Neutral Pion Measurements from PHENIX in
Polarized Proton Collisions at RHIC
B. Fox for the PHENIX Collaboration1
RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973-5000, USA
Abstract. This report presents the preliminary result for the absolute neutral pion (π Æ ) production
cross section at s 200 GeV for η 050 which was obtained from the proton-proton data
collected by the PHENIX experiment in January, 2002 as a part of Run02 at Relativistic Heavy Ion
Collider (RHIC). We compare this result to the prediction of a next-to-leading order perturbative
QCD calculation and find good agreement. Since the beams were transversely polarized, these data
will be used to measure the single-spin transverse asymmetry (A N ). So, we also discuss the statistical
precision for such a measurement. In future runs, the gluon polarization (∆GG) will be probed by
measuring double-spin longitudinal asymmetries (A LL ). We present an estimate for the statistical
precision which is expected for the neutral pion measurement in the upcoming run and compare it
to predictions from pQCD calculations using different polarized gluon densities.
INTRODUCTION
A detailed understanding of hadron production in proton-proton collisions is essential
to both the heavy-ion and spin physics programs at the Relativistic Heavy Ion Collider
(RHIC). For the heavy-ion program, proton-proton data provide the reference to which
hadron production in heavy-ion collisions can be compared so that novel phenomena,
such as jet energy loss or suppression, can be delineated from more prosaic effects. In the
spin physics program, hadron production is a key probe of transverse and longitudinal
spin structure functions and thus an understanding of the unpolarized cross section
with next-to-leading order (NLO) perturbative QCD (pQCD) calculations provides the
theoretical underpinnings for the physics interpretation of the polarized data.
During the 2001/02 run, RHIC was successfully operated for the first time as a
proton collider at a center of mass energy ( s) of 200 GeV with transversely polarized
beams.[1] From the data collected by the PHENIX experiment [2], we report the spinaveraged neutral pion (π Æ ) cross section measurement at mid-rapidity and compare it
with a next-to-leading order (NLO) perturbative QCD calculation [3, 4].
From this data sample, we also anticipate extracting a measurement of the single
spin transverse asymmetry (AN ) for neutral pions produced at xF 0 with pt up to
8 GeVc. Interest in this measurement arises from the observation of large ( 30%)
asymmetries in pp π X at forward angles by the Fermilab E704 experiment [5, 6] at
s 194 GeV and single-spin azimuthal asymmetries in semi-inclusive deep-inelastic
1 For the full PHENIX Collaboration author list and acknowledgments, see Appendix “Collaborations”
of this volume.
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
412
scattering by the HERMES experiment at DESY [7]. Such large asymmetries were
surprising because, at leading order, pQCD predicted only small effects. Presently, it is
recognized that it is possible to have large asymmetries due to for example, the Sivers’s
effect [8], the Collin’s effect [9], twist-three contributions [10] or combinations of the
three. We report on the projected statistical precision of the measurement at PHENIX
and compare it to that of the E704 measurement and a prediction of the Qiu-Sterman
twist-three calculation.
During the upcoming run in 2003, the protons will be longitudinally polarized so
that the gluon polarization (∆G) can be probed by measuring double-spin, longitudinal
asymmetries (ALL ). Since the acceptance of the PHENIX detector is limited, we intend
to measure the asymmetry for neutral pions as an alternative to jets. We report on the
anticipated statistical precision of the forthcoming dataset and compare it with pQCD
predictions for the asymmetry performed with different gluon polarization densities.
EXPERIMENTAL SETUP
In Run-02, the PHENIX experiment operated with two central arm spectrometers, one
muon arm spectrometer, and other detectors for triggering. This work utilized the electromagnetic calorimeters (EMCal) in the central arms, each of which has an azimuthal
coverage of 90Æ and a pseudo-rapidity coverage of 035. This detector consists of six
lead scintillator sampling calorimeter (PbSc) sectors and two lead glass (PbGl) sectors.
In this paper, we will report only the measurement done with five of the six PbSc sectors.
These sectors have nominal energy and position resolutions of 82% E GeV 19%
and 57 mm E GeV 16 mm, respectively.
During the proton-proton run in 2001-2002, PHENIX recorded an integrated luminosity of 015 pb1 . For the central arm, these data were collected by using two triggers:
the minimum bias (MB) trigger and the newly installed electromagnetic calorimeter
(EMCal) triggers. The MB trigger was formed by applying a loose ( 75 cm) cut to the
interaction position reconstructed with timing information from the beam-beam counters which detect charged particles in the pseudo-rapidity range of 3.0 to 3.9. Events
collected with this trigger covered the pt range up to 5 GeVc. The sample at high pt
was collected with a coincidence between the MB trigger and one of the EMCal triggers. The latter consisted of two types: a 2x2 non-overlapping tower sum trigger with an
0.8 GeV threshold and several 4x4 overlapping tower sum triggers with thresholds ranging from 2 to 3 GeV. For this work, the 2x2 trigger, which had a rejection factor of 90,
provided the data at higher pt . Data collected with 4x4 triggers were used for systematic
studies. In the analysis, a more stringent cut of 30 cm was imposed on the interaction
vertex position.
ANALYSIS PROCEDURE
The cross section is the ratio of the yield of neutral pions after being corrected for
efficiency, acceptance, and smearing ( π Æ ) to the effective integrated luminosity ( )
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where, for the MB sample, these two quantities are computed according to:
reco
π Nπ pεt Cpπ pt Æ
Æ
Æ
πÆ
t
ε MB
trig
pp
MB
σ Ntrig
1
with: Nπ Æ pt is the raw yield of π Æ ’s, Cπreco
Æ pt is the reconstruction efficiency, smearing, and acceptance correction, επ Æ pt is the correction for the bias imposed on the
event geometry by the MB trigger requirement, σ pp is the proton-proton inelastic cross
MB is the efficiency of the MB trigger, and N MB is the number of observed
section, εtrig
trig
MB triggers. For the 2x2 trigger sample, the π Æ yield was also corrected for the trigger
efficiency and the luminosity was corrected for the prescale factors.
The raw yield of neutral pions in each pt bin [Nπ Æ pt ] was determined from the
invariant mass distribution for two photon clusters. To extract these quantities, the
spectrum for each bin was fit over a variety of ranges with a gaussian for the π Æ peak
and several functions – including a gaussian and some order of polynomial – for the
combinatorial background. The systematic error was estimated from the variation in
these fits and the run-to-run stability of the yield.
The acceptance,2 efficiency, and smearing correction [Cπreco
Æ pt ] was computed from
a Monte Carlo simulation of the calorimeter which had been tuned using results from
the test beam measurements[11] and the analyzed data itself. The pt dependences of the
mass and the width of the π Æ peak are very sensitive to the calorimeter calibration and
performance parameters. So, the systematic error in the correction factor was estimated
from the change in it as the parameters in the Monte Carlo were varied over the range
for which the peak’s mass and width in the simulation was consistent with that in data
up to pt 9 GeVc, the maximum value for which these quantities could be determined
with precision.
TABLE 1. Summary of the pt dependent systematic error; there is also a normalization error of 30% not noted here since it is independent of p t .
Correction Term
Source
Estimate
Nπ Æ
Background subtraction
Hot/Warm towers
Run dependence
5%
2-3%
10%(MB) 6%(2x2)
Fast MC statistical error
Edge towers
Position resolution
Energy absolute calibration
Energy non-linearity
Energy resolution
1%
5%
0-1%
3-8%
0-10%
3%
2x2 high pt trigger threshold
10%
Cπreco
Æ pt 2
επ2
Æ pt π and η 05 by assuming
The result is corrected from φ π 2 and η 035 of the detector to φ
the cross section has no φ and η dependences at mid-rapidity.
2
414
2
E*d σ/dp (mb/GeV )
2
E*d σ/dp (mb/GeV )
PHENIX 200GeV π0(MB)
10
PHENIX 200GeV π0(2x2)
10
10
10
10
10
10
Sys. Err.(%)
10
-1
PRELIMINARY
1
3
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
10
-9
10
30% normalization error is not shown
20
10
0
Sys. Err.(%)
3
10
PHENIX 200GeV p+p→π0+X
PRELIMINARY
3
3
1
10
10
pT dependent systematic error
2
4
6
8
10
12
14
p T(GeV/c)
NLO pQCD
-1
F. Aversa et.al. NPB327(1989)105
CTEQ5M pdf/PKK frag
Scales: µ=p T/2, p T, 2pT
-2
-3
-4
-5
-6
-7
-8
-9
30% normalization error is not shown
20
10
0
pT dependent systematic error
2
4
6
8
10
12
14
p T(GeV/c)
FIGURE 1. [left] The inclusive neutral pion cross section for the MB (open circle) and the 2x2 (solid
triangles) trigger samples. [right] a comparison of the combined measurement with an NLO pQCD
calculation using pt 2 (top line), pt (middle line), and 2p t (bottom line) renormalization and factorization
scales. The pt dependent systematic error of the data is shown in the lower box of each panel.
Using the MB dataset, the π Æ threshold curve in pt determined for the 2x2 trigger
and found to plateau at 80% above a pt of 3 GeVc. A systematic error of 10% was
assigned to this quantity based upon a comparison between this threshold curve and that
determined with the Monte Carlo simulation to which the trigger performance had been
included by using the measured efficiencies for the tiles that formed the trigger.
The bias for π Æ detection arising from the MB trigger condition [ε πMB
Æ pt ] was
measured to be 75%, independent of pt up to 5 GeVc, by using the data sample
collected with a 4x4 trigger which, unlike the 2x2 trigger, did not impose the MB
requirement. This value was consistent with an estimate from a PYTHIA+GEANT
simulation of the experiment and thus also used to correct the data at higher p t .
MB ] of 51% was obtained from a PYTHIA+GEANT
The MB trigger efficiency [εtrig
simulation of the experiment. Presently, we have assigned a normalization error of
30% based on the difference between the cross section measurement from a van der
Meer/vernier scan and the total (elastic+inelastic) p p cross section. We anticipate that
this error will be reduced to 15% with further analysis.
415
FIGURE 2. [left] The expected precision for a measurement of the single-spin transverse asymmetry
(AN ) (points) in comparison to the precision of the E704 measurement (dashed line) and a prediction from
the Qiu-Sterman model (solid line). [right] The anticipated precision for a measurement of the double-spin
longitudinal asymmetry (A LL ) (points) from Run-3 data in comparison with predictions from NLO pQCD
calculations using two polarized gluon densities (dashed and solid lines).
RESULTS AND DISCUSSION
The left panel of Figure 1 shows the measured cross sections for the MB and the
2x2 trigger samples along with the pt dependent systematic error which are separately
tabulated in Table 1. The results from the two samples are consistent within the error. In
the right panel of this figure, this result is compared with an NLO pQCD calculation[3]
using the formalism of F. Adversa et al.[4] with the CTEQ5M parton distribution
functions[14] and the PKK fragmentation functions[15]. The data for the lower pt
range is shown from the MB trigger samples to avoid the larger systematic error of
the 2x2 trigger samples. Over the full pt range, this calculation is consistent with our
measurement within the systematic errors. This measurement provides a baseline for
high pt heavy-ion physics[17].
FUTURE MEASUREMENTS
Since the protons were transversely polarized with, on average, 14% polarization in
one beam and 17% in the other (as measured by the RHIC CNI polarimeters [16]), we
anticipate making a measurement of AN . The left panel of Figure 2 shows the statistical
precision of such a measurement in comparison to the precision of the E704 result and
416
a prediction based upon the Qiu-Sterman twist-three calculation. 3[10]
In the upcoming run, we expect higher polarization ( 40%) and an integrated luminosity of at least 3 pb 1 . In the right panel of Figure 2, the anticipated precision for
the measurement of the double-spin, longitudinal asymmetry from this dataset assuming
that we achieve the minimal of the expected performance in the collider. This precision
is compared with predictions from NLO pQCD calculations using two polarized gluon
densities.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
H. Huang, these proceedings.
J. T. Mitchell et al., Nucl. Instrum. Meth. A482 491 (2002).
Private communication with W. Vogelsang.
F. Aversa, P. Chiappetta, M. Greco and J.-Ph. Guillet, Nucl. Phys. B327, 105 (1989).
D. L. Adams, et al., Phys. Lett. B264, 462-466 (1991).
D. L. Adams et al., Phys. Rev. D53, 4747-4755 (1996).
A. Airapetian et al, Phys. Rev. Lett. 84 4047-4051 (2000).
D. W. Sivers, Phys. Rev. D41 83 (1990).
J. C. Collins, Nucl. Phys. B396 161-182 (1993).
J. W. Qiu and G. Sterman, Phys. Rev. D59 014004 (1999).
G. David, et al., IEEE Trans. Nucl. Sci. 42 (1995) 306; G. David, et al., IEEE Trans. Nucl. Sci.45
(1998) 705; G. David, et al., IEEE Trans. Nucl. Sci. 47 (2000) 1982; references therein.
C. Albajar et al., Nucl. Phys. B335 261 (1990).
B. Alper et al., Nucl. Phys. B100 237 (1975).
H. L. Lai et al. (CTEQ5), Eur. Phys. Jour. C12 375(2000).
B. A. Kniehl, G. Kramer and B. Potter, Nucl. Phys. B582 514 (2000).
O. Jinnouchi, these proceedings.
D. G. d’Enterria et al. (PHENIX), Proceedings for the XVI International Conference on Ultrarelativistic Nucleus-Nucleus Collisions, in press.
It should be noted that the formalism of Qiu and Sterman is applicable to the high x F ( 05) regime
whereas, in our measurement, we are probing the x F 0 regime.
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