Measurement of the transverse spin dependence of the di-jet opening angle in
pp collisions at sqrt{s}=200 GeV has been performed by the STAR collaboration.
An analyzing power consistent with zero has been observed over a broad range in
pseudorapidity sum of the two jets with respect to the polarized beam
direction. A non-zero (Sivers) correlation between transverse momentum
direction of partons in the initial state and transverse spin orientation of
the parent proton has been previously observed in semi-inclusive deep inelastic
scattering (SIDIS).
  The present measurements are much smaller than deduced from predictions made
for STAR di-jets based on non-zero quark Sivers functions deduced from SIDIS,
and furthermore indicate that gluon Sivers asymmetries are comparably small.Comment: 4 pages, 3 figures, talk presented at SPIN 2006, Kyoto, October 200

Balewski, J

Barnby, Lee

Burton, Thomas

Gaillard, Leon

Jones, Peter

Nelson, John

Timmins, Anthony

English

arXiv

J. Balewski

null null

Crossref

Measurement of Sivers Asymmetries for Di-jets in s = 200 GeV pp Collisions at STAR

ar
X
iv
:h
ep
-e
x/
06
12
03
6v
1 
 1
4 
D
ec
 2
00
6
Measurement of Sivers Asymmetries for Di-jets
in
√
s = 200GeV pp Collisions at STAR
J. Balewski for the STAR Collaboration
Indiana University Cyclotron Facility, 2401 Milo B. Sampson Lane, Bloomington, IN, 47408
Abstract. Measurement of the transverse spin dependence of the di-jetopening angle in pp col-
lisions at
√
s = 200 GeV has been performed by the STAR collaboration. An analyzing power
consistent with zero has been observed over a broad range in pseudorapidity sum of the two jets
with respect to the polarized beam direction. A non-zero (Sivers) correlation between transverse
momentum direction of partons in the initial state and transver e spin orientation of the parent pro-
ton has been previously observed in semi-inclusive deep inelastic scattering (SIDIS). The present
measurements are much smaller than deduced from predictions made for STAR di-jets based on
non-zero quark Sivers functions deduced from SIDIS, and furthermore indicate that gluon Sivers
asymmetries are comparably small.
Keywords: pp collisions, RHIC, STAR, di-jet, transverse polarization, single spin asymmetry,
Sivers functions, An, pseudorapidity-dependence
PACS: 12.39, 13.87, 13.88, 24.85
Experimental determination of the contribution from orbital angular momentum of
the proton’s constituents to its spin is difficult. A possible manifestation of orbital
momentum are Sivers correlations [1] between the transverse spin (~ST ) direction of a
polarized proton and transverse momentum (~k⊥) directional preferences of unpolarized
partons carrying longitudinal momentum fractionx of the proton:
1
2
∆N f (x,k⊥)
~P ·
(
~k⊥× ~ST
)
|~P| · |~k⊥| · |~ST |
(1)
where~P is the momentum vector of the polarized proton and∆N f (x,k⊥) is called the
Sivers function.
Recently measurement of a non-zero Sivers function forπ+ in SIDIS has been
reported by the HERMES collaboration [2]. The same group found an asymmetry
consistent with zero forπ−, leading to an interpretation [3] that the Sivers functionsare
opposite in sign and different in magnitude foru vs. d quarks. Boer and Vogelsang [4]
suggested that the Sivers effect would be manifested as a spin-de endent azimuthal
side preference for almost back-to-back di-jets produced in proton collisions involving
transversely polarized beam.
In this paper we report Sivers single spin asymmetry (AN) measurements for di-jet
production in kinematic regions that allow us to distinguish quark from gluon Sivers
functions. We compare our results to predictions [3] derived from SIDIS, in order to
judge the universality of the extracted quark Sivers functions.
EMC Barrel
E
M
C
 E
n
d
ca
p
TPC
η = −1
η =
 +2
+Z beam -Z beam
BBC
East
BBC
West
ox  +x
+y
FIGURE 1. Geometry of the STAR detector.
The di-jet measurement has been performed in the 2006 run using the STAR detec-
tor at RHIC [5]. A 3 week-long run resulted in a sampled luminosity of 1.1 pb−1. Two
polarized beams collided in the center of the STAR detector,as shown in Fig. 1. Elec-
tromagnetic calorimeters (EMC) covering pseudorapidity rangeη ∈ [−1,+2] and full
azimuthal angleφ have been used to trigger on di-jets. A dedicated software trigge
accepted events with two EMC patches covering 0.6×0.6 in ∆η ×∆φ , separated az-
imuthally by at least 60◦, and containing at least 3.3 and 3.6 GeV of transverse energy
(ET ), respectively. Additionally, the hardware trigger required ET ≥ 14 GeV summed
over the whole EMC and a coincidence between 2 forward segmented scintillators
(BBC) placed at 3.3 ≤ |η| ≤ 5.0 on either side of the interaction point. In this analy-
sis we have used the on-line values ofη andφ for both jets obtained fromET -weighted
centroids of the EMC tower locations included in the jet patches. The results reported
here include only those events where both detected jets had EMC ET ≤ 8.0 GeV within
their respective 0.6×0.6 ∆η ×∆φ patch.
The azimuthal correlation between the two jets is shown in Fig. 2a, where back-
to-back di-jets dominate the spectrum. For the Sivers analysis, we define the “signed”
azimuthal di-jet opening angleζ (Fig. 2b), chosen to be> 180◦ whencosφb > 0 and
< 180◦ otherwise, whereφb is the di-jet bisector angle measured with respect to STAR’s
+x-axis (see Fig. 1). The spectrum of averageη1+η22 is shown in Fig. 2c. The most
forward measured di-jets whenη1+η2 > 2 involve preferentially quark (gluon) from
the polarized beam heading toward +z (-z) direction.
The vertical beam spin orientation alternated for each successive bunch of one beam
and each pair of bunches of the other. An integrated SiversAN was extracted for each
beam from spin-sortedζ -spectra using a cross-ratio in which “left” and “right” yields
were deduced fromζ > 180◦ andζ < 180◦, respectively, for the+z beam and the op-
posite assignment was used for the−z beam. On-line values of beam polarization have
been used and a systematic normalization error of±20% is assigned toAN until final
beam polarization values are known. The cross-ratio methoddoes not require indepen-
dent luminosity monitors if the detector has approximatelyequal left-right efficiency, as
is true for this measurement.
The jet direction deduced from its electromagnetic component only can deviate from
the direction of the parent parton due to fragmentation processes and finite detector
1 (deg)φ
0 50 100 150 200 250 300 350
2 
(d
eg
)
φ
0
50
100
150
200
250
300
350
°
2| 
< 
60
 
φ
1 -
 
φ|
a)
 (deg) ζ 
0 50 100 150 200 250 300 350
0
2000
4000
6000
8000 <0Txk >0Txk
b)
2) / 2η1 + η (
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
0
c)
FIGURE 2. Characteristic distribution of events that pass the STAR di-jet trigger: a) azimuthal correla-
tion, b) signed opening angleζ , and c) averaged pseudorapidity, all from trigger-level EMC information
only.
resolution. Simulations with the Pythia 6.205 event generator and full GEANT modeling
of the STAR detector have been used to estimate this azimuthal smearing to beσ ≈ 6.3◦.
This φ -smearing is small compared to the observed overallζ width of ∼ 20◦, driven
by the intrinsick⊥ smearing of the partons inside the proton. However, thisφ -smearing
does cause a dilution of the measuredAN by 10% of the input parton-level asymmetry,
as determined from a toy model simulation.
The toy model assumed a binary parton collision with an initial Gaussian~k⊥ dis-
tribution with added exponential tails. To simulate the Sivers effect it assumed a small
offset in the centroid of the model~k⊥ distribution, in the direction~ST ×~P, using the
randomly assigned spin direction for each beam. Azimuthal directions of the outgoing
partons were smeared with a Gaussian ofσ = 6.3◦ to mimic fragmentation and detec-
tion processes. The toy model parameters were tuned to reproduce the observed jetET -
(from full jet reconstruction including charge-particle tracks) andζ -spectra.
Fig. 3 shows the measured analyzing power for both beams (heading toward±z)
compared to predictions [3] as function ofη1+η2 integrated over the full STAR EMC
η acceptance and for|ζ −180◦| ≤ 68◦. The full analyzed sample yields 2.6×106 di-
jets with averageA±zN values consistent with zero for both beams, within statistical
uncertainties of±0.002. Based on the toy model these results probe a Sivers〈kxT 〉
preference as small as±3 MeV, or ±0.2 % of the inferred rms width of thekx,yT
distributions.
The systematic error bands in Fig. 3 arise from two sources combined in quadrature.
An error of±20% of the statistical uncertainty on each bin allows for multi-jet event
contribution to theζ distribution wings (see Fig. 2b). In addition, we include a model-
dependent uncertainty on the dilution factor (0.9 ±0.05) deduced from the toy model.
The 20% uncertainty on the on-line beam polarization valuesis not included in the error
band.
The predictions [3] in Fig. 3 are based on two models (labeledVY1 and VY2) of
the u andd quark Sivers functions fitted to HERMES SIDIS results [2]. The models
differ in tying the d-quark Sivers function shape to either the u(x) (VY1) or d(x)
(VY2) unpolarized parton distribution function. Both calculations assume zero gluon
)      -z / x+z2    ~    ln(xη1+ηSTAR detector 
-2 -1 0 1 2 3 4
-0.02
-0
0.02
0.04
0.06
0.08
0.1
ST
AR
 P
re
lim
in
ar
y
syst error
STAR data
model VY1
model VY2
 , +z   beam polarizedNA
)      -z / x+z2    ~    ln(xη1+ηSTAR detector 
-2 -1 0 1 2 3 4
-0.02
-0
0.02
0.04
0.06
0.08
0.1
ST
AR
 P
re
lim
in
ar
y
syst error
STAR data
model VY1 
model VY2 
 , -z   beam polarizedNA
FIGURE 3. Comparison of STAR results forA+zN (left) andA
−z
N (right) as function ofη1 +η2 with
predictions [3], based on two models of quark Sivers functions deduced from fits to HERMES SIDS
results [2].
Sivers function. The predictions are integrated over a jetpT range (5-10 GeV/c) well
matched to our measurements, and further over the STAR detector a ceptance within
eachη1+η2 bin. In these calculations, di-jet production was treated like Drell-Yan di-
lepton production, with gauge link factors for initial-state interactions only [3]. We have
reversed the sign of the predictions to adhere to the Madisonconvention used for our
measured asymmetries.
In the regionη1 + η2 ≥ 2, A+zN (A−zN ) preferentially probes quark (gluon) Sivers
functions. The predictedA+zN values in this region reflect the sizable HERMES Sivers
asymmetries, whileA−zN ≃ 0 because gluon Sivers effects have been ignored.
All measured di-jet asymmetries are within two standard deviations of zero, suggest-
ing that both quark and gluon Sivers effects are considerably smaller for di-jet produc-
tion in pp collisions than are the quark Sivers effects inferred from the HERMES results.
The experiment-theory discrepancies in Fig. 3 might reflecta breakdown of pQCD
factorization for the softk⊥ values probed for back-to-back di-jets (nearζ = 180◦). It
remains an open challenge for theory to account simultaneously for the present di-jet
results and for the sizable transverse single-spin asymmetries seen in SIDIS [2] and in
forward pp → π◦X [6].
REFERENCES
1. D. W. Sivers,Phys. Rev. D 41, 83 (1990) andPhys. Rev. D 43, 261 (1991).
2. M. Dienfenthaler [HERMES Collaboration],hep-ex/0507013.
3. W. Vogelsang and F Yuan,Phys. Rev. D 72, 054028 (2005) and private communication.
4. D. Boer and W. Vogelsang,Phys. Rev. D 69, 094025 (2004)
5. K.H. Ackermann,et al. [STAR Collaboration],Nucl. Instrum. Meth. A 499, 624 (2003); M. Beddoet
al., ibid. 725; C.E. Allgoweret al., ibid. 740.
6. J. Adamset al. [STAR Collaboration],Phys. Rev. Lett. 92, 171801 (2004).


University of Birmingham Research Portal