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

2. 2 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 Jefferson Lab Fpi2 Collaboration

3. 3 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 from collective degrees of freedom to quarks and gluons, i.e., from the non-perturbative to the perturbative regime Short Distance Asymptotic Freedom Perturbative QCD Long Distance Binding Collective DOF ? Hadronic Form Factors

4. 4 The study of F π is one of the most fundamental experimental studies for understanding hadronic structure –Simple qq valence structure of π + –The pQCD description is expected to be valid at much lower values of Q 2 compared to the nucleon At very large Q 2 one can calculate F π in pQCD, which reduces to the factorized form as Q 2 →∞ where f 2 π=93 MeV is the π + → μ + ν decay constant – –This asymptotic normalization does NOT exist for nucleon form factors The Pion Charge Form Factor The Q 2 dependence of F π data allows for the determination of the role of non-perturbative vs. perturbative physics – –At what values of Q 2 will pQCD contributions dominate?

5. 5 Perturbative QCD(LO) hard calculations under-predict experimental data by a factor of 2-3 –At experimentally accessible Q 2 both hard and soft components contribute –Transverse momentum effects have to be taken into account The interplay of hard and soft components is not well understood –Non-perturbative hard components of higher twist cancel soft components [V. Braun et al., PRD 61 (2000) 07300] –Different theoretical perspectives on the dominance of higher twist effects up to large momentum transfer The charged pion presents a clean test case for our understanding of bound quark systems –Experiments measured the  + form factor measured via  + e -   + e - and p(e,e’  + )n to Q 2 =2.5 GeV 2 Context

6. 6 At low Q 2, 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)] –Accurate measure of the π + charge radius, r π =0.657 ± 0.012 fm To extend measurement of F π to larger Q 2 values, one must use the “virtual pion cloud” of the proton, p(e,e’ π +)n reaction –t-channel diagram dominates σ L at small –t In the Born term model Measuring F π Measuring F π

7. 7 Extraction of F π relies on the pole dominance of σ L –To get the maximum contribution from the π + pole to σ L, requires data at the smallest possible –t –At fixed Q 2, a higher value of W allows for smaller -t min For the extraction of F π, one needs to know the -t dependence of σ L – –Only three of the quantities Q 2, W, t, and θ π are independent – –needs to vary θ π to measure the -t dependence (off-parallel) – –In off-parallel kinematics, LT and TT must also be determined Q 2 = |q| 2 – ω 2 t=(q - p π ) 2 W=√-Q 2 + M 2 + 2Mω scattering plane reaction plane Pion Electroproduction Kinematics

8. 8 Extraction of F π from p(e,e’ π +)n data Extraction of F π from p(e,e’ π +)n data  + production data are obtained at –t>0 (away from the t=m π 2 pole) Early experiments used “Chew-Low” extrapolation technique – –Need to know the –t dependence through the unphysical region – –A reliable extrapolation is not possible More reliable technique is to use a model including the π + reaction mechanism and extract F π from σ L data – –Fit data in the physical region

9. 9 An improved check will be performed after the JLab Upgrade – –Lower Q 2 (Q 2 =0.30 GeV 2 ) – –Lower –t (-t=0.005 GeV 2 ) Electroproduction Method Test Electroproduction Method Test Electroproduction starts from a virtual pion –Can this method yield the physical form-factor Test the method by comparing F π values extracted from p(e,e’ π + )n data with those obtained from π + e elastic data at the same kinematics DESY electroproduction data at Q 2 = 0.35 GeV 2 consistent with extrapolation of elastic data [Ackerman et al., NP B277 (1986) 168]

10. 10 Old data at large Q 2 (> 1 GeV 2 ) extracted F  from unseparated cross sections Used extrapolation of  T fit at low Q 2 to isolate  L Largest Q 2 points also taken at large –t min Carlson and Milana predict M pQCD /M pole grows dramatically for -t min >0.2 GeV 2 Pole term may not dominate! PRL 65, 1717(1990) ? F π before 1997

11. 11 ExpQ 2 (GeV 2 ) W (GeV) |t| (Gev) 2 E e (GeV) F pi 1 1.6 0.6-1.61.95 0.150 0.03-0.1502.445-4.045 F pi 2 1.6 1.6,2.452.22 0.093 0.093,0.1893.779-5.246 Fpi2 extends the earlier Fpi1 data to the highest possible value of Q 2 with 6 GeV beam at JLab – –Fpi2 data at higher W, smaller -t – –Repeat Q 2 =1.60 GeV 2 closer to t=m 2 π to study model uncertainties Full L/T/TT/LT separation in π + production Measurement of separated π + / π - ratio to test the reaction mechanism HMS: 6 GeVSOS: 1.7 GeV The F π Program at JLab

12. 12 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 p(e,e’ π +)n Event Selection

13. 13 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 Fpi2 Kinematic Coverage

14. 14 σ L is isolated using the Rosenbluth separation technique – –Measure the cross section at two beam energies and fixed W, Q 2, -t – –Simultaneous fit using the measured azimuthal angle (φ π ) allows for extracting L, T, LT, and TT Careful evaluation of the systematic uncertainties is important due to the 1/ ε amplification in the σ L extraction – –Spectrometer acceptance, kinematics, and efficiencies Determination of the Experimental Cross Section

15. 15 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% Systematic Uncertainties

16. 16 Λ π 2 =0.513 (0.491) GeV2, Λ π 2 =1.7 GeV2 Use VGL Regge, which models pion electroproduction in terms of the exchange of π and ρ like particles – –Model parameters fixed from pion photoproduction – –Free parameters: F π and F ρ through the trajectory cutoff - 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. Extraction of F π from Fpi2 data

17. 17 Extract F π for each tbin separately – –F π values are insensitive (<2%) to the t-bin used This result gives confidence in the applicability of the VGL Regge model in the kinematic regime of Fpi2 data Fpi2 model test

18. 18 Fpi1 data were acquired in 1997, when the maximum beam energy was limited to E=4 GeV – –Experimental data constrained to W=1.95 GeV σ L t-dependence of VGL Regge is significantly flatter than the data – –May indicate background VGL Regge under-predicts σ T data for any value of Λ ρ 2 – –More data needed to resolve this puzzle Fitting VGL to Fpi1 data

19. 19 Deficiencies in the description of Fpi1 data Deficiencies may be due to resonance contributions – –Not included in Regge model – –At higher Q 2, the resonance form factor is expected to reduce the resonance contribution Fpi1 analysis assumes that the contribution of backgrounds is small at t min – –Fit VGL to each t-bin, Λ π 2 (Q 2,t) – –Λ π 2 decreases with -t – –Linear fit to Λ π 2 to t min gives the best estimate of F π at each Q 2 – –Assign additional model uncertainty

20. 20 Data point at Q 2 =1.60 GeV 2 to check model dependence of mass pole extrapolation –Good agreement between Fpi1 (W=1.95 GeV) and Fpi2 (W=2.22 GeV) gives confidence in the reliability of the method F π precision data deviate from 0.657 fm charge radius at Q 2 =2.45 GeV 2 by about ~1σ –The monopole reflects the soft (VMD) physics at low Q2 –The deviation suggests that the π + “harder” at this Q 2 T. Horn et al., Phys. Rev. Lett. 97 (2006)192001. V. Tadevosyan et al., nucl-ex/0607007. JLab Experimental Results P. Brauel et al., Z. Phys. C3 (1979) 101 H. Ackermann et al., Nucl. Phys. B137 (1978) 294 S. R. Amendolia et al., Nucl. Phys. B277 (1986) 168

21. 21 F π is still far from the pQCD prediction –Including transverse momentum effects has no significant impact 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. Comparison with QCD Inspired Models

22. 22 A.P. Bakulev et al. Phys. Rev. D70 (2004). The Pion Distribution Amplitude Chernyak & Zhitnitsky (CZ) DA Asymptotic DA Bakulev et al use analytic perturbation theory at the parton amplitude level – –pion DA is consistent to 1sigma level with CLEO pigamma transition data F π 0 results taken as evidence that asymptotic pion DA appropriate as low as Q 2 =1 GeV 2 For Fpi+ FF soft contributions from quark-hadron duality model need to be included to describe the data

23. 23 Non-pole contributions to σ L in the GPD Framework Amplitudes for π + and π o composed of the same GPDs, but different linear combinations Obtain non-pole contributions by comparing π o and π + production amplitudes, M L ~A pN +B pN – –In the limit t →(m π ) 2 the π + amplitude contains a strong singularity (pion pole) πo πo π+ π+ VGG/GPD prediction

24. 24 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) Hall C at 12 GeV

25. 25 Significant progress on theoretical front expected in next 5 years – Lattice, GPDs etc. The 11 GeV electron beam and the SHMS in Hall C with θ=5.5º allows for – –Precision data up tp Q2=6 GeV2 to study the transition to hard QCD – –Best way to test the electroproduction method at Q2=0.3 GeV2 with the upper limit of elastic scattering data – –Most stringent test of the model dependence in the Fpi extraction by comparing data at several values of W The F π Measurement after the JLab Upgrade

26. 26 F π is a good observable to study the transition from collective degrres of freedom to quarks and gluons F π 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 The highest Q 2 JLab results indicate that Q 2 F π is still increasing, but ~1σ below the monopole parameterization of the charge radius –Still far from the QCD prediction Studies of F π at higher electron beam energies will allow to reach the kinematic range where hard contributions are expected to dominate –Planned measurement of F π at JLab after the upgrade to Q 2 =6 GeV 2 Further development of QCD techniques for the non-perturbative physics are anticipated Summary

27. 27 Extraction of F π relies on dominance of t-channel (pole dominance) –t-channel diagram is purely isovector R consistent with the model predictions indicates t-channel dominance of the data Competing Reaction Channels Pole dominance tested using π - / π + from D(e,e’p) – –G-parity: If pure pole then necessary R=1

28. 28 Experiments must access small –t for t-channel dominance in sigL Background in the extraction of Fpi Interpretation of F π data considered reliable for -t<0.2 GeV 2 Carlson & Milana, Phys. Rev. Lett. 65, 1717 (1990) Carlson&Milana indicated a significant contribution of non-leading processes complicating the extraction of F π – –Background ratio rises dramatically once t min >0.2 The VGL Regge model describes σ L for π + well – –This implies that non-pole contributions are small – –A more rigorous constraint requires additional data (proposed to PAC31)

29. 29 Problematic L/T separations Previous data from Cornell

30. 30 Results from Bakulev The Pion Wave function

31. 31 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). At what value of Q2 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 The Q 2 dependence of F π

32. 32 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) QCD Inspired Models for F π

33. 33 Lattice QCD allows for calculations from first principles –This is different from QCD-inspired models where confinement must be put in by hand 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 F π on the Lattice F π on the Lattice

34. 34 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 extrapolation errors – –Require higher Q 2 data to validate new LQCD methods pQCD → F π from a recent unquenched Lattice QCD calculation F π from a recent unquenched Lattice QCD calculation Fpi1 Fpi2

35. 35 The charged pion is one of the simplest QCD objects –The Q 2 dependence of the form factor provides information on hadronic structure at finite values of Q 2 The limits on F π are well defined and many treatments for soft physics are available, – –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 At moderate values of Q 2 both hard and soft contributions must be taken into account – –At what values of Q 2 will the hard pQCD component dominate – –Different theoretical viewpoints on the role of higher twist mechanisms up to large momentum transfer F π Calculations Summary F π Calculations Summary

36. 36 The use of a model that includes the π + production mechanism to extract F π from σ L data is more reliable –To test the method: compare the extracted F π values at low Q 2 with the exact values measured in elastic e- π scattering –Existing Q 2 =0.35 GeV 2 data from DESY are consistent with the elastic e- π scattering data [H. Ackermann et al., NP B137 (1978) 294] In t-pole approximation Extracting F π from π + production Chew Low extrapolation method has large systematic uncertainties – –A reliable phenomenological extrapolation is not possible

37. 37 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 Pion Electroproduction Models

38. 38 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 Jefferson Lab