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

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 2 Jefferson Lab Fpi2 Collaboration

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? 3 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

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 4 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

At experimentally accessible Q 2 both hard and soft components contribute –Transverse momentum effects 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 5 F π at intermediate Q 2

The charged pion presents a clean test case for our understanding of bound quark systems –Structure of pion at all Q 2 values At what value of Q 2 will hard pQCD contributions dominate? –Perturbative QCD(LO) hard calculations under-predict experimental data by a factor of Context Many studies of F π, but the interplay of hard and soft contributions is not well understood –Constraints on theoretical models require high precision data –JLab is the only experimental facility capable of the necessary measurements

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 ± fm At larger Q 2 values, one must use the “virtual pion cloud” of the proton to extend the F π measurement –t-channel diagram dominates σ L at small –t In the Born term model: 7 Measuring F π Measuring F π Pion electroproduction

Extraction of F π relies on the pole dominance of σ L –For maximum contribution from the π + pole to σ L, need data at the smallest possible –t –At fixed Q 2, a higher value of W allows for smaller -t min 8 Extraction of F π requires knowledge of the -t dependence of σ L –Only three of Q 2, W, t, and θ π are independent –Must 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

9 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

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 scattering 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 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

11 ? F π before 1997 Large Q 2 data from Cornell –Use extrapolation of σ T fit at low Q 2 to isolate σ L –Extract F π from unseparated cross sections Largest Q 2 points also taken at large –t –Carlson&Milana predict M pQCD /M pole grows significantly for –t min >0.2 GeV 2 [PRL 65 (1990) 1717] –Pole term may not dominate

–t min <0.2 GeV 2 constraint limits Q 2 reach of F  measurements Measurement of σ L for  0 could help constrain pQCD backgrounds In a GPD framework,  + and  0 cross sections involve different combinations of same GPDs – but  0 has no pole contribution 12 00 ++ VGG GPD-based calculation pole non-pole F π Backgrounds

ExpQ 2 (GeV 2 ) W (GeV) |t| (Gev) 2 E e (GeV) Fpi Fpi , , 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

Coincidence measurement between charged pions in HMS and electrons in SOS –Coincidence time resolution ~ 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 14 After PID cuts almost no random coincidences p(e,e’ π +)n Event Selection

15 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

16 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 σ L

17 Λ π 2 =0.513 (0.491) GeV 2, Λ π 2 =1.7 GeV 2 uses the VGL Regge model, which describes pion electroproduction in terms of the exchange of π and ρ like particles [Vanderhaeghen, Guidal, Laget, PRC 57 (1998), 1454] –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) Extraction of F π from Fpi2 data

18 Extract F π for each t-bin 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 F π t-dependence

F π precision data deviate from fm charge radius at Q 2 = 2.45 GeV 2 by ~1σ –The monopole reflects the soft (VMD) physics at low Q 2 –The deviation suggests that the π+ “harder” at this Q 2 19 T. Horn et al., Phys. Rev. Lett. 97 (2006) V. Tadevosyan et al., nucl-ex/ 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 F π is still far from the pQCD prediction –Including transverse momentum effects has no significant impact New point from π CT (2004) in good agreement with Fpi experiments T. Horn et al., arXiv: (2007).

20 T. Horn et al., Phys. Rev. Lett. 97 (2006) F π in 2007 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 Bethe-Salpeter/Dyson-Schwinger [P.Maris and P. Tandy, Phys.Rev.C62 (2000)055204] –Systematic expansion in terms of dressed particle Schwinger equations Anti de Sitter/Conformal Field Thry [S.J. Brosdky and G.F. de Teramond, arXiv: ] T. Horn et al., arXiv: (2007). [ [A.P. Bakulev et al, Phys. Rev. D70 (2004)]  Hard contribution to NLO with improved π DA  Soft contribution from local duality

Interpretation Issues 21 t dependence of Fpi1 σ L is significantly steeper than VGL/Regge at the lowest Q 2 –May be due to resonance contributions not included in Regge –Linear fit to Λ π 2 to t min gives the best estimate of F π at each Q 2 Check the model dependence of the mass pole extrapolation –Good agreement between Fpi1 (t min =0.093 GeV2) and Fpi2 (t min =0.150 GeV2) gives confidence in the reliability of the method

Significant progress on theoretical front expected in next 5 years –Lattice, GPDs etc. 22 The 11 GeV electron beam and the SHMS in Hall C with θ=5.5º allows for –Precision data up tp Q 2 =6 GeV 2 to study the transition to hard QCD –Test of the electroproduction method at Q 2 =0.3 GeV 2 with the upper limit of elastic scattering data –Most stringent test of the model dependence in the F π extraction by comparing data at several values of W F π after the JLab Upgrade

F π is a good observable to study the transition from collective degrees 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 23 Summary