# Measurement of the charged pion electromagnetic form factor.

**ABSTRACT** Separated longitudinal and transverse structure functions for the reaction 1H(e,e(')pi(+))n were measured in the momentum transfer region Q2 = 0.6--1.6 (GeV/c)(2) at a value of the invariant mass W = 1.95 GeV. New values for the pion charge form factor were extracted from the longitudinal cross section by using a recently developed Regge model. The results indicate that the pion form factor in this region is larger than previously assumed and is consistent with a monopole parametrization fitted to very low Q2 elastic data.

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**ABSTRACT:**Lattice QCD simulations with a twisted mass term (tmLQCD) offer solutions to problems associated with simulations using Wilson fermions and a standard mass term. A summary of recent results from quenched simulations using tmLQCD at maximal twist for the pion form factor and hadron spectrum is presented.International Journal of Modern Physics A 01/2012; 20(27). · 1.09 Impact Factor - SourceAvailable from: export.arxiv.org[Show abstract] [Hide abstract]

**ABSTRACT:**The pion electromagnetic form factor at spacelike momentum transfer is calculated in relativistic impulse approximation using the Covariant Spectator Theory. The same dressed quark mass function and the equation for the pion bound-state vertex function as discussed in the companion paper are used for the calculation, together with a dressed quark current that satisfies the Ward-Takahashi identity. The results obtained for the pion form factor are in agreement with experimental data, they exhibit the typical monopole behavior at high momentum transfer and they satisfy some remarkable scaling relations.Physical Review D 10/2013; 89. · 4.86 Impact Factor - SourceAvailable from: Anna Dubnickova[Show abstract] [Hide abstract]

**ABSTRACT:**The utility of an application of the analyticity in a phenomenology of electro-weak structure of hadrons is demonstrated in a number of obtained new and experimentally verifiable results. With this aim first the problem of an inconsistency of the asymptotic behavior of VMD model with the asymptotic behavior of form factors of baryons and nuclei is solved generally and a general approach for determination of the lowest normal and anomalous singularities of form factors from the corresponding Feynman diagrams is reviewed. Then many useful applications by making use of the analytic properties of electro-weak form factors and amplitudes of various electromagnetic processes of hadrons are carried out.Acta Physica Slovaca 02/2010; 60(1):1-153. · 2.00 Impact Factor

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arXiv:nucl-ex/0010009v2 15 Mar 2001

Measurement of the charged pion electromagnetic form factor

J. Volmer11,21, D. Abbott19, H. Anklin4,19, C. Armstrong2, J. Arrington1, K. Assamagan5, S. Avery5, O.K.

Baker5,19, H.P. Blok11,21, C. Bochna6, E.J. Brash16, H. Breuer8, N. Chant8, J. Dunne19, T. Eden12,19, R. Ent19, D.

Gaskell14, R. Gilman17,19, K. Gustafsson8, W. Hinton5, G.M. Huber16, H. Jackson1, M.K. Jones2, C. Keppel5,19,

P.H. Kim7, W. Kim7, A. Klein13, D. Koltenuk15, M. Liang19, G.J. Lolos16, A. Lung19, D.J. Mack19, D. McKee10, D.

Meekins2, J. Mitchell19, H. Mkrtchyan22, B. Mueller1, G. Niculescu5, I. Niculescu5, D. Pitz18, D. Potterveld1, L.M.

Qin13, J. Reinhold1, I.K. Shin7, S. Stepanyan22, V. Tadevosyan22, L.G. Tang5,19, R.L.J. van der Meer16,19, K.

Vansyoc13, D. Van Westrum3, W. Vulcan19, S. Wood19, C. Yan19, W.-X. Zhao9, B. Zihlmann19,20

(The Jefferson Lab FπCollaboration)

1Argonne National Laboratory, Argonne, Illinois 60439

2College of William and Mary, Williamsburg, Virginia 23187

3University of Colorado, Boulder, Colorado 76543

4Florida International University, Miami, Florida 33119

5Hampton University, Hampton, Virginia 23668

6University of Illinois, Champaign, Illinois 61801

7Kyungpook National University, Taegu, Korea

8University of Maryland, College Park, Maryland 20742

9M.I.T.–Laboratory for Nuclear Sciences and Department of Physics, Cambridge, Massachussetts 02139

10New Mexico State University, Las Cruces, New Mexico 88003-8001

11NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands

12Norfolk State University, Norfolk, Virginia 23504

13Old Dominion University, Norfolk, Virginia 23529

14Oregon State University, Corvallis, Oregon 97331

15University of Pennsylvania, Philadelphia, Pennsylvania 19104

16University of Regina, Regina, Saskatchewan S4S-0A2, Canada

17Rutgers University, Piscataway, New Jersey 08855

18DAPNIA/SPhN, CEA/Saclay, F-91191 Gif-sur-Yvette, France

19Physics Division, TJNAF, Newport News, Virginia 23606

20University of Virginia, Charlottesville, Virginia 22901

21Faculteit Natuur- en Sterrenkunde, Vrije Universiteit, NL-1081 HV Amsterdam, The Netherlands

22Yerevan Physics Institute, 375036 Yerevan, Armenia

(February 8, 2008)

Separated longitudinal and transverse structure functions

for the reaction1H(e,e′π+)n were measured in the momen-

tum transfer region Q2= 0.6 - 1.6 (GeV/c)2at a value of

the invariant mass W = 1.95 GeV. New values for the pion

charge form factor were extracted from the longitudinal cross

section by using a recently developed Regge model. The re-

sults indicate that the pion form factor in this region is larger

than previously assumed and is consistent with a monopole

parameterization fitted to very low Q2elastic data.

14.40.Aq,11.55.Jy,13.40.Gp,25.30.Rw

The pion occupies an important place in the study of

the quark-gluon structure of hadrons. This is exemplified

by the many calculations that treat the pion as one of

their prime examples [1] – [8]. One of the reasons is that

the valence structure of the pion, being ?q¯ q?, is relatively

simple. Hence it is expected that the value of the four-

momentum transfer squared Q2, down to which a pQCD

approach to the pion structure can be applied, is lower

than e.g. for the nucleon. Furthermore, the asymptotic

normalization of the pion wave function, in contrast to

that of the nucleon, is known from the pion decay.

The charge form factor of the pion, Fπ(Q2), is an essen-

tial element of the structure of the pion. Its behaviour at

very low values of Q2, which is determined by the charge

radius of the pion, has been determined up to Q2=0.28

(GeV/c)2from scattering high-energy pions from atomic

electrons [9]. For the determination of the pion form fac-

tor at higher values of Q2one has to use high-energy

electroproduction of pions on a nucleon, i.e., employ the

1H(e,e′π+)n reaction. For selected kinematical condi-

tions this process can be described as quasi-elastic scat-

tering of the electron from a virtual pion in the proton.

In the t-pole approximation the longitudinal cross section

σLis proportional to the square of the pion form factor.

In this way the pion form factor has been studied for Q2

values from 0.4 to 9.8 (GeV/c)2at CEA/Cornell [10] and

for Q2= 0.7 (GeV/c)2at DESY [11]. In the DESY ex-

periment a longitudinal/transverse (L/T) separation was

performed by taking data at two values of the electron

energy. In the experiments done at CEA/Cornell this

was done in a few cases only, and even then the resulting

uncertainties in σLwere so large that the L/T separated

1

Page 2

data were not used. Instead for the actual determination

of the pion form factor σL was calculated by subtract-

ing from the measured (differential) cross section a σT

that was assumed to be proportional to the total virtual

photon cross section. No uncertainty in σTwas included

in this subtraction. This means that existing values of

Fπabove Q2= 0.7 (GeV/c)2are not based on L/T sep-

arated cross sections. This, together with the already

relatively large statistical (and systematic) uncertainties

of those data, precludes a meaningful comparison with

theoretical calculations in that region.

Because of the excellent properties of the electron

beam and experimental setup at CEBAF it is now possi-

ble to determine L/T separated cross sections with high

accuracy and thus to study the pion form factor in the

regime of Q2= 0.5 - 3.0 (GeV/c)2. Using the High Mo-

mentum Spectrometer and the Short Orbit Spectrometer

of Hall C and electron energies between 2.4 and 4.0 GeV,

data for the reaction1H(e,e′π+)n were taken for cen-

tral values of Q2of 0.6, 0.75, 1.0 and 1.6 (GeV/c)2, at a

central value of the invariant mass W of 1.95 GeV.

The cross section for pion electroproduction can be

written as

d3σ

dE′dΩe′dΩπ

= ΓV

d2σ

dtdφ,

(1)

where ΓV is the virtual photon flux factor, φ is the az-

imuthal angle of the outgoing pion with respect to the

electron scattering plane and t is the Mandelstam vari-

able t = (pπ−q)2. The two-fold differential cross section

can be written as

2πd2σ

dtdφ= ǫdσL

dt

+dσT

dt

+

?

2ǫ(ǫ + 1)dσLT

dt

cosφ

+ǫdσTT

dt

cos2φ, (2)

where ǫ is the virtual-photon polarization parameter.

The cross sections σX ≡

dt

The longitudinal cross section σLis dominated by the t-

pole term, which contains Fπ. The φ acceptance of the

experiment allowed the interference terms σLTand σTT

to be determined. Since data were taken at two energies

at every Q2, σLcould be separated from σTby means of

a Rosenbluth separation.

The analysis of the experimental data included the fol-

lowing [12]. Electron identification in the Short Orbit

Spectrometer was done by using the combination of lead

glass calorimeter and gas Cerenkov containing Freon-12

at atmospheric pressure. Pion identification in the High

Momentum Spectrometer was largely done using time

of flight between two scintillating hodoscope arrays. A

small contamination by real electron-proton coincidences

at the highest Q2setting was removed by a single beam-

burst cut on e − π+coincidence time.

t, and the mass of the undetected neutron were recon-

dσX

depend on W, Q2and t.

Then Q2, W,

structed. Cuts on the latter excluded additional pion pro-

duction. Backgrounds from the aluminum target window

and random coincidences were subtracted. Yields were

determined after correcting for tracking efficiency, pion

absorption, local target-density reduction due to beam

heating, and dead times. Cross sections were obtained

from the yields using a detailed Monte Carlo (MC) simu-

lation of the experiment, which included the magnets,

apertures, detector geometries, realistic wire chamber

resolutions, multiple scattering in all materials, recon-

struction matrix elements, pion decay, muon tracking,

and internal and external radiative processes.

Calibrations with the overdetermined1H(e,e′p) reac-

tion were critical in several applications. The beam mo-

mentum and the spectrometer central momenta were de-

termined absolutely to 0.1%, while the incident beam

angle and spectrometer central angles were absolutely

determined to better than 1 mrad. The spectrometer

acceptances were checked by comparison of data to MC

simulations. Finally, the overall absolute cross section

normalization was checked. The calculated yields for e+p

elastics agreed to better than 2% with predictions based

on a parameterization of the world data [13].

In the pion production reaction the experimental ac-

ceptances in W, Q2and t were correlated. In order to

minimize errors resulting from averaging the measured

yields when calculating cross sections at average values

of W, Q2and t, a phenomenological cross section model

[12] was used in the simulation program. In this cross

section model the terms representing the σX of Eqn. (2)

were optimized in an iterative fitting procedure to glob-

ally follow the t− and Q2-dependence of the data. The

dependence of the cross section on W was assumed to

follow the phase space factor (W2− M2

The experimental cross sections can then be calculated

from the measured and simulated yields via the relation

p)−2.

?dσ(¯ W,¯Q2,t)

dt

?

exp

=?Yexp?

?YMC?

?dσ(¯ W,¯Q2,t)

dt

?

MC

. (3)

This was done for five bins in t at the four Q2-values.

Here, ?Y ? indicates that the yields were averaged over the

W and Q2acceptance,¯ W and¯Q2being the acceptance

weighted average values for that t-bin. Even while the

average values of W and Q2differed slightly at high and

low ǫ, the use of Eq. (3) with a MC cross section that

globally reproduces the data allows one to take a common

average (¯ W,¯Q2) value.

A representative example of the cross section as func-

tion of φ is given in Figure 1. The dependence on φ was

used to determine the interference terms σLT and σTT

after which the combination σuns = σT+ ǫσL was ob-

tained at both the high and low electron energy in each

t bin for each Q2point. The statistical uncertainty in

these cross sections ranges from 2 to 5%. Furthermore,

there is a total systematic uncertainty of about 3%, the

2

Page 3

φπ

2π d2σ/(dt dφπ) (µb/(GeV/c)2)

0

π/2

π

3π/22π

Q2 = 1.0 (GeV/c)2

-t = 0.09 - 0.13 (GeV/c)2

θπq = 1.1o - 6.8o

0

5

10

15

FIG. 1.

high and low ǫ (filled and empty circles, resp.). The curves

represent the results of the fits.

φ dependence of

d2σ

dtdφat Q2=1.0 (GeV/c)2for

most important contributions being: simulation of the

detection volume (2%), dependence of the extracted cross

sections on the MC cross section model (typically less

than 2%), target density reduction (1%), pion absorption

(1%), pion decay (1%), and the simulation of radiative

processes (1%) [12]. Since the same acceptances in W

and Q2and the same average values¯ W and¯Q2were

used at both energies, σLand σTcould be extracted via

a Rosenbluth separation.

These cross sections are displayed in Figure 2. The

error bars represent the combined statistical and system-

atic uncertainties. Since the uncertainties that are un-

correlated in the measurements at high and low electron

energies are enlarged by the factor 1/(∆ǫ) in the Rosen-

bluth separation, where ∆ǫ is the difference (typically

0.3) in the photon polarization between the two mea-

surements, the total error bars on σLare typically about

10%.

The experimental data were compared to the results

of a Regge model by Vanderhaeghen, Guidal and Laget

(VGL) [14]. In this model the pion electroproduction

process is described as the exchange of Regge trajecto-

ries for π and ρ like particles. The only free parameters

are the pion form factor and the πργ transition form fac-

tor. The model globally agrees with existing pion photo-

and electroproduction data at values of W above 2 GeV.

The VGL model is compared to the data in Figure 2. The

value of Fπwas adjusted at every Q2to reproduce the σL

data at the lowest value of t. The transverse cross section

σT is underestimated, which can possibly be attributed

to resonance contributions at W = 1.95 GeV that are

not included in the Regge model. Varying the πργ tran-

sition form factor within reasonable bounds changes σT

by up to 30%, but has a negligible influence on σL, which

is completely determined by the π trajectory. This t-

pole dominance was checked by studying the reactions

2H(e,e′π+)nn and2H(e,e′π−)pp, which gave within the

uncertainties a ratio of unity for the longitudinal cross

0

10

20

30

40

00.1 0.2

0

5

10

15

20

25

00.1 0.2

0

10

20

0 0.10.2

Q2=0.60

dσ/dt (µb/(GeV/c)2)

Q2=0.75

Q2=1.00Q2=1.60

-t (GeV/c)2

0

10

00.10.2

FIG. 2.

symbols, resp.)

for L, dashed curve for T). The Q2values are in units of

(GeV/c)2.

Separated cross sections σL and σT (full and open

compared to the Regge model (full curve

sections. Hence the VGL model is still considered to be

a good starting point for determining Fπ.

The comparison with the σLdata shows that the t de-

pendence in the VGL model is less steep than that of the

experimental data. As suggested by the analysis [15] of

older data, where a similar behaviour was observed, we

attributed the discrepancy between the data and VGL to

the presence of a negative background contribution to the

longitudinal cross section, presumably again due to reso-

nances. Since virtually nothing is known about the effect

of these resonances on σL, we proceeded on two paths to

determine a trustworthy value of Fπ. First we fitted the

VGL prediction for σLto the data by adjusting Fπat the

lowest |t| bin, as shown in Fig. 2, where it is assumed to

be most reliable, owing to the dominant t pole behaviour.

However, since there is no reason to believe that the (neg-

ative) background is zero at the lowest −t, the result is

an underestimate for Fπ. Secondly, Fπ was determined

adding a Q2dependent negative background to σL(VGL)

and fitting it together with the value of Fπ. The back-

ground term was taken to be independent of t.

was suggested by looking at the ’missing background’ in

σT, i.e., the difference between the data and VGL for

σT. That background is almost constant or slightly ris-

ing with |t|. Then, assuming that the background in σL

has a similar t-dependence, a constant background leads

to an overestimate of Fπ. Our best estimate for Fπ is

taken as the average of the two results. The model un-

certainty (in relative units) is taken to be the same for

the four Q2points, and equal to one half of the average of

the (relative) differences. The results are listed in Table

I and shown in the form of Q2Fπ in Fig. 3. The error

This

3

Page 4

bars were propagated from the statistical and systematic

uncertainties on the cross section data. The model un-

certainty is displayed as the gray bar. The fact that the

value of Fπat Q2= 0.6 (GeV/c)2is close to the extrap-

olation of the model independent data from [9], and that

the value of the background term is lower at higher W

(see below), gives some confidence in the procedure used

to determine Fπ.

For consistency we have re-analysed the older L/T

separated data at Q2= 0.7 (GeV/c)2and W = 2.19

GeV from DESY [11]. We took the published cross sec-

tions and treated them in the same way as ours. The

background term in σLwas found to be smaller than in

the Jefferson Lab data, presumably because of the larger

value of W of the DESY data, and hence the model un-

certainty is smaller, too. The resulting best value for Fπ,

also shown in Fig. 3, is larger by 12% than the origi-

nal result, which was obtained by using the Born term

model by Gutbrod and Kramer [15]. Here it should be

mentioned that those authors used a phenomenological

t-dependent function, whereas the Regge model by itself

gives a good description of the t-dependence of the (un-

separated) data from Ref. [10].

The data for Fπin the region of Q2up to 1.6 (GeV/c)2

globally follow a monopole form obeying the pion charge

radius [9]. It should be mentioned that the older Bebek

data in this region suggested lower Fπvalues. However,

as mentioned, they did not use L/T separated cross sec-

tions, but took a prescription for σT. Our measured data

for σTindicate that the values used were too high, so that

the values for Fπcame out systematically low.

In Fig. 3 the data are also compared to theoretical

calculations. The model by Maris and Tandy [16] pro-

vides a good description of the data. It is based on the

Bethe-Salpeter equation with dressed quark and gluon

propagators, and includes parameters that were deter-

mined without the use of Fπ data. The data are also

well described by the QCD sum rule plus hard scattering

estimate of Ref. [2]. Other models [5,7] were fitted to the

older Fπ data and therefore underestimate the present

data. Figure 3 also includes the results from perturba-

tive QCD calculations [3].

In summary, new accurate separated cross sections for

the1H(e,e′π+)n reaction have been determined in a kine-

TABLE I.

from the re-analyzed data from Ref. [11]. The total (system-

atic and statistical) experimental uncertainty is given first,

and second the model uncertainty.

Best values for Fπ from the present data and

Q2(GeV/c)2

0.60

0.75

1.00

1.60

0.70

W (GeV)

1.95

1.95

1.95

1.95

2.19

Fπ

0.493 ± 0.022 ± 0.040

0.407 ± 0.031 ± 0.036

0.351 ± 0.018 ± 0.030

0.251 ± 0.016 ± 0.021

0.471 ± 0.032 ± 0.037

Q2 (GeV/c)2

Q2 Fπ (Gev/c)2

Jefferson Lab

DESY [11], re-analyzed

Amendolia et al. [9]

Nesterenko+Radyushkin [2]

Jakob+Kroll [3]

Cardarelli [5]

Ito+Buck+Gross [7]

Maris+Tandy [16]

0

0.2

0.4

0.6

0.8

0123

FIG. 3.

values for Fπ in comparison to the results of several calcu-

lations. The model uncertainty is represented by the gray

area. The (model-independent) data from Ref. [9] are also

shown. A monopole behaviour of the form factor obeying the

measured charge radius is almost identical to the Maris and

Tandy curve.

The Jefferson Laboratory and reanalyzed DESY

matical region where the t-pole process is dominant. Val-

ues for Fπ were extracted from the longitudinal cross

section using a recently developed Regge model. Since

the model does not give a perfect description of the t-

dependence of the data, our results for Fπ contain a

sizeable model uncertainty. Improvements in the theo-

retical description of the1H(e,e′π+)n reaction hopefully

will reduce those. The data globally follow a monopole

form obeying the pion charge radius, and are well above

values predicted by pQCD calculations.

The authors would like to thank Drs. Guidal, Laget

and Vanderhaeghen for stimulating discussions and for

making their computer program available to us. This

work is supported by DOE and NSF (USA), FOM

(Netherlands), NSERC (Canada), KOSEF (South Ko-

rea), and NATO.

[1] H.-N. Li and G. Sterman, Nucl. Phys. B381 (1992) 129

[2] V. A. Nesterenko and A. V. Radyushkin,

Lett. B115 (1982) 410; A.V. Radyushkin, Nucl. Phys.

A532 (1991) 141

[3] R. Jakob and P. Kroll, Phys. Lett. B315 (1993) 463

[4] V.M.Braun,A. Khodjamirian

Phys. Rev. D 61 (2000) 073004

[5] F. Cardarelli et al.,Phys. Lett. B332 (1994) 1;

Phys. Lett. B357 (1995) 267

Phys.

andM.Maul,

4

Page 5

[6] N.G. Stefanis, W. Schroers and H.-Ch. Kim, Phys. Lett.

B449 (1999) 299 and hep-ph/0005218

[7] H. Ito, W. W. Buck and F. Gross, Phys. Rev. C 45 (1992)

1918

[8] P. Maris and C. D. Roberts, Phys. Rev. C 58 (1998) 3659

[9] S. R. Amendolia et al., Nucl. Phys. B277 (1986) 168

[10] C. J. Bebek et al., Phys. Rev. D 17 (1978) 1693

[11] P. Brauel et al., Z. Phys. C3 (1979) 101

[12] J. Volmer, PhD thesis, Vrije Universiteit, Amsterdam

(2000), unpublished

[13] P. E. Bosted, Phys. Rev. C 51 (1995) 409

[14] M. Vanderhaeghen,M.

Phys. Rev. C 57 (1998) 1454; Nucl. Phys. A627 (1997)

645

[15] F. Gutbrod and G. Kramer, Nucl. Phys. B49 (1972) 461

[16] P. Maris and P. C. Tandy, preprint nucl-th/0005015

GuidalandJ.-M.Laget,

5

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