The Pion Form Factor Tanja Horn University of Maryland Calculation of the Pion Form Factor -> The road to a hard place F π measurement via pion electroproduction -> Extracting F π from H(e,e’π + ) data -> F π -2 in Hall C Preliminary Cross Sections Hall C Workshop, 5 Jan 2006

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 consistent analysis of different length scales in a single process not easyBut, 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 form factors –Experiments – form factors, neutral weak nucleon structure Short Distance Asymptotic Freedom Long Distance Binding, collective dof

Pion Form Factor in QCD “Hydrogen Atom of QCD”Why pions? - Simplest QCD system ( ) - “Hydrogen Atom of QCD” Good observable for study of interplay between hard and soft physics in QCD Large Q 2 behaviorLarge Q 2 behavior predicted by Brodsky-Farrar small Q 2 F π (0)=1so where is pQCD?At small Q 2 vector meson dominance gives accurate description with normalization F π (0)=1 by charge conservation – data fits well so where is pQCD?

Nonperturbative Physics At moderate Q 2 nonperturbative corrections to pQCD can be largeAt moderate Q 2 nonperturbative corrections to pQCD can be large – Braun et al calculate ~30% at Q 2 =1 GeV 2 to F π transition to asymptotic behaviorNeed a description for transition to asymptotic behavior how do we know which one is “right”?Variety of effective F π models on the market – how do we know which one is “right”? Feynman Mechanism 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.

Pion Form Factor via Electroproduction Charge radius well known from  e scattering No “free pion” target – to extend measurement of F  to larger Q 2 values use “virtual pion cloud” of the protonNo “free pion” target – to extend measurement of F  to larger Q 2 values use “virtual pion cloud” of the proton Method check - Extracted results are in good agreement with  +e data J. Volmer et al. Phys Rev. Lett. 86 (2001)

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 pionp π = momentum of scattered pion θ π = angle between scattered pion and virtual photonθ π = angle between scattered pion and virtual photon φ π = angle between scattering and reactionφ π = angle between scattering and reaction plane

Cross Section Separation Cross Section Extraction –φ acceptance not uniform –Measure σ LT and σ TT Extract σ L by simultaneous fitExtract σ L by simultaneous fit using measured azimuthal angle (φ π ) and knowledge of photon polarization (ε)

Extracting F π from σ L data Extraction of F π requires a model incorporating pion electroproduction – VGL Regge modelExtraction of F π requires a model incorporating pion electroproduction – VGL Regge model –One recent model based on constituent quark model by Obukhovsky et al. In t-pole approximation:

Competing Reaction Channels Extraction of F π relies on dominance of t-channel, BUT there are other diagrams –t-channel purely isovector –Background: isoscalar Pole dominance tested using π - /π + from D(e,e’  )Pole dominance tested using π - /π + from D(e,e’  ) –G-parity: If pure pole then necessary R=1 t-channel process γ*γ* π π*π* pn

F π -2 (E01-004) ExpQ2 (GeV/c) 2 W (GeV) |t| (Gev/c) 2 E e (GeV) Fπ Fπ , , Goal: –Separate σ L /σ T via Rosenbluth separation for extracting F π using pole dominance Experiment –Successfully completed in Hall C in 2003 –Measure 1 H(e,e’,π + ) and 2 H(e,e’π ± )NN Extension of F π -1 –Higher W –Repeat Q 2 =1.60 GeV 2 closer to t=m π pole –Highest possible value of Q2 at JLab

F π -2 Collaboration D. GaskellD. Mack 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 G.M. Huber, V. Kovaltchouk, G.J. Lolos, C. Xu University of Regina, Regina, SK, Canada H. Blok H. Blok, V. Tvaskis Vrije Universiteit, Amsterdam, Netherlands E. Beise 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

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

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

HMS Tracking Efficiency At high rates: multiple particles within allowed timing window –Consider efficiency for one good track Original efficiency algorithm: biased towards single tracks –But there are multiple track events with lower intrinsic efficiency Overall tracking efficiency was too goodOverall tracking efficiency was too good

Target Density - Luminosity Scans Three scans on H, D, Al and carbon – beam currents between uA –HMS rates: kHz –SOS rates: < 100 kHz Include modified tracking efficiency calculation Small rate dependence for carbon at very high rates (~1%/600kHz) 600 kHz Carbon HMS Analysis

HMS Trigger Efficiency Localized scintillator inefficiency at negative HMS acceptance –Both elastic and π ± data Could be problem if apply global efficiency correction F π -2 acceptance ±5% - can avoid region by applying cut F π -2 acceptance cut

SOS Saturation Correction (1) Current SOS saturation correction not enough at large SOS momenta ( ~ 1.6 GeV) Can eliminate correlation using new SOS delta matrix elements + small correctionCan eliminate correlation using new SOS delta matrix elements + small correction P=1.74 GeV (current) P=1.74 GeV (new)

SOS Saturation Correction (2) Problem: Missing mass high ~2MeV (p SOS =1.65 GeV) Need additional correction to SOS saturation parametrization –Relevant for SOS momenta ~1.6 GeV –Consistent with elastics

HMS – More Correlations Problem: missing mass correlated with Y’ tar in both elastic and π data – spectrometer opticsProblem: missing mass correlated with Y’ tar in both elastic and π data – spectrometer optics Can be eliminated by modification to HMS δCan be eliminated by modification to HMS δ –Simulation suggests effect from Q3 current/field offset Do not see in elastic data due to different illuminationDo not see in elastic data due to different illumination

Cross Section Extraction Monte Carlo Model of spectrometer optics and acceptance Compare Data to Hall C Monte Carlo - SIMC –COSY model for spectrometer optics –Model for H(e,e’π + ) –Radiative Corrections, pion decay Iterate model until achieve agreement with data

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.

Y’ tar Acceptance Cut Investigate various aspects regarding Y’ tar acceptanceInvestigate 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 extractionThis talk: Limit to well understood Y’ tar acceptance region in cross section extraction Acceptance Cut

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

To Do - For Final Result Studies of rate dependent corrections and relevant correlation - doneStudies of rate dependent corrections and relevant correlation - done Finalize Systematic Studies - in progressFinalize Systematic Studies - in progress –Y’ acceptance –Radiative processes Theory Uncertainties - in progressTheory Uncertainties - in progress –Models for F π extraction (VGL/Obukhovsky) Pole dominance : π+/π- ratios - in progressPole dominance : π+/π- ratios - in progress

Other

Preliminary F π Results Datapoint at Q 2 =1.60 GeV 2 to check model dependence of mass pole extrapolation –Good agreement between F π 1/F π 2 F π at Q 2 =2.45 GeV 2 not asymptotic To Do:To Do: –(more) Radiative Correction Tests –Theory uncertainties –Pole dominance: π+/π- ratios, in progress

F π 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 approachedExperiments 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 Q 2 =6 GeV 2SHMS+HMS in Hall C will allow Fπ to be measured up to Q 2 =6 GeV 2 – 12 GeV proposal Small Forward angle crucial for F π experiment since need to reach low –t values.

Constituent Quark Model Obukhovsky et al. use microscopic description on basis of CQMObukhovsky et al. use microscopic description on basis of CQM –Calculate σ L using both t-pole and s-, u-pole contributions –Free parameters: F π and strong F πNN Calculation at Λ π 2 =0.54 –Shape similar for σ L –Significant difference in σ T I. Obukhovsky et al hep-ph/ M. Vanderhaeghen, M Guidal, J-M Laget Phys Rev C57 (1998)

Constituent Quark Model Compare to pole exchange model (Obukhovsky et al. ) with Λ π 2 =0.54, Λ ρ 2 =0.54Compare to pole exchange model (Obukhovsky et al. ) with Λ π 2 =0.54, Λ ρ 2 =0.54 Description of σ T better – model difference: ρNN interactionDescription of σ T better – model difference: ρNN interaction Sensitivity of σ T from F π 2 may be direct measurement of Fρπγ and ρNN vertexSensitivity of σ T from F π 2 may be direct measurement of Fρπγ and ρNN vertex –Analogous to relation between σ L and F π /πNN vertex Statistical Error onlyStatistical Error only PRELIMINARY

Summary F π good observable to study transition region to pQCD Results from F π -1 shows Q 2 F π clearly not asymptotic yet –π - /π + suggests dominance of pion exchange F π -2 results in a region of Q 2 where F π calculations begin to divergeF 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 Studies of F π at 12 GeV will allow us to reach the kinematic range where pQCD expectation may be approachedStudies of F π at 12 GeV will allow us to reach the kinematic range where pQCD expectation may be approached

F π -1 (E93-021) J. Volmer and K. VansyocData taken in 1998, thesis students: J. Volmer and K. Vansyoc –Q 2 = GeV 2 at W=1.95 GeV VGL under-predicts σ T Steeper t-dependence for σ L at low Q 2 than in Regge model –attributed to resonance background contribution J. Volmer et al PRL 86 (2001)

“Strange” Features of Data Observe peak at ~1.16 GeV in missing mass spectrum –Only in high epsilon acceptance Not part of regular analysisNot part of regular analysis – eliminated by missing mass cut

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

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

F π -2 Kinematic Coverage W/Q 2 phase space covered at low and high ε is differentW/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 uniformHave 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

VGL Regge Model 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 ρ exchange does not influence σ L at small -tρ exchange does not influence σ L at small -t Fit to σ L to model gives F π at each Q 2

Calibration Data (F π -2) HMS Sieve runs – shifted sieve to extend vertical acceptanceHMS Sieve runs – shifted sieve to extend vertical acceptance –θ HMS =15º, p HMS =3.5 GeV/c SOS sieve runs – Corrections to SOS matrix elements in angle and momentumSOS sieve runs – Corrections to SOS matrix elements in angle and momentum –θ SOS =15º, p SOS =0.9, 1.74 GeV/c High rate and high statistics Luminosity ScansHigh rate and high statistics Luminosity Scans –Include carbon target as control –Study of rate dependent corrections –Dead times at high rates HMS H(e,e’) at every energy – fit kinematic offsetsHMS H(e,e’) at every energy – fit kinematic offsets H(e,e’p) at every energy – fit kinematic offsets and global normalization checkH(e,e’p) at every energy – fit kinematic offsets and global normalization check

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

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 CorrectionApply Correction

Kinematic Calibrations QuantityHMSSOS In-plane angle0.0 mrad Momentum-0.13 %f(p SOS ) Study of H(e,e’) constrained by W-m p =0 –Best result: take into account dθ HMS AND effect from HMS Q3 current offset Study of over-constrained H(e,e’p) –Input: Best HMS kinematic offsets –Get spectrometer angles and momenta

Preliminary π + /π - Ratios (F π -1) Preliminary analysis of F π -1 data suggests pole process dominatesPreliminary analysis of F π -1 data suggests pole process dominates Gives confidence that can extract F π from σ L data