Measurements of Single and Double Spin
Asymmetry in pp Elastic Scattering in the CNI
Region with Polarized Hydrogen Gas Jet Target
H. Okada∗,†, I. Alekseev∗∗, A. Bravar‡, G. Bunce§,¶, S. Dhawan‖,
K.O. Eyser††, R. Gill§, W. Haeberli‡‡, H. Huang§, O. Jinnouchi§§,
Y. Makdishi§, I. Nakagawa¶¶, A. Nass∗∗∗, N. Saito∗,§§, E. Stephenson†††,
D. Sviridia∗∗, T. Wise‡‡, J. Wood§ and A. Zelenski§
∗Kyoto University, Kyoto Japan
†RIKEN, Wako, JAPAN
∗∗Institute for Theoretical and Experimental Physics (ITEP), 117259 Moscow, Russia
‡University of Geneva , 1205 Geneva, Switzerland
§Brookhaven National Laboratory, Upton, NY 11973, USA
¶RIKEN BNL Research Center, Upton, NY 11973, USA
‖Yale University, New Haven, CT 06520, USA
††University of California, Riverside, CA 92521, USA
‡‡University of Wisconsin, Madison, WI 53706, USA
§§KEK, Tukuba, Japan
¶¶RIKEN, Wako, JAPAN
∗∗∗University of Erlangen, 91058 Erlangen, Germany
†††Indiana University Cyclotron Facility, Bloomington, IN 47408, USA
Abstract. Precise measurements of the single spin asymmetry, AN and the double spin asymmetry,
ANN , in proton-proton (pp) elastic scattering in the region of four-momentum transfer squared
0.001 < −t < 0.032 (GeV/c)2 have been performed using a polarized atomic hydrogen gas jet
target and the RHIC polarized proton beam at 24 GeV/c and 100 GeV/c. The polarized gaseous
proton target allowed us to achieve the measurement of ANN in the CNI region for the first time. Our
results of AN and ANN provide significant constraints to determine the magnitude of poorly known
hadronic single and double spin-flip amplitudes at this energy.
Keywords: Elastic scattering, spin, coulomb nuclear interference
PACS: 13.88.+e, 13.85.Dz, 29.27.Pj, 29.27.Hj
Introduction. pp elastic scattering is one of the most fundamental reactions in
particle-nuclear physics and is described in transition amplitudes by use of helicity of
initial and final states. Requiring that the interaction is invariant under space inversion,
time reversal and rotation in spin space, pp scattering in a given spin state is described
in five independent transition amplitudes (φi, i = 1− 5) as functions of the center-of-
mass energy squared, s, and t [1]. The understanding of these amplitudes would provide
crucial guidelines to investigate the reaction mechanism.
Each transition amplitude is described as a sum of the hadronic amplitude (φ hadi ) and
the electro-magnetic amplitude (φ emi ). In the small −t region, φ emi and φ hadi become
similar in strength and interfere with each other. We call this interference the Coulomb
Nuclear Interference (CNI). Thanks to the great successes of QED and the past pre-
http://arxiv.org/abs/0704.1031v1
RHIC proton beam
Forward scattered 
proton
proton target 
recoil proton recoil proton 
measure!measure!
( ) 0Tm2ppt Rp2inout <-=-=
-t (GeV/c)
-310 -210
-0.01
FIGURE 1. Left: Example of "parallel" case, p↑p↑ → pp. Right: εNN , εN and εb at
s = 13.7 GeV as
a function of −t.
cisely measured quantities (ex. magnetic moment), φ emi is precisely described. On the
other hand, φ hadi is not fully described by theory, because the perturbative QCD is not
applicable in the CNI region. By use of the experimental data of total and differen-
tial cross-section of unpolarized pp elastic scattering, we can determine the sum of two
non-spin-flip hadronic amplitudes (φ had+ = φ
3 ) [3]. In order to approach to the
hadronic single and double spin-flip amplitudes (φ had5 and φ
2 ), we measure AN and
ANN in the CNI region. AN is defined by the asymmetry of cross-section with up-down
transverse polarization for one of the protons. Similarly ANN is defined by the asymme-
try of cross-section for parallel and anti-parallel transverse polarization for both of the
protons. The left side of Fig. 1 depicts "parallel" case. We define the scattering plane
from 3-momenta of incident and recoil particles, which is normal to the spin directions.
By use of transition amplitudes, AN is expressed as,
−Im[φ em5 (s, t)φ
+ (s, t)+φ
5 (s, t)φ
+ (s, t)]
|φ+(s, t)|2
. (1)
The first term of Eq. 1 is calculable and has a peak around −t ≃ 0.003 (GeV/c)2 [2]
which is generated by proton’s anomalous magnetic moment. Because the presence of
φ had5 introduces a deviation in shape and magnitude from the first term, a measurement
of AN in the CNI region, therefore, can be a sensitive probe for φ had5 .
ANN is expressed as,
ANN ≈
2|φ had5 (s, t)|
2+Re[(φ+(s, t))∗φ had2 (s, t)]
|φ+(s, t)|2
. (2)
Because the first term is 2nd order of φ had5 and the second term is 1st order of φ
2 , ANN
is sensitive to φ had2 [4]. From a consequence of angular momentum conservation at small
−t and large
s, we use φ had4 ∝ t → 0 for these expressions.
Experiment. Experiment has been performed using a polarized hydrogen gas jet
target and polarized RHIC proton beam at 24 GeV/c (
s = 6.7 GeV) and 100 GeV/c
s = 13.7 GeV). We detect the recoil protons by silicon detectors which are located on
both sides of the target. The details of experimental setup are described in [5, 6].
In the pp elastic scattering process, both forward-scattered particle and recoil particle
are protons and there are no other particles involved nor new particles produced in the
process. Since initial states are well defined, the elastic process can be, in principle,
identified by detecting the recoil particle only. By measuring kinetic energy TR, time of
flight, and recoil angle of recoil particle, we measure the mass of recoil particle and all
the forward scattered rest particles. We collected 4.3 M events at
s = 13.7 GeV and
0.8 M events at
s = 6.7 GeV, respectively. The details of event selection is described
in [5].
The selected event yield is sorted by −t bins, which is obtained measuring the kinetic
energy of the recoil particle: −t = 2mpTR, and spin states. mp is the proton mass. Then
we calculate two types of single spin raw asymmetries, εN for the target spin state and
εb for the beam spin state. We also calculate double spin raw asymmetry, εNN for the
target and beam spin states.
The right side of Fig. 1 displays these raw asymmetries of
s = 13.7 GeV data as a
function of −t in the region 0.001 ≤ −t ≤ 0.035 (GeV/c)2 (0.5 ≤ TR ≤ 17 MeV).
The polarized gaseous proton target allowed us to achieve the measurement in the CNI
region for the first time. In order to cancel out the asymmetries of up-down luminosity,
and detector acceptance, we employed so-called "square root formula" for εN and εb
calculation. On the other hand, εNN needs to be corrected by the luminosity asymmetry.
The target spin flips every 5 minutes and the density of both spin states are the same
and stable during the experimental period (∼ 90 hours). The beam intensity , which is
measured by the wall current monitor [7], varies by bunch (every 106 nsec in 2004)
and fill (every several hours). By accumulating intensity for the experimental period, the
variation is compensated. Therefore the luminosity asymmetry is quite small compared
to statistical error of εNN .
Results and discussions. AN is measured normalizing εN by well measured the target
polarization Pt [6],
. (3)
Utilizing the measured AN , we also measure the beam polarization, Pb = εb/AN 1.
Normalizing εNN by Pt and Pb, ANN is obtained via
ANN =
. (4)
The left and right plots of Fig. 2 display the results of AN and ANN at
s = 6.7 GeV
with filled circles and 13.7 GeV with open circles, respectively. The errors on the data
1 This experimental setup also plays an important role in the RHIC spin program to measure the absolute
beam polarization [8].
-t (GeV/c)
-310 -210
=6.7 GeVs
=13.7 GeVs
 = 6.7 GeVsNo had. func. 
 = 13.7 GeVsNo had. func. 
-t (GeV/c)
-310 -210
-0.06
-0.04
-0.02
=6.7 GeVs
=13.7 GeVs
FIGURE 2. The left and right plots display the results of AN and ANN at
s = 6.7 GeV with filled
circles and 13.7 GeV with open circles, respectively. The errors on the data points are statistical. The
lower bands represents the total systematic errors. The solid and dashed lines in the left plots correspond
to the first term in Eq. 1 for these
s, respectively.
points are statistical. The lower bands represent the total systematic errors. The solid and
dashed lines correspond to the first term in Eq. 1 for these
s, respectively.
AN at
s = 13.7 GeV are consistent with the dashed line (χ2/ndf=13.4/14). On the
other hand, although the accuracy is statistically limited, AN at
s = 6.7 GeV are not
consistent with the solid line (χ2/ndf=35.5/9) and this discrepancy implies the presence
of φ had5 . ANN for these
s have no clear −t dependence and the average values are
consistent with zero within 1.5 σ .
In summary, measurements of AN and ANN provide experimental knowledge to poorly
known φ had5 and φ
2 . The
s dependence of φ had5 is provided by AN results and
the theoretical interpretation is under way [9]. However, there is no comprehensive
understanding of φ had2 and φ
5 yet. Further measurements at different
s are required
to fully describe the behavior of φ had2 and φ
REFERENCES
1. M. Jacob and G.C. Wick , Annals Phys. 7, 404 (1959).
2. N.H. Buttimore et al., Phys. Rev. D 59, 114010 (1999).
3. M.M. Block and R.N. Cahn, Czech. J. Phys. 40, 164-175 (1990).
4. T.L. Trueman, RHIC Spin Note, September 27, (2005), hep-ph/0604153.
5. H. Okada et al., Phys. Lett. B 638, 450 (2006); H. Okada, Doctororal thesis, July (2006);
http://www.star.bnl.gov/∼hiromi/HiromiOkadaThesis.pdf
6. A. Zelenski et al., Nucl. Inst. and Meth. A 536, 248 (2005);
T. Wise et al., Nucl. Inst. and Meth. A 559, 1 (2006).
7. P.R. Cameron et al., Nucl.Instrum.Meth. A345, 226-229 (1994).
8. K.O. Eyser, these proceedings (2006).
9. Private discussion with L. Trueman.
http://arxiv.org/abs/hep-ph/0604153
http://www.star.bnl.gov/~hiromi/HiromiOkadaThesis.pdf

  Precise measurements of the single spin asymmetry, $A_N$ and the double spin
asymmetry, $A_{NN}$, in proton-proton (\textit{pp}) elastic scattering in the
region of four-momentum transfer squared $0.001 < -t < 0.032 ({\rm GeV}/c)^2$
have been performed using a polarized atomic hydrogen gas jet target and the
RHIC polarized proton beam at 24 GeV/$c$ and 100 GeV/$c$. The polarized gaseous
proton target allowed us to achieve the measurement of $A_{NN}$ in the CNI
region for the first time. Our results of $A_N$ and $A_{NN}$ provide
significant constraints to determine the magnitude of poorly known hadronic
single and double spin-flip amplitudes at this energy.

Introduction. pp elastic scattering is one of the most fundamental reactions in
particle-nuclear physics and is described in transition amplitudes by use of helicity of
initial and final states. Requiring that the interaction is invariant under space inversion,
time reversal and rotation in spin space, pp scattering in a given spin state is described
in five independent transition amplitudes (φi, i = 1− 5) as functions of the center-of-
mass energy squared, s, and t [1]. The understanding of these amplitudes would provide
crucial guidelines to investigate the reaction mechanism.
Each transition amplitude is described as a sum of the hadronic amplitude (φ hadi ) and
the electro-magnetic amplitude (φ emi ). In the small −t region, φ emi and φ hadi become
similar in strength and interfere with each other. We call this interference the Coulomb
Nuclear Interference (CNI). Thanks to the great successes of QED and the past pre-
http://arxiv.org/abs/0704.1031v1
RHIC proton beam
Forward scattered 
proton
proton target 
recoil proton recoil proton 
measure!measure!
( ) 0Tm2ppt Rp2inout <-=-=
-t (GeV/c)
-310 -210
-0.01
FIGURE 1. Left: Example of "parallel" case, p↑p↑ → pp. Right: εNN , εN and εb at
s = 13.7 GeV as
a function of −t.
cisely measured quantities (ex. magnetic moment), φ emi is precisely described. On the
other hand, φ hadi is not fully described by theory, because the perturbative QCD is not
applicable in the CNI region. By use of the experimental data of total and differen-
tial cross-section of unpolarized pp elastic scattering, we can determine the sum of two
non-spin-flip hadronic amplitudes (φ had+ = φ
3 ) [3]. In order to approach to the
hadronic single and double spin-flip amplitudes (φ had5 and φ
2 ), we measure AN and
ANN in the CNI region. AN is defined by the asymmetry of cross-section with up-down
transverse polarization for one of the protons. Similarly ANN is defined by the asymme-
try of cross-section for parallel and anti-parallel transverse polarization for both of the
protons. The left side of Fig. 1 depicts "parallel" case. We define the scattering plane
from 3-momenta of incident and recoil particles, which is normal to the spin directions.
By use of transition amplitudes, AN is expressed as,
−Im[φ em5 (s, t)φ
+ (s, t)+φ
5 (s, t)φ
+ (s, t)]
|φ+(s, t)|2
. (1)
The first term of Eq. 1 is calculable and has a peak around −t ≃ 0.003 (GeV/c)2 [2]
which is generated by proton’s anomalous magnetic moment. Because the presence of
φ had5 introduces a deviation in shape and magnitude from the first term, a measurement
of AN in the CNI region, therefore, can be a sensitive probe for φ had5 .
ANN is expressed as,
ANN ≈
2|φ had5 (s, t)|
2+Re[(φ+(s, t))∗φ had2 (s, t)]
|φ+(s, t)|2
. (2)
Because the first term is 2nd order of φ had5 and the second term is 1st order of φ
2 , ANN
is sensitive to φ had2 [4]. From a consequence of angular momentum conservation at small
−t and large
s, we use φ had4 ∝ t → 0 for these expressions.
Experiment. Experiment has been performed using a polarized hydrogen gas jet
target and polarized RHIC proton beam at 24 GeV/c (
s = 6.7 GeV) and 100 GeV/c
s = 13.7 GeV). We detect the recoil protons by silicon detectors which are located on
both sides of the target. The details of experimental setup are described in [5, 6].
In the pp elastic scattering process, both forward-scattered particle and recoil particle
are protons and there are no other particles involved nor new particles produced in the
process. Since initial states are well defined, the elastic process can be, in principle,
identified by detecting the recoil particle only. By measuring kinetic energy TR, time of
flight, and recoil angle of recoil particle, we measure the mass of recoil particle and all
the forward scattered rest particles. We collected 4.3 M events at
s = 13.7 GeV and
0.8 M events at
s = 6.7 GeV, respectively. The details of event selection is described
in [5].
The selected event yield is sorted by −t bins, which is obtained measuring the kinetic
energy of the recoil particle: −t = 2mpTR, and spin states. mp is the proton mass. Then
we calculate two types of single spin raw asymmetries, εN for the target spin state and
εb for the beam spin state. We also calculate double spin raw asymmetry, εNN for the
target and beam spin states.
The right side of Fig. 1 displays these raw asymmetries of
s = 13.7 GeV data as a
function of −t in the region 0.001 ≤ −t ≤ 0.035 (GeV/c)2 (0.5 ≤ TR ≤ 17 MeV).
The polarized gaseous proton target allowed us to achieve the measurement in the CNI
region for the first time. In order to cancel out the asymmetries of up-down luminosity,
and detector acceptance, we employed so-called "square root formula" for εN and εb
calculation. On the other hand, εNN needs to be corrected by the luminosity asymmetry.
The target spin flips every 5 minutes and the density of both spin states are the same
and stable during the experimental period (∼ 90 hours). The beam intensity , which is
measured by the wall current monitor [7], varies by bunch (every 106 nsec in 2004)
and fill (every several hours). By accumulating intensity for the experimental period, the
variation is compensated. Therefore the luminosity asymmetry is quite small compared
to statistical error of εNN .
Results and discussions. AN is measured normalizing εN by well measured the target
polarization Pt [6],
. (3)
Utilizing the measured AN , we also measure the beam polarization, Pb = εb/AN 1.
Normalizing εNN by Pt and Pb, ANN is obtained via
ANN =
. (4)
The left and right plots of Fig. 2 display the results of AN and ANN at
s = 6.7 GeV
with filled circles and 13.7 GeV with open circles, respectively. The errors on the data
1 This experimental setup also plays an important role in the RHIC spin program to measure the absolute
beam polarization [8].
-t (GeV/c)
-310 -210
=6.7 GeVs
=13.7 GeVs
 = 6.7 GeVsNo had. func. 
 = 13.7 GeVsNo had. func. 
-t (GeV/c)
-310 -210
-0.06
-0.04
-0.02
=6.7 GeVs
=13.7 GeVs
FIGURE 2. The left and right plots display the results of AN and ANN at
s = 6.7 GeV with filled
circles and 13.7 GeV with open circles, respectively. The errors on the data points are statistical. The
lower bands represents the total systematic errors. The solid and dashed lines in the left plots correspond
to the first term in Eq. 1 for these
s, respectively.
points are statistical. The lower bands represent the total systematic errors. The solid and
dashed lines correspond to the first term in Eq. 1 for these
s, respectively.
AN at
s = 13.7 GeV are consistent with the dashed line (χ2/ndf=13.4/14). On the
other hand, although the accuracy is statistically limited, AN at
s = 6.7 GeV are not
consistent with the solid line (χ2/ndf=35.5/9) and this discrepancy implies the presence
of φ had5 . ANN for these
s have no clear −t dependence and the average values are
consistent with zero within 1.5 σ .
In summary, measurements of AN and ANN provide experimental knowledge to poorly
known φ had5 and φ
2 . The
s dependence of φ had5 is provided by AN results and
the theoretical interpretation is under way [9]. However, there is no comprehensive
understanding of φ had2 and φ
5 yet. Further measurements at different
s are required
to fully describe the behavior of φ had2 and φ
REFERENCES
1. M. Jacob and G.C. Wick , Annals Phys. 7, 404 (1959).
2. N.H. Buttimore et al., Phys. Rev. D 59, 114010 (1999).
3. M.M. Block and R.N. Cahn, Czech. J. Phys. 40, 164-175 (1990).
4. T.L. Trueman, RHIC Spin Note, September 27, (2005), hep-ph/0604153.
5. H. Okada et al., Phys. Lett. B 638, 450 (2006); H. Okada, Doctororal thesis, July (2006);
http://www.star.bnl.gov/∼hiromi/HiromiOkadaThesis.pdf
6. A. Zelenski et al., Nucl. Inst. and Meth. A 536, 248 (2005);
T. Wise et al., Nucl. Inst. and Meth. A 559, 1 (2006).
7. P.R. Cameron et al., Nucl.Instrum.Meth. A345, 226-229 (1994).
8. K.O. Eyser, these proceedings (2006).
9. Private discussion with L. Trueman.
http://arxiv.org/abs/hep-ph/0604153
http://www.star.bnl.gov/~hiromi/HiromiOkadaThesis.pdf
