Precision Measurement of The Pion Form Factor Tanja Horn July 13, 2006 JLab Science and Technology Review Pion Form Factor via Pion Electroproduction Precision Measurements in Hall C JLab Results and future directions

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. JLAB –We know that there is an asymptotic limit, but how do we get there and what governs the transition? - JLAB 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 degrees of freedom FπFπFπFπ

Pion Electric Form Factor F π (Q 2 ) and pQCD F π is a good object for studies of hadronic structure –Simple valence structure, –Expect pQCD description to be valid at lower values of Q 2 relative to nucleon High Q 2High Q 2 behavior can be calculated in pQCD, e.g. Farrar- Jackson (PRL 43 (1979) 246) f 2  =133 MeV is the  +→  + decay constant Limits on F π well defined and many treatments for soft physics available - experimental data needed to study behavior of QCD in transition from soft to hard physics

F π via Pion Electroproduction F π can be measured directly from π+e scattering (S.R. Amendolia et al., NP B277 (1986)) up to Q 2 ~0.3 GeV 2 No “free pion” target – to extend measurement of F π to larger Q 2 values use “virtual pion cloud” of the proton Method check - Extracted results are in good agreement with π+e data S.R. Amendolia et al., Nucl. Phys. B277 (1986) P. Brauel, et al., Z. Phys. C3 (1979) 101. J. Volmer et al PRL 86 (2001)

Extracting F π from Pion Electroproduction Data Q 2 = |q| 2 – ω 2 t=(q - p π ) 2 W=√-Q 2 + M 2 + 2Mω In most analyses F π is from σ L data using a model incorporating pion electroproduction ( we use VGL/Regge)In most analyses F π is extracted from σ L data using a model incorporating pion electroproduction ( we use VGL/Regge) In t-pole approximation: The lab cross section can be expressed: scattering plane reaction plane

Precision F π at JLab First phase of the measurement ran in Hall C at JLab in 1997, thesis students: J. Volmer and K. Vansyoc –Measured pion electroproduction from H and 2 H –Extracted  L  L,  T,  TT, and  LT at W=1.95 GeV, Q 2 = 0.6, 0.75, 1.0, 1.6 GeV 2 F π was determined by comparing  L to a Regge calculation by Vanderhaeghen, Guidal, Laget (VGL, PRC 57(1998)1454) –Model parameters fixed from pion photo-production, free parameters: F π and F ρ. Fit to σ L to model gives F π at each Q 2

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 F π , , Extension of 1997 run 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 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

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 )

Experiment E Spokespeople: Henk Blok, Garth Huber, Dave Mack Analysis Team –Tanja Horn: Analyzer ENGINE, detector calibrations and tracking studies, spectrometer optics calibrations, acceptance and normalization studies, refit kinematic offsets, HMS optics improvements, Monte Carlo simulation, cross section extraction, F π extraction, publication –Dave Gaskell: analysis coordination, electronic dead time studies –Chuncheng Xu: Initial ENGINE setup, SOS optics improvements –Dave Mack: Cerenkov calibration response –Garth Huber: aerogel software, omega analysis

Cross Section Extraction 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 fitExtract σ L by simultaneous fit using measured azimuthal angle (φ π ) and knowledge of photon polarization (ε).

Comparison to VGL Model Points include 1.0(0.6)% point- to-point systematic uncertainty (dominated by acceptance) 3.5 % normalization (correlated) uncertainty (radiative corrections, pion absorption, pion decay, kinematic uncertainties) 1.8(1.9)% “t-correlated” uncertainties, influence t- dependence at fixed ε Compare to VGL/Regge model with Λ π 2 =0.513 (0.491) – σ L well described, but σ T under-predicted systematically

F π Results Data point at Q 2 =1.60 GeV 2 to check model dependence of extraction to the pion pole –Agreement between at Q 2 =1.60 GeV 2 gives confidence in reliability of this method F π precision data ~1σ below monopole form factor, Λ 2 π =0.54 GeV 2, obeying the measured charge radius. Several calculations describe data Still far from pQCD prediction 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)

F π at 11 GeV Overview 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 F π to be measured up to Q 2 =6 GeV 2 – 11 GeV proposal The proposed data points will constrain models in a region where calculation diverge.

Summary F π is a good object to study transition region to pQCD Results from JLab (1997) show Q 2 F π still increasing, but ~1σ below monopole form factor obeying measured charge radius Results from JLab (2003) in a region of Q 2 where F π calculations begin to diverge –Most precise data at these values of Q 2 will help constraining existing treatments of non-perturbative physics –Good agreement with data point at Q 2 =1.60 GeV 2 gives confidence in reliability of method –Still far from pQCD prediction Studies of F π at higher electron beam energy will allow us to reach the kinematic range where pQCD expectation may be approached –Measurement at JLab with 11GeV beam up to about Q 2 =6 GeV 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

Good Event Selection 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 /Calorimeter Exclusive neutron final state selected with missing mass cut: 0.92 ‹ MM ‹ 0.98 GeV After PID cuts almost no random coincidences.After PID cuts almost no random coincidences.

Data Analysis Issues Kinematic Offsets – directly affect physics quantities –Using the H(e,e’)p and over- constrained H(e,e’p) reactions, one can fit angle and momentum offsets. SOS saturation requires momentum dependent modification to reconstruction –~1.5% effect at p SOS =1.74 GeV HMS optics effects: Correlations in reconstructed on focal plane variables –HMS Q3 current/field offset –~4 MeV across acceptance

Comparison to VGL – ρ trajectory Λ π 2 =0.513, GeV 2 Influence of ρ cutoff on cross sections – vary Λ ρ between 1.1 and 5 GeV 2 –σ T, σ TT systematically underpredicted –Little influence on σ L Q2 (GeV/c) 2 |t| (Gev/c) 2 ρ exchange effect % % Q 2 =1.60 GeV 2

F π Time-like vs. Space-like Timelike F π via e + e - →μ + μ -Timelike F π via e + e - →μ + μ - –Most recent result from CLEO/Fermilab Expect same asymptotic prediction for both space- like and time-like dataExpect same asymptotic prediction for both space- like and time-like data –The way one gets there may be different Calculations in time-like region complicated by explicit resonancesCalculations in time-like region complicated by explicit resonances Timelike data from P.K. Zweber Ph.D. thesis (2006)

Random Background Subtraction 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

Spectrometer Uncertainties Point-to-point errors amplified by 1/Δε in L-T separation Scale errors propagate directly into separated cross section 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 Acceptance 1.0(0.6) % 1.0%0.6% Radiative Corrections 0.1%2.0%0.4% Pion Absorption -2.0%0.1% Pion Decay 0.03%1.0%- Model Dependence 0.2%-1.1(1.3)% Kinematics 0.2%-1.0% HMS Tracking 0.1%1.0%0.4% Charge -0.5%0.3% Target Thickness -0.8%0.2% Detection Efficiency -0.5%0.3% Uncertainty in separated cross sections has both statistical and systematic sources Statistical uncertainty in ranges between 1 and 2%