1

Tanja Horn

Jefferson Lab

The Pion Form The Pion Form Factor Factor

European Research Conference on

Electromagnetic Interactions with Nucleons and Nuclei Milos, Greece, 2007

The present status and future outlook

2

R. Ent, D. Gaskell, M.K. Jones, D. Mack, D. Meekins, J. Roche, G. Smith, W. Vulcan, G. Warren, S.

WoodJefferson 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. TvaskisVrije Universiteit, Amsterdam, Netherlands

E. Beise, H. Breuer, C.C. Chang, T. Horn, P. King, J. Liu,

P.G. RoosUniversity of Maryland, College Park, MD, USA

W. Boeglin, P. Markowitz, J. ReinholdFlorida International University, FL, USA

J. Arrington, R. Holt, D. Potterveld, P. Reimer, X. Zheng

Argonne National Laboratory, Argonne, IL, USA

H. Mkrtchyan, V. TadevosyanYerevan Physics Institute, Yerevan, Armenia

S. Jin, W. KimKyungook National University, Taegu, Korea

M.E. Christy, L.G. TangHampton University, Hampton, VA, USA

J. VolmerDESY, Hamburg, Germany

T. Miyoshi, Y. Okayasu, A. MatsumuraTohuku University, Sendai, Japan

B. Barrett, A. SartySaint Mary’s University, Halifax, NS Canada

K. Aniol, D. Margaziotis California State University, Los Angeles, CA, USA

L. Pentchev, C. PerdrisatCollege of William and Mary, Williamsburg, VA, USA

I. NiculescuJames Madison University, Harrisonburg, VA, USA

V. PunjabiNorfolk State University, Norfolk, VA, USA

E. GibsonCalifornia State University, Sacramento, CA, USA

Jefferson Lab Fpi2 Jefferson Lab Fpi2 CollaborationCollaboration

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 FactorsHadronic Form Factors

4

• The study of Fπ 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 Q2 compared to the nucleon

• At very large Q2 one can calculate Fπ in pQCD, which reduces to the factorized form as Q2→∞

2

2πs2

π Qfα

π16)(QF where f2π=93 MeV is the π+→μ+ν decay constant

– This asymptotic normalization does NOT exist for nucleon form factors

The Pion Charge Form FactorThe Pion Charge Form Factor

• The Q2 dependence of Fπ data allows for the determination of the role of non-perturbative vs. perturbative physics– At what values of Q2 will pQCD contributions dominate?

5

• Perturbative QCD(LO) hard calculations under-predict experimental data by a factor of 2-3 – At experimentally accessible Q2 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 Q2=2.5 GeV2

ContextContext

6

• At low Q2, Fπ can be measured directly from π+e scattering up to Q2~0.3 GeV2 [S.R. Amendolia et al., NP B277 (1986)] – Accurate measure of the π+ charge radius, rπ=0.657 ± 0.012 fm

• To extend measurement of Fπ to larger Q2 values, one must use the “virtual pion cloud” of the proton, p(e,e’π+)n reaction– t-channel diagram dominates σL at small –t

• In the Born term model

πNNg

Measuring FMeasuring Fππ

),()()(

2222

2

tQFtgmt

tQ

dt

dNN

L

7

• Extraction of Fπ relies on the pole dominance of σL

– To get the maximum contribution from the π+ pole to σL, requires data at the smallest possible –t

– At fixed Q2, a higher value of W allows for smaller -tmin

• For the extraction of Fπ, one needs to know the -t dependence of σL

– Only three of the quantities Q2, W, t, and θπ are independent

– needs to vary θπ to measure the -t dependence (off-parallel)

– In off-parallel kinematics, LT and TT must also be determined

Q2= |q|2 – ω2t=(q - pπ)2

W=√-Q2 + M2 + 2Mω

scattering plane

reaction plane

Pion Electroproduction Pion Electroproduction KinematicsKinematics

πcos2φdφdt

dσεπcosφdφdt

dσ1)(εε2dφdtσ2d TTLT

dφdtdσε

dφdtdσ LT

1)]2eθ

(2tan)2Q

2ω(12[1ε

8

Extraction of FExtraction of Fππ from from p(e,e’p(e,e’ππ+)n data+)n data

• + production data are obtained at –t>0 (away from the t=mπ

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 Fπ from σL data– Fit data in the physical region

9

• An improved check will be performed after the JLab Upgrade– Lower Q2 (Q2=0.30 GeV2)– Lower –t (-t=0.005 GeV2)

Electroproduction Method TestElectroproduction Method Test• Electroproduction starts from a

virtual pion– Can this method yield the

physical form-factor

• Test the method by comparing Fπ 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 Q2 = 0.35 GeV2 consistent with extrapolation of elastic data

[Ackerman et al., NP B277 (1986) 168]

10

•Old data at large Q2 (> 1 GeV2) extracted F from unseparated cross sections

•Used extrapolation of T fit at low Q2 to isolate L

•Largest Q2 points also taken at large –tmin

•Carlson and Milana predict MpQCD/Mpole grows dramatically for -tmin>0.2 GeV2

•Pole term may not dominate!

PRL 65, 1717(1990)

?

FFππ before 1997 before 1997

11

Exp Q2

(GeV2)

W (GeV)

|t|

(Gev)2

Ee

(GeV)

Fpi1 0.6-1.61.6 1.95 0.03-0.1500.150 2.445-4.045

Fpi2 1.61.6,2.45 2.22 0.0930.093,0.189 3.779-5.246

• Fpi2 extends the earlier Fpi1 data to the highest possible value of Q2 with 6 GeV beam at JLab– Fpi2 data at higher W,

smaller -t

– Repeat Q2=1.60 GeV2 closer to t=m2

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 GeV SOS: 1.7 GeV

The FThe Fππ Program at JLab Program at JLab

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’p(e,e’ππ+)n Event Selection+)n Event Selection

13

• 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

• Have full coverage in φ BUT acceptance not uniform

• Measure σTT and σLT by taking data at three angles: θπ=0, +4, -3 degrees

Θπ=0Θπ=+4 Θπ=-3

-t=0.1

-t=0.3Q2=1.60, High ε

Radial coordinate: -t, azimuthal coordinate: φ

Q2=1.60 GeV2

Q2=2.45 GeV2

Fpi2 Kinematic CoverageFpi2 Kinematic Coverage

14

πcos2φdφdt

dσεπcosφdφdt

dσ1)(εε2dφdt

dσεdφdtσd TTLTT

2 dφdt

dσL

• σL is isolated using the Rosenbluth separation technique– Measure the cross section at two

beam energies and fixed W, Q2, -t– Simultaneous fit using the measured

azimuthal angle (φπ) allows for extracting L, T, LT, and TT

• Careful evaluation of the systematic uncertainties is important due to the 1/ε amplification in the σL extraction– Spectrometer acceptance, kinematics,

and efficiencies

Determination of the Determination of the Experimental Cross SectionExperimental Cross Section

15

• Uncertainties in spectrometer quantities parameterized using over-constrained 1H(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%

Source Pt-Pt Scale t-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%

• Statistical uncertainty in ranges between 1 and 2%

Systematic UncertaintiesSystematic Uncertainties

16

Λπ2=0.513 (0.491) GeV2, Λπ

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: Fπ and Fρ

through the trajectory cutoff

/Q11

πF 2

2πΛ

- 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 σL to model gives Fπ at each Q2

T. H

orn et al., Phys. R

ev. Lett. 97 (2006) 192001.

Extraction of FExtraction of Fππ from Fpi2 data from Fpi2 data

17

• Extract Fπ for each tbin separately– Fπ 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 testFpi2 model test

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

• σL t-dependence of VGL Regge is significantly flatter than the data– May indicate background

• VGL Regge under-predicts σT data for any value of Λρ2

– More data needed to resolve this puzzle

Fitting VGL to Fpi1 dataFitting VGL to Fpi1 data

19

Deficiencies in the description of Deficiencies in the description of Fpi1 dataFpi1 data

• Deficiencies may be due to resonance contributions– Not included in Regge model

– At higher Q2, the resonance form factor is expected to reduce the resonance contribution

• Fpi1 analysis assumes that the contribution of backgrounds is small at tmin

– Fit VGL to each t-bin, Λπ2(Q2,t)

– Λπ2 decreases with -t

– Linear fit to Λπ2 to tmin gives the best estimate of Fπ at each Q2

– Assign additional model uncertainty

20

• Data point at Q2=1.60 GeV2 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

• Fπ precision data deviate from 0.657 fm charge radius at Q2=2.45 GeV2 by about ~1σ

– The monopole reflects the soft (VMD) physics at low Q2

– The deviation suggests that the π+ “harder” at this Q2

T. Horn et al., Phys. Rev. Lett. 97 (2006)192001.

V. Tadevosyan et al., nucl-ex/0607007.

JLab Experimental ResultsJLab 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

• Fπ 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 Q2=1.60 GeV2

– Agreement at Q2=2.45 GeV2 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 Comparison with QCD Inspired ModelsModels

22

A.P. Bakulev et al. Phys. Rev. D70 (2004).

The Pion Distribution The Pion Distribution AmplitudeAmplitude

Chernyak & Zhitnitsky(CZ) DAAsymptotic 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

• Fπ0 results taken as evidence that asymptotic pion DA appropriate as low as Q2=1 GeV2

• For Fpi+ FF soft contributions from quark-hadron duality model need to be included to describe the data

23

Non-pole contributions to σL in the GPD Framework

• Amplitudes for π+ and πo composed of the same GPDs, but different linear combinations

• Obtain non-pole contributions by comparing πo and π+ production amplitudes, ML~ApN+BpN

– In the limit t →(mπ)2 the π+ amplitude contains a strong singularity (pion pole)

)~~

(~ dd

uup

HeHeA o

)~~

(~ dd

uup

EeEeB o

))(~~

(~ dudu

peeHHA

))(~~

(~ dudu

peeEEB

πo

π+

VGG/GPD prediction

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

SHMSSHMS

HMS HMS (QQQD)(QQQD)

SOS SOS (QQD)(QQD)

Hall C at 12 GeVHall C at 12 GeV

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 FThe Fππ Measurement after the Measurement after the JLab UpgradeJLab Upgrade

26

• Fπ is a good observable to study the transition from collective degrres of freedom to quarks and gluons

• Fπ 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 Q2 JLab results indicate that Q2Fπ is still increasing, but ~1σ below the monopole parameterization of the charge radius– Still far from the QCD prediction

• Studies of Fπ at higher electron beam energies will allow to reach the kinematic range where hard contributions are expected to dominate– Planned measurement of Fπ at JLab after the upgrade to Q2=6 GeV2

• Further development of QCD techniques for the non-perturbative physics are anticipated

SummarySummary

27

• Extraction of Fπ relies on dominance of t-channel (pole dominance)– t-channel diagram is purely

isovector

2sv

2sv

L

L

|AA||AA|

σ

σR

• R consistent with the model predictions indicates t-channel dominance of the data

Competing Reaction Competing Reaction ChannelsChannels

• Pole dominance tested using π-/π+ from D(e,e’p) – G-parity: If pure pole then

necessary R=1

28

• Experiments must access small –t for t-channel dominance in sigL

Background in the extraction Background in the extraction of Fpiof Fpi

Interpretation of Fπ data considered reliable for -t<0.2 GeV2

Carlson & Milana, Phys. Rev. Lett. 65, 1717 (1990)

• Carlson&Milana indicated a significant contribution of non-leading processes complicating the extraction of Fπ

– Background ratio rises dramatically once tmin>0.2

• The VGL Regge model describes σL for π+ well– This implies that non-pole

contributions are small– A more rigorous constraint

requires additional data (proposed to PAC31)

29

• Problematic L/T separations

Previous data from CornellPrevious data from Cornell

30

• Results from Bakulev

The Pion Wave functionThe Pion Wave function

31

• Bakulev et al. calculate the factorizable pQCD contribution to Fπ in NLO– Model φπ using QCD Sum

Rules prescription

A.P. Bakulev et al. Phys. Rev. D70 (2004).

hard

πF

soft

πF

πF

• 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 QThe Q22 dependence of F dependence of Fππ

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 FQCD Inspired Models for Fππ

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

FFππ on the Lattice on the Lattice

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 mπ sufficiently small to yield small chiral extrapolation errors– Require higher Q2 data to validate new LQCD methods

pQCD→

FFππ from a recent unquenched from a recent unquenched Lattice QCD calculationLattice QCD calculation

Fpi1

Fpi2

35

• The charged pion is one of the simplest QCD objects– The Q2 dependence of the form factor provides information on

hadronic structure at finite values of Q2

• The limits on Fπ 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 Q2

– This study of Fπ is unique to JLab

• At moderate values of Q2 both hard and soft contributions must be taken into account – At what values of Q2 will the hard pQCD component dominate– Different theoretical viewpoints on the role of higher twist

mechanisms up to large momentum transfer

FFππ Calculations Summary Calculations Summary

36

• The use of a model that includes the π+ production mechanism to extract Fπ from σL data is more reliable– To test the method: compare the extracted Fπ values at low Q2 with the

exact values measured in elastic e-π scattering – Existing Q2=0.35 GeV2 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 FExtracting Fππ from from ππ++ production production

• Chew Low extrapolation method has large systematic uncertainties– A reliable phenomenological

extrapolation is not possible

)(QFmt

gtσ 22

2

NNπ2π

2π

L

37

• MAID – unitary isobar model for pion photo- and electroproduction– Only useful for W < 2 GeV, Fπ-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– Fπ is the only free parameter in the calculation of σL

• 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 Pion Electroproduction Models

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 ~1038

Fπ measurements

Jefferson LabJefferson Lab