New Measurement of Parity Violation in Elastic Electron-Proton Scattering and Implications for Strange Form Factors

Abstract

We have measured the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from the proton. The result is A = -15.05 +- 0.98(stat) +- 0.56(syst) ppm at the kinematic point theta_lab = 12.3 degrees and Q^2 = 0.477 (GeV/c)^2. The measurement implies that the value for the strange form factor (G_E^s + 0.392 G_M^s) = 0.025 +- 0.020 +- 0.014, where the first error is experimental and the second arises from the uncertainties in electromagnetic form factors. This measurement is the first fixed-target parity violation experiment that used either a `strained' GaAs photocathode to produce highly polarized electrons or a Compton polarimeter to continuously monitor the electron beam polarization. Comment: 8 pages, 4 figures, Tex, elsart.cls; revised version as accepted for Phys. Lett. B

Full text

Page 1

arXiv:nucl-ex/0006002v3 12 Apr 2001
New Measurement of Parity Violation in
Elastic Electron-Proton Scattering and
Implications for Strange Form Factors
K. A. Aniola, D. S. Armstrongah, T. Averettah, M. Baylacaa,
E. Burtinaa, J. Calarcot, G. D. Catesx, C. Cavataaa, Z. Chais,
C. C. Changq, J.-P. Chenℓ, E. Chudakovℓ, E. Cisbanik,
M. Comand, D. Dalen, A. Deurℓ, P. Djawothoah,
M. B. Epsteina, S. Escoffieraa, L. Ewellq, N. Fallettoaa,
J. M. Finnah, A. Flecky, B. Froisaa, S. Frullanik, J. Gaos,
F. Garibaldik, A. Gaspariang, G. M. Gerstnerah, R. Gilmanℓ,z,
A. Glamazdino, J. Gomezℓ, V. Gorbenkoo, O. Hansenℓ,
F. Hersmant, D. W. Higinbothamag, R. Holmesac, M. Holtropt,
B. Humenskyx, S. Incertiad, M. Iodicej, C. W. de Jagerℓ,
J. Jardillieraa, X. Jiangz, M. K. Jonesah, J. Jordaaa,
C. Jutierw, W. Kahlac, J. J. Kellyq, D. H. Kimp, M.-J. Kimp,
M. S. Kimp, I. Kominisx, E. Kooijmanm, K. Kramerah,
K. S. Kumarr,x, M. Kussℓ, J. LeRoseℓ, R. De Leoi,
M. Leuschnert, D. Lhuillieraa, M. Liangℓ, N. Liyanages,
R. Lourieab, R. Madeym, S. Malovz, D. J. Margaziotisa,
F. Marieaa, P. Markowitzℓ, J. Martinoaa, P. Mastromarinox,
K. McCormickw, J. McIntyrez, Z.-E. Mezianiad, R. Michaelsℓ,
B. Milbrathc, G. W. Millerx, J. Mitchellℓ, L. Morande,aa,
D. Neyretaa, G. G. Petratosm, R. Pomatsalyuko, J. S. Priceℓ,
D. Proutm, T. Pussieuxaa, G. Qu´ em´ enerah, R. D. Ransomez,
D. Relyeax, Y. Roblinb, J. Rocheah, G. A. Rutledgeah,
P. M. Ruttℓ, M. Rvachevs, F. Sabatiew, A. Sahaℓ,
P. A. Souderac, M. Spradlinh,x, S. Strauchz, R. Suleimanm,
J. Templonf, T. Teresawaae, J. Thompsonah, R. Tieulentq,
L. Todorw, B. T. Tongucac, P. E. Ulmerw, G. M. Urciuolik,
B. Vlahovicℓ,v, K. Wijesooriyaah, R. Wilsonh,
B. Wojtsekhowskiℓ, R. Wooaf, W. Xus, I. Younusac, C. Zhangq
aCalifornia State University - Los Angeles,Los Angeles, California 90032, USA
Preprint submitted to Physics Letters B 4 February 2008

Page 2

bUniversit´ e Blaise Pascal/IN2P3, F-63177 Aubi` ere, France
cEastern Kentucky University, Richmond, Kentucky 40475, USA
dFlorida International University, Miami, Florida 33199, USA
eUniversit´ e Joseph Fourier, F-38041 Grenoble, France
fUniversity of Georgia, Athens, Georgia 30602, USA
gHampton University, Hampton, Virginia 23668, USA
hHarvard University, Cambridge, Massachusetts 02138, USA
iINFN, Sezione di Bari and University of Bari, I-70126 Bari, Italy
jINFN, Sezione di Roma III, 00146 Roma, Italy
kINFN, Sezione Sanit` a, 00161 Roma, Italy
ℓThomas Jefferson National Accelerator Laboratory, Newport News, Virginia
23606, USA
mKent State University, Kent, Ohio 44242, USA
nUniversity of Kentucky, Lexington, Kentucky 40506, USA
oKharkov Institute of Physics and Technology, Kharkov 310108, Ukraine
pKyungpook National University, Taegu 702-701, Korea
qUniversity of Maryland, College Park, Maryland 20742, USA
rUniversity of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
sMassachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
tUniversity of New Hampshire, Durham, New Hampshire 03824, USA
uNorfolk State University, Norfolk, Virginia 23504, USA
vNorth Carolina Central University, Durham, North Carolina 27707, USA
wOld Dominion University, Norfolk, Virginia 23508, USA
xPrinceton University, Princeton, New Jersey 08544, USA
yUniversity of Regina, Regina, Saskatchewan S4S 0A2, Canada
zRutgers, The State University of New Jersey, Piscataway, New Jersey 08855,
USA
aaCEA Saclay, DAPNIA/SPhN, F-91191 Gif-sur-Yvette, France
abState University of New York at Stony Brook, Stony Brook, New York 11794,
USA
acSyracuse University, Syracuse, New York 13244, USA
adTemple University, Philadelphia, Pennsylvania 19122, USA
aeTohoku University, Sendai 9890, Japan
afTRIUMF, Vancouver, British Columbia V6T 2A3, Canada
agUniversity of Virginia, Charlottesville, Virginia 22901, USA
ahCollege of William and Mary, Williamsburg, Virginia 23187, USA
2

Page 3

Abstract
We have measured the parity-violating electroweak asymmetry in the elastic
scattering of polarized electrons from the proton. The result is A = −15.05 ±
0.98(stat) ±0.56(syst) ppm at the kinematic point ?θlab? = 12.3◦and ?Q2? = 0.477
(GeV/c)2. Both errors are a factor of two smaller than those of the result re-
ported previously. The value for the strange form factor extracted from the data
is (Gs
M) = 0.025 ± 0.020 ± 0.014, where the first error is experimental
and the second arises from the uncertainties in electromagnetic form factors. This
measurement is the first fixed-target parity violation experiment that used either a
“strained” GaAs photocathode to produce highly polarized electrons or a Compton
polarimeter to continuously monitor the electron beam polarization.
E+ 0.392Gs
Key words:
PACS: 13.60.Fz, 11.30.Er, 13.40.Gp, 14.20.Dh
It is well known that strange quarks and antiquarks are present in the nucleon.
An important open question is the role that sea (non-valence) quarks in general
and strange quarks in particular [1] play in the fundamental properties of the
nucleon. For example, do strange quarks contribute to the charge radius or
magnetic moment of the proton? If so, the strange form factors Gs
are relevant. A number of papers have suggested that indeed these form factors
may be large [1–10]. Others models suggest small contributions [11–14].
Eand Gs
M
Strange form factors can be isolated from up and down quark form factors by
measuring the parity-violating asymmetry A = (σR− σL)/(σR+ σL) in the
elastic scattering of polarized electrons from protons [15,16]. The experiments
are challenging since A ≈ A0τ ≈ 10 parts per million (ppm). Here A0 =
(GFM2
decay and Mpis the proton mass. Also τ = Q2/4M2
the four-momentum transfer. Nevertheless, several experiments have recently
published results for A [17–19]. In this letter, we present the most precise
measurement to date for A of the proton and determine new limits for the
possible contribution of strange form factors.
p)/(√2πα) = 316.7 ppm, where GF is the Fermi constant for muon
pwhere Q2is the square of
Measurements of elastic electromagnetic and electroweak nucleon scattering
provide three sets of vector form factors. From this information, the form
factors for each flavor may be determined [20]: Gu
convenient alternate set, which is directly accessible in experimental mea-
surements, is the electromagnetic form factors Gpγ
E,M, Gd
E,M, and Gs
E,M. A
E,M, Gnγ
E,M, plus G0
E,M. Here
Email addresses:
(P. A. Souder).
finn@physics.wm.edu (J. M. Finn), souder@phy.syr.edu
3

Page 4

G0= (Gu+Gd+Gs)/3, Gpγ=2
where the last expression assumes charge symmetry. G0cannot be accessed
in electromagnetic scattering and thus represents new information on nucleon
dynamics that can be accessed only via measurements of the weak neutral
current amplitude.
3Gu−1
3Gd−1
3Gs, and Gnγ=2
3Gd−1
3Gu−1
3Gs,
The theoretical asymmetry in the Standard Model has a convenient form in
terms of G0:
Ath= −A0τρ′
eq
?
2 − 4ˆ κ′
eqsin2θW−
εηp
p+ τµ2
εη2
p
G0
(Gγp
E+ βG0
M/µp)
M
?
− AA
(1)
where µp(µn) ≈ 2.79(−1.91) is the proton(neutron) magnetic moment in nu-
clear magnetons, ηp = ηp(Q2) = Gpγ
τ)tan2θ/2)−1is the longitudinal photon polarization, and β = τµp/(εηp).
The scattering angle of the electron in the laboratory is θ. The contribution
from the proton axial form factor, AA= (0.56 ± 0.23) ppm, is calculated to
be small for our kinematics [21,22]. The recent datum from the SAMPLE
collaboration [23] is 1.5 standard deviations larger than the prediction. [21,22]
E(Q2)/(Gpγ
M(Q2)/µp), ε = (1 + 2(1 +
The parameters ρ′
radiative corrections [24], and sin2θW = 0.2314. If, in addition to G0
proton and neutron electromagnetic form factors Gpγ
the strange form factors may be determined from
eq= 0.9879 and ˆ κ′
eq= 1.0029 include the effect of electroweak
E,M, the
E,Mand Gnγ
E,Mare known,
Gs
E,M= G0
E,M− Gpγ
E,M− Gnγ
E,M. (2)
This experiment took place in Hall A at the Thomas Jefferson National Ac-
celerator Facility. An approximately 35µA beam of 67-76% polarized electrons
with an energy of 3.3 GeV scattered from a 15 cm liquid hydrogen target. Elas-
tic events were detected by integrating the signal in total-absorption counters
located at the focal plane of a pair of high-resolution magnetic spectrome-
ters. [18,25]
It is important that the signal be purely elastic, since background processes
may have large asymmetries. For example, the production of the prominent
∆−resonance is calculated to have 3 times the asymmetry of elastic scat-
tering. [20] To measure the rejection of unwanted events by our system, we
measured the response of the detector, both in counting and integrating mode,
as a function of the mismatch between the spectrometer setting and the mo-
mentum of elastic events. The result, shown in Fig. 1, is that the integrated
response drops many orders of magnitude as the momentum mismatch in-
creases. Based on these data, we determined that only 0.2% of our signal
arises from inelastic background processes. Quasi-elastic scattering from the
4

Page 5

Al target windows contributed 1.5% to the measured signal. The net effect of
all the backgrounds is listed in Table 1.
A new feature of the experiment is that the beam polarization Pe ≈ 70%.
This was achieved by using photoemission by circularly polarized laser light
impinging on a “strained” GaAs crystal. A plot of the polarization versus
time for part of the run is given in Fig. 2. The starred points are from Møller
scattering and the dots are preliminary data from the recently commissioned
Compton polarimeter. The errors in the Møller data have been reduced by a
factor of two from those of Ref. [18] by improving our knowledge of the polar-
ization of the electrons in the magnetized foil target and our understanding
of rate effects in the Møller spectrometer. The Compton device continuously
monitored the polarization of the beam on target and ruled out possible sig-
nificant variations in polarizations between the daily Møller measurements.
Both devices have an overall systematic error ∆Pe/Pe∼ 3.2%.
To study possible systematic errors in our small asymmetry, we sometimes
inserted a second half-wave (λ/2) plate in the laser beam at the source to
reverse the sign of the helicity. Data were obtained in sets of 24-48 hour du-
ration, and the state of the λ/2 plate was reversed for each set. The resulting
asymmetries are shown in Fig. 3a. The asymmetry reverses as expected but
otherwise behaves statistically.
The strained GaAs crystal, in contrast to the bulk GaAs used for our previous
work [18], has a large analyzing power for linearly polarized light. [26] The
consequence was a tendency for much larger helicity-correlated differences in
the beam position. We found that an additional half-wave plate in the laser
beam reduced this problem to a manageable level. In addition, the intensity
asymmetry of the beam in another experiental hall was nulled to prevent beam
loading in the accelerator from inducing position correlations in our beam.
The remaining position and energy differences were measured with precision
microwave monitors. One example of monitor data is shown in Fig. 3b. The
effect of these beam differences on the asymmetry was measured by calibrating
the apparatus with beam correction coils and an energy vernier. The resultant
correction, shown in Fig. 3c, proved to have an average of 0.02 ± 0.02 ppm.
The experimental asymmetry, corrected for the measured beam polarization,
is Aexp= −15.1 at Q2= 0.477 (GeV/c)2for the 1999 data. We also include
the previously reported 1998 data, [18] which gives Aexp= −14.7 ppm when
extrapolated to the same Q2value but with approximately twice the statistical
and systematic errors. In addition, three small corrections based on subsequent
data analysis were made to the 1998 data: i) the background correction was
included; ii) the measured beam polarization was reduced by 1.5%; and iii) the
Q2value was determined to be 0.474 (GeV/c)2instead of 0.479 (GeV/c)2. An
increase of 1% in Q2is expected to increase the magnitude of the asymmetry
5

Page 6

by 1.5%. The errors for the full data set are given in Table 1. Systematic
errors in the beam polarimetry and in the measurement of the spectrometer
angle were the most significant sources. The combined result is Aexp−15.05±
0.98(stat) ± 0.56(syst) ppm at the average kinematics Q2=0.477 (GeV/c)2
and θ = 12.3◦. This is the average asymmetry over the finite solid angle of the
spectrometers; we estimate the value at the center of acceptance is smaller by
0.7%.
By using Eq. 1 and the theoretical value for AA [21,22], we obtain (G0
βG0
tistical, the second systematic, and the last error is due to the uncertainty
from AA. For our kinematics β = 0.392. The sensitivity to ηpis negligible. To
determine the contribution due to strange form factors, we use Eq. 2 and data
for the electromagnetic form factors. The values we use [27–34] are summa-
rized in Table 2. Thus we have Gs
first error is the errors in G0combined in quadrature and the second due to
the electromagnetic form factors. This value is consistent with the hypothesis
that the strange form factors are negligible.
E+
M)/(Gpγ
M/µp) = 1.527 ± 0.048 ± 0.027 ± 0.011. Here the first error is sta-
E+βGs
M= 0.025±0.020±0.014, where the
We note that there are data for Gn
with those of Ref. [29]. Our result for Gs
the data from Ref. [35] were used. New data for both Gn
early stages of analysis and will be important both for validating our choices
and also for interpreting future data on strange form factors.
M[35] that are less precise but at variance
E+ βGs
Mwould increase by 0.020 if
Mand Gn
Eare in the
In Fig. 4, we plot the above value for Gs
in quadrature. The dots represent the predictions from those models that apply
at our value of Q2. Our result restricts significantly the possible “parameter
space” for strangeness to be an important degree of freedom in nucleon form
factors. However, our data are compatible with several models that predict
large strange form factors, including two with Gs
where the prediction happens to cross zero near our Q2value.[5]
E+βGs
Mas a band with the errors added
E≈ −0.39Gs
M, [8,9] and one
Our collaboration has two new experiments approved at JLab for a kinematic
point at Q2∼ 0.1 (GeV/c)2. One, using a hydrogen target, will measure the
same combination of strange form factors at a low Q2[36] and the other, using
a4He target, will be sensitive to Gs
might detect the presence of strange form factors that cannot be excluded by
the present result.
Ebut not Gs
M. [37] Thus these experiments
We wish to thank the entire staff at JLab for their tireless work in devel-
oping this new facility, and particularly C. K. Sinclair and M. Poelker for
their timely work on the polarized source. This work was supported by DOE
contract DE-AC05-84ER40150 under which the Southeastern Universities Re-
search Association (SURA) operates the Thomas Jefferson National Acceler-
6

Page 7

ator Facility and by the Department of Energy, the National Science Foun-
dation, the Korean Science and Engineering Foundation (Korea), the INFN
(Italy), the Natural Sciences and Engineering Research Council of Canada,
the Commissariat ` a l’´Energie Atomique (France), and the Centre National de
Recherche Scientifique (France).
References
[1] P. Geiger and N. Isgur, Phys. Rev. D 55 (1997) 299.
[2] R. L. Jaffe, Phys. Lett. B 229 (1989) 275.
[3] H. -W. Hammer, Ulf-G. Meissner, and D. Drechsel, Phys. Lett. B 367 (1996)
323.
[4] M. J. Musolf and M. Burkhardt, Z. Phys. C 61 (1994) 433.
[5] H. Weigel et al., Phys. Lett. B 353 (1995) 20.
[6] N. W. Park, J. Schecter, and H. Weigel, Phys. Rev. D 43 (1991) 869.
[7] N. W. Park and H. Weigel, Nucl. Phys. A 541 (1992) 453.
[8] S. J. Dong, K. F. Liu, and A. G. Williams, Phys. Rev. D 58 (1998) 074504.
[9] H.-W. Hammer and M. J. Ramsey-Musolf, Phys. Rev. C 60 (1999) 045205.
[10] S-T. Hong, B-Y. Park, and D-P. Min, Phys. Lett. B 414 (1997) 229.
[11] H. Ito, Phys. Rev. C 52 (1995) R1750.
[12] W. Koepf, E. M. Henley, and J. S. Pollock, Phys. Lett. B 288 (1992) 11.
[13] Ulf-G. Meissner, V. Mull, J. Speth, and J. W. Van Orden, Phys. Lett. B 408
(1997) 381.
[14] B.-Q Ma, Phys. Lett. B 408 (1997) 387.
[15] D. B. Kaplan and A. Manohar, Nucl. Phys. B310 (1988) 527.
[16] R. D. McKeown, Phys. Lett. B 219 (1989) 140.
[17] B. Mueller et al., Phys. Rev. Lett. 78 (1997) 3824.
[18] K. Aniol et al., Phys. Rev. Lett. 82 (1999) 1096.
[19] D. T. Spayde et al., Phys. Rev. Lett. 84 (2000) 1106.
[20] M. J. Musolf et al., Phys. Rep. 239, 1 (1994) and references therein.
[21] M. J. Musolf and B. R. Holstein, Phys. Lett. B 242 (1990) 461.
[22] S.-L Zhu et al., Phys. Rev. D 62 (2000) 033008.
7

Page 8

[23] R. Hasty, et al., Science 290 (2000) 2117.
[24] Particle Data Group, C. Caso et al., Eur. Phys. J. C 3 (1998) 1. The electroweak
radiative corrections are essentially the same as for atoms. In addition, the
peaking approximation is used to correct for the radiative tail.
[25] W. E. Kahl, Ph.D. thesis, Syracuse University, 2000; G. W. Miller, Ph.D. thesis,
Princeton University, 2000; see also K. S. Kumar and P. A. Souder. Prog. Part.
Nucl. Phys 45 (2000) S333,
[26] R. A. Mair et al., Phys. Lett. A 212 (1996) 231.
[27] R. C. Walker et al., Phys. Rev. D 49 (1994) 5671.
[28] M. K. Jones et al., Phys. Rev. Lett. 84 (2000) 1398.
[29] H. Anklin et al., Phys. Lett. B 428 (1998) 248.
[30] I. Passchier et al., Phys. Rev. Lett. 82 (1999) 4988.
[31] C. Herberg et al., Eur. Phys. Jour. A 5 (1999) 131.
[32] M. Ostrick et al., Phys. Rev. Lett. 83 (1999) 276.
[33] J. Becker et al., Eur. Phys. Jour. A 6 (1999) 329.
[34] D. Rohe et al., Phys. Rev. Lett. 83 (1999) 4257.
[35] E. E. W. Bruins et al., Phys. Rev. Lett. 75 (1995) 21. We have corrected these
data down by 25% of the difference of these data and those of Ref. [29], based
on a private communication from B. Schoch.
[36] JLab experiment E99-115, K. Kumar and D. Lhuillier, spokespersons.
[37] JLab experiment E00-114, D. Armstrong and R. Michaels, spokespersons.
8

Page 9

Table 1
Summary of corrections and contributions to the errors in % for the measured
asymmetry.
SourceCorrection (%)δA/A(%):1998 δA/A(%):1999
Statistics−
−
−
1.2
13.37.2
Pe
7.0 3.2
Q2
1.81.8
Backgrounds0.6 0.6
Table 2
Electromagnetic form factors normalized to Gp
Athfrom the quoted error in the corresponding form factor.
M/µp. The last column is the error in
Form Factor ValueRef. δAth/Ath
Gp
E/(Gp
M/µp)0.99 ± 0.02
0.16 ± 0.03
1.05 ± 0.02
[27,28]3%
Gn
E/(Gp
M/µp) [30–34]4%
(Gn
M/µn)/(Gp
M/µp) [29]2%
Spectrometer Mismatch (%)
Relative Detected Energy
Counting
Integrating
Fig. 1. Fraction of energy deposited in the detector as a function of spectrometer
mismatch. The inelastic threshold corresponds to a mismatch of about 4.5%, where
the response of the detector is already reduced by a factor of 100.
9

Page 10

Days of data taking
Pe (%)
Fig. 2. Electron beam polarization for part of the run. The statistical errors on the
Møller data are smaller than the points.
a)
Araw(ppm)
b)
nm
Data Set Number
c)
ppm
Fig. 3. a) Raw asymmetry versus data set. Solid(open) circles are from the left(right)
spectrometer. The step pattern is due to the insertion of the half-wave plate. The
χ2= 33.7 for 39 degrees of freedom. b) Helicity-correlated horizontal position dif-
ference measured near the target. c) Correction to left spectrometer data due to all
of the beam parameter differences. The corrections for the right spectrometer are
smaller.
10

Page 11

GM(0.48) s
GE(0.48)
s
(3)
(9)
(9)
(7)
(5)
(8)
Fig. 4. Plot of Gs
region derived from our results. The width of the band is computed by adding
the errors in quadrature. The points are various estimates from models that make
predictions at our value of Q2. The numbers in the brackets are the reference of the
models. Ref. [9] is plotted twice due to an ambiguity in the predicted sign.
Eversus Gs
Mat Q2= 0.477 (GeV/c)2. The band is the allowed
11