine the L/T ratio for π- production to test the possibility to determine σL without an explicit L/T separation 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

Experiment Overview The kinematics for the LD2/π- measurement Measure separated cross sections for the p(e,e’π+)n reaction at three values of xB Near parallel kinematics to separate L,T,LT,TT 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 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

Projected Uncertainties for Q-n scaling QCD scaling predicts σL~Q-6 and σT~Q-8 Projected uncertainties for σL use an Fπ parameterization for L/T ratio Based on previous π+ L/T data Fit: 1/Qn 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 -

π- cross section – measure σL without explicit L/T? Fpi1 and Fpi2 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 Fpi1 and Fpi2 results)

12 GeV Proposals Actions 12 GeV Proposal # TITLE CONTACT PERSON HALL DAYS PAC Action 12-07-101 Hadronization in Nuclei by Deep Inelastic Electron Scattering B.Norum C 15 Conditional Approval 12-07-102 Precision Measurement of the Parity-Violating Asymmetry in Deep Inelastic Scattering off Deuterium using Baseline 12 GeV Equipment in Hall C P. Reimer 36 12-07-103 The Nuclear Transparency of Pion-photoproduction from 4He at 12 GeV D. Dutta 14.5 Defer 12-07-104 Measurement of the Neutron Magnetic Form Factor at High Q2 Using the Ratio Method on Deuterium G. Gilfoyle B 56 Approval 12-07-105 Scaling Study of the L-T Separated Pion Electroproduction Cross Section at 11 GeV T. Horn 42 12-07-106 The A-dependence of J/Psi Photoproduction near Threshold E. Chudakov 23 12-07-107 Studies of Spin-Orbit Correlations with Longitudinally Polarized Target H. Avakian 103 12-07-108 Precision Measurement of the Proton Elastic Cross Section at High Q2 B. Moffit A 31 12-07-109 Large Acceptance Proton Form Factor Ratio Measurements at 13 and 15 (GeV/c)2 Using Recoil Polarization Method L. Pentchev 60

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 to study the transition to hard QCD Requires good understanding of spectrometer optics and acceptance Collimator to define acceptance Radiative heating studies of horizontal bend magnet

Fπ Backgrounds 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 PAC31 proposal (T. Horn, D. Gaskell, G. Huber) 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 38

Factorization Summary The Q2-dependence of L/T separated π+ σL from Jefferson Lab is in relatively good agreement with the Q2-scaling prediction σT still significant at Q2=3.91 GeV2, and drops more slowly than the Q-8 scaling expectation The measured Q2-dependence of Fπ is also consistent with the Q2 scaling expected from the hard scattering mechanism, but pQCD calculations do not reproduce its magnitude L/T separated π+ cross sections will be essential for understanding the reaction mechanism at 12 GeV (E12-07-105) Relative contribution of σL and σT in π+ production - interpretation of asymmetry and ratios If transverse contributions are larger than anticipated, this may influence the accessible phase space for GPD studies π- data will check the possibility of measuring σL without explicit L/T separation

Measurement of K+ Form Factor Similar to p+ form factor, elastic K+ scattering from electrons used to measure charged kaon for factor at low Q2 [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 p(e,e’K+)Λ ? Kaon pole further from kinematically allowed region, but mass is larger Can we demonstrate that the “pole” term dominates the reaction mechanism?

Kaon Form Factor at Large Q2 JLAB experiment E93-018 extracted –t dependence of K+ longitudinal cross section near Q2=1 GeV2 A trial Kaon FF extraction was attempted using a simple Chew-Low extrapolation technique gKLN poorly known Assume form factor follows monopole form Used measurements at Q2=0.75 and 1 GeV2 to constrain gKLN and FK simultaneously Improved extraction possible using VGL model?

Test Extraction of K+ Form Factor G. Niculescu, PhD. Thesis, Hampton U. -t dependence shows some “pole-like” behavior “Chew-Low” type extraction

Form Factor Summary Fπ is a good observable to study the transition from collective degrees of freedom to quarks and gluons Fπ measurements from JLab yield high quality data – in part due to Continuous electron beam provided by JLab accelerator Magnetic spectrometers and detectors with well-understood properties Studies of FK at higher electron beam energies will allow to reach the kinematic range where direct measurement of the kaon form factor were made even better Due to the larger mass, lattice calculations of kaon form factors are facilitated Planned proposal for PAC34 (T. Horn, D. Gaskell, P. Markowitz) 43