University of Maryland The Pion Form Factor Tanja Horn University of Maryland Calculation of the Pion Form Factor -> The road to a hard place Fπ measurement via pion electroproduction -> Extracting Fπ from H(e,e’π+) data -> Fπ-1/Fπ-2 in Hall C Results and new directions Hall C Seminar, 20 Dec 2005

Hadronic Form Factors in QCD Fundamental issue: Quantitative description of hadrons in terms of underlying constituents. Theory: QCD describes strong interactions Degrees of freedom: quarks and gluons However, consistent analysis of different length scales in a single process not easy. Studies of short/long distance scales Theory – QCD framework, GPD’s, lattice, models Experiments – form factors, neutral weak nucleon structure, charge structure of 2-quark systems Why pions? - Simplest QCD system (qq) - “Hydrogen Atom of QCD”, good observable for study of interplay between hard and soft physics -

Pion Form Factor in pQCD π Hard scattering Time Scale ~1/Q Factorization: Can separate soft/hard physics on time scale 1/Q (G.P.Lepage and S.J. Brodsky) Hard scattering well defined Wave Function: Amplitude for pion to be found in particular state Cannot be calculated in pQCD φ at finite Q2 model dependent But evolves to a simple form, φAs, in large Q2 limit

Pion Form Factor Limits Large Q2 behavior predicted by Brodsky-Farrar pQCD(LO) and asymptotic wave function At small Q2 vector meson dominance gives accurate description with normalization Fπ(0)=1 by charge conservation Transition region: where is pQCD?

Shortcomings of LO pQCD Theoretical challenge: How to reconcile discrepancy between experimental data and theory description? First try to resolve in pQCD framework Parton pairs in reaction are separated by transverse distance – ignored in simple pQCD calculation. Can include transverse momenta and separations, but avoid large transverse qq configurations Pion wave function, φπ How to model the shape of the amplitude at finite Q2 ? How to deal with long distance effects not described in pQCD? -

Pion Form Factor (NLO pQCD) Bakulev et al. calculate Fπ in NLO pQCD Separate interaction into hard and soft contributions Model φπ using QCD Sum Rules prescription Include soft contribution via local duality to compare with data What happens to the predictive power of the theory when include soft contributions? A.P. Bakulev et al. Phys. Rev. D70 (2004).

Nonperturbative Physics Feynman Mechanism At moderate Q2 nonperturbative corrections to pQCD can be large – Braun et al calculate ~30% at Q2=1 GeV2 to Fπ Need a description for transition to asymptotic behavior Variety of effective Fπ models on the market – how do we know which one is “right”? V.A. Nesterenko and A.V. Radyushkin, Phys. Lett. B115 (1982) 410 P. Maris and P. Tandy Phys Rev C61 (2000) F. Cardarelli et al. Phys. Lett. B357 (1995) 267.

Quark-Hadron Duality (1) Idea: relate hadronic content of exclusive, elastic pion form factor and inclusive pion structure function Local duality sum rule derived by Moffat and Snell (Phys. Rev. D4 (1971) 1452) – analogous to proton duality studies Assuming duality holds, can predict either Fπ or Fπ2 Elastic contribution determined by xmin π ~ σL ~ σT x

Quark-Hadron Duality (2) To predict Fπ at x~1, need either model of Fπ2 or structure function data for calculation input Fπ(Q2) F2π(x) Duality? Elastic scattering limited to Q2< ~0.28 GeV2 πN Drell-Yan data from E615 (Conway et al., Phys. Rev D37 92 (1989)) Pion electroproduction Fπ-1, JLab Q2=0.6, 0.75, 1.0, 1.6 GeV2 Brauel DESY data, Q2=0.7, 1.35 GeV2 Bebek Cornell data 0.2 < x < 0.99 Semi-inclusive DIS at low x, x < 0.01 and high W: (C.Adloff et al. (H1), S.Chekanov (ZEUS))

Quark-Hadron Duality (3) W. Melnitchouk calculates Fπ using LO fit to E615 data on Fπ2 Shape of Fπ determined by x dependence of Fπ2 Drell-Yan-West predict Fπ2~(1-x) if Fπ~(1/Q2) NLO analysis of E615 data suggests non-linear x dependence (K.Wijesooriya et al., nucl-ex/0509012) W. Melnitchouk, Eur. Phys. J. A17 (2003) 223 More data needed for testing duality relation Inclusive σL,σT at high Q2, π spectrum at low W Fπ at higher Q2 Fπ-2 exclusive L/T up to Q2=2.5 GeV2

Summary Fπ Calculations Limits on Fπ well defined and many model calculations available for transition region Key Point: Know there is asymptotic limit, but how to get there and what governs transition? ?? Long distance Low Q2 Short distance High Q2 Need experimental data to study behavior of QCD in transition from long distance to short distance scales

Pion Form Factor via Electroproduction Charge radius well known from p+e scattering No “free pion” target – to extend measurement of Fp to larger Q2 values use “virtual pion cloud” of the proton Method check - Extracted results are in good agreement with p+e data J. Volmer et al. Phys Rev. Lett. 86 (2001) 1713-1716

Pion Electroproduction Kinematics Hadronic information determined by Lorentz invariants Q2= |q|2 – ω2 W=√-Q2 + M + 2Mω t=(q - pπ)2 pπ = momentum of scattered pion θπ = angle between scattered pion and virtual photon φπ = angle between scattering and reaction plane

Pion Electroproduction Cross Section Unpolarized pion electroproduction cross section In general, LT and TT → 0 by integrating over φ acceptance

“Simple” Longitudinal-Transverse Separation From φ-dependence have σTT and σLT Determine σT+ ε σL for high and low ε in each t-bin for each Q2 Isolate σL, by varying photon polarization, ε

“Real” Cross Section Separation Cross Section Extraction φ acceptance not uniform Measure σLT and σTT Extract σL by simultaneous fit using measured azimuthal angle (φπ) and knowledge of photon polarization (ε)

Extracting Fπ from σL data In t-pole approximation: Want smallest possible –t for proximity to π-pole Need to know t-dependence Extraction of Fπ requires a model incorporating pion electroproduction

Pion Electroproduction Models MAID Only useful for W < 2 GeV, Fπ-2 kinematics above this region Born term models Do not describe t-dependence well away from pole VGL/Regge Appropriate at W > 2 GeV Seems to under-predict σT consistently Constituent Quark Model Same kinematic range as VGL/Regge, two free parameters Not previously used in data analysis

VGL Regge Model Pion electroproduction in terms of exchange of π and ρ like particles Model parameters fixed from pion photoproduction Free parameters: Fπ and Fρ ρ exchange does not influence σL at small -t Fit to σL to model gives Fπ at each Q2

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

Preliminary π+/π- Ratios (Fπ-1) Preliminary analysis of Fπ-1 data suggests pole process dominates Gives confidence that can extract Fπ from σL data

Fπ-1 (E93-021) Data taken in 1998, thesis students: J. Volmer and K. Vansyoc Q2=0.6-1.6 GeV2 at W=1.95 GeV Transverse cross section smaller and slightly steeper t-dependence in σL at low Q2 than in Regge model – attributed to resonance background contribution J. Volmer et al PRL 86 (2001)

Fπ-2 (E01-004) Higher W Repeat Q2=1.60 GeV2 closer to t=mπ pole Goal: Separate σL/σT via Rosenbluth separation for extracting Fπ using pole dominance Experiment Successfully completed in Hall C in 2003 Measure pion electroproduction from H and D Extension of Fπ-1 Higher W Repeat Q2=1.60 GeV2 closer to t=mπ pole Highest possible value of Q2 at JLab Exp Q2 (GeV/c)2 W (GeV) |t| (Gev/c)2 Ee (GeV) Fπ-1 0.6-1.6 1.95 0.03-0.150 2.445-4.045 Fπ-2 1.6,2.5 2.22 0.093,0.189 3.779-5.246

Fπ-2 Collaboration R. Ent, D. Gaskell, M.K. Jones, D. Mack, J. Roche, G. Smith, W. Vulcan, G. Warren Jefferson Lab, Newport News, VA , USA 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. Tadevosn 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, K. Aniol, D. Margaziotis, L. Pentchev, C. Perdrisat, I. Niculescu, V. Punjabi, E. Gibson

Fπ-2 Experimental Details Hall C spectrometers Coincidence measurement SOS detects e- HMS detects π+ HMS Aerogel First use in 2003 Built by Yerevan group (Nucl. Instrum. Meth. A548:364, 2005) Targets Liquid 4-cm H/D cells Al (dummy) target for background measurement 12C solid targets for optics calibration

Fπ-2 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 Θπ=0 Θπ=+4 Θπ=-3 -t=0.1 -t=0.3 Q2=1.60, High ε

Good Event Selection: Cuts Spectrometer Quantities Restrict momentum to nominal acceptance region HMS dp/p: ± 8% SOS dp/p: -15% to +14% Loose cuts on spectrometer angles, allow collimator to define acceptance Missing Mass Cuts Restrict missing mass to range 0.92 to 0.96 GeV (4σ) PID Coincidence Time, HMS Aerogel, SOS gas Cerenkov, shower counter Acceptance Cuts W/Q2 cut to define common phase space at high and low ε

Good Event Selection: Coincidence Time Coincidence measurement between charged pions in HMS and electrons in SOS Coincidence time resolution ~200-230 ps π+ detected in HMS – Aerogel Cerenkov and Coincidence time for PID π - selected in HMS using Gas Cerenkov Electrons in SOS – identified by Cerenkov /Calorimeter 2π threshold After PID cuts almost no random coincidences

Good Event Selection: Particle Identification (Pion) Cannot distinguish p/π+ at momenta ~ 3 GeV by TOF or gas Cerenkov Tune detection threshold for particle of interest n=1.03 for proton rejection in Fπ-2 Aerogel Cut Efficiency (npe=3) 99.5% Proton Rejection 1:300 Note: cannot distinguish K+/π+ here

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

Data Analysis Issues Kinematic Offsets – using elastic H(e,e’p) data Determine Ebeam and momenta to 0.1%, angles to 1 mrad Highly sensitive to deviations in E’e and Ebeam Acceptance – checked by comparison to Monte Carlo SOS saturation requires modification to momentum HMS Q3 current/field offset First observed in late 1990’s Tried to take into account by modifying field setting procedure Residual correlation observed

HMS Kinematic Calibrations Fπ-2 extremely sensitive to uncertainties in kinematic quantities Study of H(e,e’) constrained by W-mp=0 Sensitivity to θHMS: 0.5 mrad/MeV Best result: take into account dθHMS AND effect from HMS Q3 current offset Consistent with elastic singles data from Spring 2003 and 1999 Quantity Value In-plane angle 0.0 mrad Momentum -0.13 %

SOS Kinematic Offsets Study of over-constrained H(e,e’p) Input: Best HMS kinematic offsets Get spectrometer angles and momenta Assume beam energy correct Momentum dependent offset consistent with zero at pSOS=0 Quantity Value In-plane angle 0.0 mrad Momentum f(pSOS)

Data Analysis Charge normalized experimental yields, background subtracted, all corrections applied Efficiencies: Computer dead time: ~10% Electronic dead time: 0.5-1% (HMS), ~0.2-0.5% (SOS) Tracking Efficiency: ~97% (HMS), ~99% (SOS) Other (Coincidence Blocking, cuts etc.) Data binned in t and φπ at fixed common values of W/Q2 for high and low epsilon Compare Data to Hall C Monte Carlo – SIMC Model for H(e,e’π+) Radiative Corrections, pion decay, energy loss, multiple scattering COSY model for spectrometer optics Overall normalization confirmed to 2% based on ep elastics using parameterization of world data (J.Arrington, Phys.Rev.C69:022201,2004)

SIMC – Radiative Corrections Charged particles radiate in presence of electric field External: radiate independently – no interference terms Internal: Coherent radiation in field of primary target nucleon Description of elastic data looks good H(e,e’p) Pion radiation important, changes SIMC yield ratio ~3.5% Point-to-point uncertainty ~1% based on radiative tail studies between ε points.

Cross Section Extraction Cross Section Extraction requires Monte Carlo Model of spectrometer optics and acceptance W,Q2,t,φ – kinematic dependence of cross section model Experimental cross section extracted by iterating model until achieve agreement with data

Spectrometer Acceptance Generally looks good, BUT small regions in Y’tar acceptance not well described Likely no problem if integrating over Y’tar, but relevant for binning in –t

Y’tar Acceptance Cut Investigate various aspects regarding Y’tar acceptance Resolution Correlations Matrix element fits and corrections Different binning in -t This talk: Limit to well understood Y’tar acceptance region in cross section extraction Acceptance Cut

Preliminary Results – Compare VGL/Regge Model Fπ-2 Separated cross sections Y’tar acceptance cut applied Compare to VGL/Regge model with Λπ2=0.505, Λρ2=1.7 PRELIMINARY Point-to-point Systematic Error Goal Acceptance 3-4% 1-2% Radiative Corrections 1% Kinematics Target Density 0.5% 0.1% Charge Model Dependence Cut Dependence Detection Efficiency Statistical Error only

Preliminary Fπ Results Datapoint at Q2=1.60 GeV2 to check model dependence of mass pole extrapolation Good agreement between Fπ1/Fπ2 Fπ at Q2=2.45 GeV2 not asymptotic To Do: (more) Radiative Correction Tests Theory uncertainties Pole dominance: π+/π- ratios, in progress

Fπ at 12 GeV Kinematics Maximize t-channel contribution to σL, increase in both Q2 and W Full φ coverage at given ε over extended –t range for separating L,T,LT and TT σL/σT~1 near –t~0.6 GeV2 at Q2=6 GeV2 To reach tmin, need θπ~5º for all kinematic settings Require good understanding of systematics – kinematic offsets Sensitive to scattering angles, beam energy and momenta

Fπ at 12 GeV – Hardware Requirements Hall C Spectrometers Optics in HMS accumulated over 10 years, many successful L/T SHMS design similar to HMS, QQ(QD), point-to-point focusing, minimum angle 5º in SSA tune rigid optics -> good reproducibility of pointing and angular offsets flat acceptance reduces systematic error angle and momentum resolution Kinematics: Full φ coverage at high ε using three angles

Fπ at 12 GeV Summary Significant progress on theoretical front expected in next 5 years – Lattice, GPD etc Experiments need higher energy electron beam to reach the kinematic region where pQCD expectation may be approached SHMS+HMS in Hall C will allow Fπ to be measured up to Q2=6 GeV2 – 12 GeV proposal Small Forward angle crucial for Fπ experiment since need to reach low –t values.

Summary Fπ good observable to study transition region to pQCD Results from Fπ-1 shows Q2Fπ clearly not asymptotic yet π-/π+ suggests dominance of pion exchange Fπ-2 results in a region of Q2 where Fπ calculations begin to diverge Data will constrain models describing the treatment of soft physics at higher Q2 Studies of Fπ at 12 GeV will allow us to reach the kinematic range where pQCD expectation may be approached

Constituent Quark Model Obukhovsky et al. use microscopic description on basis of CQM Calculate σL using both t-pole and s-, u-pole contributions Free parameters: Fπ and strong FπNN Calculation at Λπ2=0.54 Shape similar for σL Significant difference in σT I. Obukhovsky et al hep-ph/0506319 M. Vanderhaeghen, M Guidal, J-M Laget Phys Rev C57 (1998)

Constituent Quark Model Compare to pole exchange model (Obukhovsky et al. ) with Λπ2=0.54, Λρ2=0.54 Description of σT better – model difference: ρNN interaction Sensitivity of σT from Fπ2 may be direct measurement of Fρπγ and ρNN vertex Analogous to relation between σL and Fπ/πNN vertex PRELIMINARY Statistical Error only

QCD Modeling via Dyson Schwinger Equations Goal: model “soft QCD” Bethe-Salpeter equation: describes relativistic bound states Dyson-Schwinger equations: Solve to get interaction Provides input for bound state equation Poincare invariant, confinement, dynamical chiral symmetry breaking Meson observable

Pion Form Factor – BSE/DSE Maris and Tandy use Dyson-Schwinger/Bethe-Salpeter approach Dressed quark propagator Constrain parameters by agreement of fπ, mπ with data Predict Fπ and rπ with no further adjustment High Q2: No solution yet, try to solve DSE with lattice input P. Maris and P.C. Tandy, Phys. Rev. C62:055204, 2000.

Y’tar Acceptance Studies Data/MC discrepancy in elastic data Data/MC disagreement in Y’tar even present in elastic data at ± (25-30) mrad Problem: Large fraction of (e,e’π+) data at low -t located in these regions

Y’tar Acceptance – Eliminate Correlations Problem: missing mass correlated with Y’tar in both elastic and π data – spectrometer optics Can be eliminated by modification to HMS δ Simulation suggests effect from Q3 current/field offset

SIMC – Pion Decay 13-15% of pions at p~3GeV decay in flight in HMS HMS drift chambers 13-15% of pions at p~3GeV decay in flight in HMS BUT nonzero probability for pion to decay AND resulting muon can produce trigger Cannot identify muon background easily by PID or time of flight BUT can simulate in SIMC using sequential implementation of optics Decay fraction of total yield ~3% HMS Dipole Target Pion decay proportional to pπ Little point-to-point uncertainty, Pπ does not change between ε points

HMS Q3 Current Offset Observe correlation in HMS elastic data Effect ~4 MeV across acceptance Simulation suggests correlation due to Q3 current offset Can eliminate – important in precision cross section measure No Correction Apply Correction

HMS Optics -Vertical Acceptance up Sieve does not entirely cover octagonal collimator Extra data taken with sieve shifted up/down by 1/2 row Special target for Ytar dependence (z=± 7cm) Default matrix elements not too bad even in extreme vertical regions

Pion Form Factor – Model φπ Bakulev et al. model a form of φπ constrained by experimental data Note: for pQCD to be valid cannot have full contribution from regions x~0 QCD vacuum structure described by product of scalar quark condensate and Gaussian shape, scale set by <λ2>q~0.4GeV2 extracted from CLEO πγ transition data Consistent description of both Fπγ and Fπ using this wave function

Fπ at 12 GeV Kinematics Maximize t-channel contribution to σL - requires increase in both W and Q2 optimal range for W~3-4 GeV2 Full φ coverage at given ε over extended –t range for separating L,T,LT and TT σL/σT~1 near –t~0.6 GeV2 at Q2=6 GeV2 Large t-range for testing cross section models To reach desired tmin, require θπ~5deg for all kinematic settings