1. Tanja Horn, Jefferson Lab1 Tanja Horn Jefferson Lab The Pion Form Factor European Research Conference on Electromagnetic Interactions with Nucleons and Nuclei Milos, Greece, 2007

2. Tanja Horn, Jefferson Lab2 JLab F π -2 Collaboration R. Ent, D. Gaskell, M.K. Jones, D. Mack, D. Meekins, J. Roche, G. Smith, W. Vulcan, G. Warren, S. Wood Jefferson Lab, Newport News, VA, USA E. Brash, E. Brash, G.M. Huber, V. Kovaltchouk, G.J. Lolos, C. Xu University of Regina, Regina, SK, Canada H. Blok, V. Tvaskis Vrije Universiteit, Amsterdam, Netherlands E. Beise, H. Breuer, C.C. Chang, T. Horn, P. King, J. Liu, P.G. Roos University of Maryland, College Park, MD, USA W. Boeglin, P. Markowitz, J. Reinhold Florida International University, FL, USA J. Arrington, R. Holt, D. Potterveld, P. Reimer, X. Zheng Argonne National Laboratory, Argonne, IL, USA H. Mkrtchyan, V. Tadevosyan Yerevan Physics Institute, Yerevan, Armenia S. Jin, W. Kim Kyungook National University, Taegu, Korea M.E. Christy, L.G. Tang Hampton University, Hampton, VA, USA J. Volmer DESY, Hamburg, Germany T. Miyoshi, Y. Okayasu, A. Matsumura Tohuku University, Sendai, Japan B. Barrett, A. Sarty Saint Mary’s University, Halifax, NS Canada K. Aniol, D. Margaziotis California State University, Los Angeles, CA, USA L. Pentchev, C. Perdrisat College of William and Mary, Williamsburg, VA, USA I. Niculescu James Madison University, Harrisonburg, VA, USA V. Punjabi Norfolk State University, Norfolk, VA, USA E. Gibson California State University, Sacramento, CA, USA

3. Tanja Horn, Jefferson Lab3 Hadronic Form Factors in QCD Quantum Chromo-Dynamics (QCD) is very successful describing strong interactions BUT, we are unable to construct a quantitative description of hadrons in terms of the underlying constituents, quarks and gluons. We know that there is an asymptotic limit, but how do we get there and what governs the transition? Form factors provide important information about the transition between non-perturbative and perturbative regimes Meaningful constraint on theoretical models requires measurements at high precision Short Distance Asymptotic Freedom Perturbative QCD Long Distance Binding Collective DOF ?

4. Tanja Horn, Jefferson Lab4 Scientific Motivation – why pions? The pion form factor is one of the simplest objects available for experimental studies Simple qq valence structure Expect pQCD description to be valid at lower values of Q 2 relative to nucleon The factorized pion form factor: at large Q 2 one can calculate F π in pQCD – in the Q 2 →∞ this reduces to the well known form where f 2 π=93 MeV is the π + → μ + ν decay constant One hard gluon exchange This asymptotic normalization does not exist for nucleon form factors

5. Tanja Horn, Jefferson Lab5 Shortcomings of LO pQCD Theoretical challenge: pQCD(LO) hard calculations under-predict the data by a factor of 2-3 Important issue: the simple pQCD calculation ignores the effect of parton pairs in the reaction that are separated by a transverse distance (soft gluon radiation) Including transverse momenta extends the region of validity of pQCD calculations to finite values of Q 2 [R. Jakob&P.Kroll, Phys. Lett. B315 (1993) 463] More complicated issue: how to model the shape of the pion wave function, φ π, at finite Q 2 ? A double-humped profile with suppressed endpoints best describes the data within 1σ and rules out other forms [A.P. Bakulev et al., Phys. Rev. D73 (2006) 056002]

6. Tanja Horn, Jefferson Lab6 Improved pQCD hard calculation Bakulev et al. calculate the factorizable pQCD contribution to F π in NLO Model φ π using QCD Sum Rules prescription A.P. Bakulev et al. Phys. Rev. D70 (2004). When will hard contributions dominate? What happens to the predictive power of the theory when one includes soft contributions? Hard component significantly under-predicts the data To describe the data must include soft contribution – here, via local duality

7. Tanja Horn, Jefferson Lab7 QCD-inspired Models for F π QCD Sum Rules [V.A. Nesterenko and A.V. Radyushkin, Phys. Lett.B115 (1982)410] Use properties of Green functions – spectral function contains pion pole Quark hadron duality [W. Melnitchouk, Eur. Phys. J.A17 (2003)223] Relate hadronic content of exclusive, elastic form factor and inclusive pion structure function, assumes duality holds Bethe-Salpeter/Dyson-Schwinger [P.Maris and P. Tandy, Phys.Rev.C62 (2000)055204] Systematic expansion in terms of dressed particle Schwinger equations Constituent Quark Model [C.-W. Hwang, Phys. Rev. D64 (2001)034001] Constituent quarks and effective interaction potential (e.g. fit from experimental data)

8. Tanja Horn, Jefferson Lab8 Alternative: Lattice pQCD Lattice QCD allows for calculations from first principles This is different from QCD-inspired models where confinement must be put in by hand This is great, BUT LQCD requires a number of approximations Lattice discretization errors – improved LQCD action helps Chiral extrapolation of LQCD is used to obtain the pion mass Quenching errors – need to include disconnected quark loops Advances in computational techniques have improved over the last two decades Potential for precision predictions of hadronic properties

9. Tanja Horn, Jefferson Lab9 F π from a recent unquenched Lattice QCD calculation Unquenched (dynamical) domain-wall action calculation Lattice Hadron Physics Collaboration (Jefferson Lab, Regina,Yale) F. Bonnet et al., hep- lat/0411028 Lattice calculations are consistent with experimental data within large statistical and systematic errors, dominated by chiral extrapolation Primary goal is to test proof-of-principle of different techniques For future calculations expect m π sufficiently small to yield small chiral extralpolation errors Require higher Q 2 data to validate new LQCD methods pQCD →

10. Tanja Horn, Jefferson Lab10 F π Calculations Summary Fundamental question: what is the structure of π + at finite values of Q 2 ? – i.e. at experimentally accessible energies At what value of Q 2 will pQCD dominate over soft contributions? The limits on F π are well defined and many treatments for soft physics are available, BUT experimental data are needed to quantify the role of soft and hard contributions at intermediate values of Q 2 This study of F π is unique to JLab Theoretical challenge: at moderate values of Q 2 both hard and soft contributions must be taken into account Feynman Mechanism

11. Tanja Horn, Jefferson Lab11 F π via Pion Electroproduction F π can be measured directly from π +e scattering up to Q 2 ~0.3 GeV 2 [S.R. Amendolia et al., NP B277 (1986)] No “free pion” target – to extend measurement of F π to larger Q 2 values use “virtual pion cloud” of the proton t-channel diagram dominates σ L at small -t Method check - Extracted results are in good agreement with π +e data [Ackerman et al., NP B277 (1986) 168]

12. Tanja Horn, Jefferson Lab12 Pion Electroproduction Kinematics Hadronic information determined by Lorentz invariants Q 2 = |q| 2 – ω 2 W=√-Q 2 + M + 2Mω t=(q - p π ) 2 p π = momentum of scattered pion θ π = angle between scattered pion and virtual photon φ π = angle between scattering and reaction plane Q 2 = |q| 2 – ω 2 t=(q - p π ) 2 W=√-Q 2 + M 2 + 2Mω scattering plane reaction plane

13. Tanja Horn, Jefferson Lab13 Exclusive π + Production Unpolarized Cross Section In general, LT and TT → 0 by integrating over φ acceptance The virtual photon cross section can be written in terms of contributions from transverse and longitudinal photons. [A. Bartl and W. Majerotto, NP B62 (1973) 267-285]

14. Tanja Horn, Jefferson Lab14 “Simple” Longitudinal-Transverse Separation For uniform φ-acceptance σ TT, σ LT →0 when integrating over φ Determine σ T + ε σ L for high and low ε in each t- bin for each Q 2 Isolate σ L, by varying photon polarization, ε

15. Tanja Horn, Jefferson Lab15 “Real” Cross Section Separation Cross Section Extraction φ acceptance not uniform In reality one must measure σ LT and σ TT Extract σ L by simultaneous fit using measured azimuthal angle (φ π ) and knowledge of photon polarization (ε)

16. Tanja Horn, Jefferson Lab16 Extracting F π from π + Electroproduction Data More reliable technique: Extract F π from σ L data using a model incorporating pion electroproduction BUT no reliable phenomenological extrapolation to the t=m π 2 pole Ultimate test of this technique: at 12 GeV we will take data in the overlap region with π -e elastic scattering data Extraction of F π from σ L relies on π + pole dominance For maximal contribution need data at smallest possible –t

17. Tanja Horn, Jefferson Lab17 Pion Electroproduction Models MAID – unitary isobar model for pion photo- and electroproduction Only useful for W < 2 GeV, F π -2 kinematics above this region Too many free parameters Born term models Do not describe t-dependence well away from pole VGL/Regge [ Vanderhaeghen, Guidal, Laget, PRC 57 (1998) 1454] Appropriate at W > 2 GeV Model parameters fixed from pion photoproduction data F π is the only free parameter in the calculation of σ L Constituent Quark Model (Obukhovsky et al., Phys. Lett. B634 (2005) Same kinematic range as VGL/Regge, two free parameters Model still in development, not yet used in data analysis

18. Tanja Horn, Jefferson Lab18 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 ~10 38 F π measurements

19. Tanja Horn, Jefferson Lab19 Precision F π data up to Q 2 =2.45 GeV 2 ExpQ 2 (GeV 2 ) W (GeV) |t| (Gev) 2 E e (GeV) F π -1 1.6 0.6-1.61.95 0.150 0.03-0.1502.445-4.045 F π -2 1.6 1.6,2.452.22 0.093 0.093,0.1893.779-5.246 Extension of 1997 run (F π -1) at highest possible value of Q 2 with 6 GeV beam at JLab New data at higher W Repeat Q 2 =1.60 GeV 2 closer to t=m 2 π to study model uncertainties F π -2 successfully completed in Hall C at JLab 2003 Coincidence measurement between charged pions in HMS and electrons in SOS Separate σ L /σ T via Rosenbluth separation HMS: 6 GeVSOS: 1.7 GeV

20. Tanja Horn, Jefferson Lab20 Experimental Details Hall C spectrometers Coincidence measurement SOS detects e - HMS detects π + Targets Liquid 4-cm H/D cells Al (dummy) target for background measurement 12 C solid targets for optics calibration HMS Aerogel Improvement of p/ π + /K + PID at large momenta, first use in 2003 Built by Yerevan group [ Nucl. Instrum. Meth. A548(2005)364 ]

21. Tanja Horn, Jefferson Lab21 Good 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.

22. Tanja Horn, Jefferson Lab22 Random Background Subtraction Random e- π background subtracted using coincidence time Contribution < 1% for H including all cuts Separate real π and p events using coincidence time Issue in random subtraction: π ’s can interact in scintillators – produce slow protons Eliminate with time of flight cut Cut Efficiency: ~96% Real protons

23. Tanja Horn, Jefferson Lab23 F π -2 Kinematic Coverage W/Q 2 phase space covered at low and high ε is different For L/T separation use cuts to define common W/Q 2 phase space Have full coverage in φ BUT acceptance not uniform Measure σ TT and σ LT by taking data at three angles: θ π =0, +4, -3 degrees Θ π =0 Θ π =+4 Θ π =-3 -t=0.1 -t=0.3 Q 2 =1.60, High ε Radial coordinate: -t, azimuthal coordinate: φ Q 2 =1.60 GeV 2 Q 2 =2.45 GeV 2

24. Tanja Horn, Jefferson Lab24 F π - 2 Data Analysis Compare experimental yields to Monte Carlo of the experiment Model for H(e,e’ π + ) based on pion electroproduction data Radiative effects, pion decay, energy loss, multiple scattering COSY model for spectrometer optics Extract σ L by simultaneous fit using measured azimuthal angle (φ π ) and knowledge of photon polarization (ε).

25. Tanja Horn, Jefferson Lab25 Spectrometer Uncertainties Uncertainties in spectrometer quantities parameterized using over-constrained 1 H(e,e’p) reaction Beam energy and momenta to <0.1% Spectrometer angles to ~0.5mrad Spectrometer acceptance verified by comparing e-p elastic scattering data to global parameterization Agreement better than 2% SourcePt-PtScalet-correlated Acceptance1.0(0.6)%1.0%0.6% Radiative Corrections 0.1%2.0%0.4% Pion Absorption-2.0%0.1% Pion Decay0.03%1.0%- Model Dependence0.2%-1.1(1.3)% Kinematics0.2%-1.0% HMS Tracking0.1%1.0%0.4% Charge-0.5%0.3% Target Thickness-0.8%0.2% Detection Efficiency -0.5%0.3% Statistical uncertainty in ranges between 1 and 2% Point-to-point errors amplified by 1/Δε in L-T separation Scale errors propagate directly into separated cross section

26. Tanja Horn, Jefferson Lab26 Comparison to VGL Model Λ π 2 =0.513 (0.491) GeV2, Λ π 2 =1.7 GeV2 Pion electroproduction in terms of exchange of π and ρ like particles Model parameters fixed from pion photoproduction Free parameters: F π and F ρ - The error bars denote statistical and systematic uncertainties in quadrature (1.0 (0.6)%) - Yellow band denotes the normalization and –t correlated systematic uncertainty (3.5%, 1.8(9)%) Fit to σ L to model gives F π at each Q 2 T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001.

27. Tanja Horn, Jefferson Lab27 F π -2 Results – Soft Contributions Data point at Q 2 =1.60 GeV 2 to check model dependence of mass pole extrapolation Good agreement between F π - 1 (W=1.95 GeV) and F π - 2 (W=2.22 GeV) gives confidence in the reliability of the method F π precision data follow monopole form, Λ 2 π =0.54 GeV 2 up to Q 2 =1.60 GeV 2 At Q 2 =2.45 GeV 2 deviates from charge radius by ~1σ Suggests that π + “harder” at this Q 2 T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001. V. Tadevosyan et al., nucl-ex/0607007.

28. Tanja Horn, Jefferson Lab28 F π -2 Results F π is still far from the pQCD prediction pQCD hard calculations predict values of 0.1-0.2 for F π V.A. Nesterenko and A.V. Radyushkin, Phys. Lett. B115 (1982) 410 P. Maris and P. Tandy Phys Rev C61 (2000) C.-W. Hwang, Phys Rev D64 (2001) Several calculations describe the data up to Q 2 =1.60 GeV 2 Agreement at Q 2 =2.45 GeV 2 with QCD sum rule and CQM Small deviation from DSE/BSE T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001.

29. Tanja Horn, Jefferson Lab29 JLab 12 GeV Upgrade CD1 was granted in February 2006 First 11 GeV beam is expected ~2012

30. Tanja Horn, Jefferson Lab30 Hall C at 12 GeV Hall C High Momentum Spectrometer and Short Orbit Spectrometer at present Form Factors and simple quark systems Color Transparency Nuclei with strange quarks Add a Super-High Momentum Spectrometer for studies of Form Factors and simple quark systems Color Transparency Semi-inclusive DIS SHMS HMS (QQQD) SOS (QQD)

31. Tanja Horn, Jefferson Lab31 F π Measurement at 12 GeV Significant progress on theoretical front expected in next 5 years – Lattice, GPDs etc. Studies of F π at higher electron beam will allow us to reach the kinematic region where hard contributions clearly dominate pQCD expectation may be approached SHMS+HMS in Hall C will allow for F π measurements up to Q 2 =6 GeV 2 after the upgrade The 12 GeV proposal was approved by the PAC in 2006

32. Tanja Horn, Jefferson Lab32 Summary F π good observable to study transition region to pQCD Results from F π -1 show Q 2 F π still increasing, but ~1σ below monopole F π -2 results in a region of Q 2 where F π calculations begin to diverge Data will constrain models describing the treatment of soft physics at higher Q 2 Good agreement between data point at Q 2 =1.60 between F π - 1 (W=1.95 GeV) and F π - 2 (W=2.22 GeV) gives confidence in the reliability of the method Still far from the pQCD prediction Studies of F π at higher electron beam energy will allow us to reach the kinematic range where hard contributions clearly dominate pQCD expectations may be approached Approved 12 GeV measurement after the upgrade to Q 2 =6 GeV 2

33. Tanja Horn, Jefferson Lab33 F π time-like vs. space-like Expect same asymptotic prediction for both space- like and time-like data The way one gets there may be different pQCD under-predicts both cases Calculations in time-like region complicated by explicit resonances Timelike data from P.K. Zweber Ph.D. thesis (2006)

34. Tanja Horn, Jefferson Lab34 Competing Reaction Channels Extraction of F π relies on dominance of t-channel (pole dominance) t-channel purely isovector Isoscalar background Pole dominance tested using π - / π + from D(e,e’p) G-parity: If pure pole then necessary R=1 t-channel process γ*γ* π π*π* pn

35. Tanja Horn, Jefferson Lab35 Preliminary π + /π - Ratios (F π -1) Preliminary analysis of F π -1 data suggests pole process dominates Gives confidence that can extract F π from σ L data