Tanja Horn

Jefferson Lab

11

The Pion Form The Pion Form Factor 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. 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. Roos

University 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

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Jefferson Lab Fpi2 Jefferson Lab Fpi2 CollaborationCollaboration

• 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?

33

• 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

• 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

44

• 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

• At experimentally accessible Q2 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

55

FFππ at intermediate Q at intermediate Q22

• The charged pion presents a clean test case for our understanding of bound quark systems– Structure of pion at all Q2 values

• At what value of Q2 will hard pQCD contributions dominate?– Perturbative QCD(LO) hard calculations under-predict experimental data

by a factor of 2-3

66

ContextContext

• Many studies of Fπ, 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 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

• At larger Q2 values, one must use the “virtual pion cloud” of the proton to extend the Fπ measurement– t-channel diagram dominates σL at small –t

• In the Born term model:

77

πNNg

Measuring FMeasuring Fππ

),()()(

2222

2

tQFtgmt

tQ

dt

dNN

L

Pion electroproduction

• Extraction of Fπ relies on the pole dominance of σL

– For maximum contribution from the π+ pole to σL, need data at the smallest possible –t

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

88

• Extraction of Fπ requires knowledge of the -t dependence of σL

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

– Must 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

99

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

• + 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

• 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 scattering 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]

1010

• 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

1111

?

FFππ before 1997 before 1997

• Large Q2 data from Cornell– Use extrapolation of σT fit at

low Q2 to isolate σL

– Extract Fπ from unseparated cross sections

• Largest Q2 points also taken at large –t

– Carlson&Milana predict MpQCD/Mpole grows significantly for –tmin>0.2 GeV2 [PRL 65 (1990) 1717]

– Pole term may not dominate

• –tmin<0.2 GeV2 constraint limits Q2 reach of F measurements

• Measurement of σL 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

1212

)~~

(~ dd

uup

HeHeA o

)~~

(~ dd

uup

EeEeB o

))(~~

(~ dudu

peeHHA

))(~~

(~ dudu

peeEEB

0+

VGG GPD-based calculation

pole

non-pole

FFππ Backgrounds Backgrounds

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

1313

• 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

• 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

1414

• After PID cuts almost no random coincidences

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

1515

• 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

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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 Determination of σσLL

1717

Λπ2=0.513 (0.491) GeV2, Λπ

2=1.7 GeV2 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: Fπ and Fρ

/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

1818

• Extract Fπ for each t-bin 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

FFππ t-dependence t-dependence

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

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

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

1919

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

• Fπ is still far from the pQCD prediction– Including transverse

momentum effects has no significant impact

• New point from πCT (2004) in good agreement with Fpi experiments

T. Horn et al., arXiv:0707.1794 (2007).

2020

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

FFππ in 2007 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:0707.3859]

T. Horn et al., arXiv:0707.1794 (2007).

• [[A.P. Bakulev et al, Phys. Rev. D70 (2004)]Hard contribution to NLO with improved π DASoft contribution from local duality

Interpretation Issues

2121

• t dependence of Fpi1 σL is significantly steeper than VGL/Regge at the lowest Q2

– May be due to resonance contributions not included in Regge

– Linear fit to Λπ2 to tmin gives the best

estimate of Fπ at each Q2

• Check the model dependence of the mass pole extrapolation– Good agreement between Fpi1

(tmin=0.093 GeV2) and Fpi2 (tmin=0.150 GeV2) gives confidence in the reliability of the method

• Significant progress on theoretical front expected in next 5 years– Lattice, GPDs etc.

2222

• 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– Test of 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 Fπ extraction by comparing data at several values of W

FFππ after the JLab Upgrade after the JLab Upgrade

• Fπ is a good observable to study the transition from collective degrees 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

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SummarySummary