arXiv:hep-ex/0308001v1 31 Jul 2003
J/ψ Polarization in 800-GeV p−Cu Interactions
T.H. Chang,7, ∗M.E. Beddo,7C.N. Brown,3T.A. Carey,6W.E. Cooper,3C.A. Gagliardi,9G.T. Garvey,6
D.F. Geesaman,2E.A. Hawker,9,6, †X.C. He,4L.D. Isenhower,1D.M. Kaplan,5S.B. Kaufman,2
D.D. Koetke,10P.L. McGaughey,6W.M. Lee,4, ‡M.J. Leitch,6J.M. Moss,6B.A. Mueller,2
V. Papavassiliou,7J.C. Peng,6, ∗P.E. Reimer,6,2M.E. Sadler,1W.E. Sondheim,6P.W. Stankus,8
R.S. Towell,1,6R.E. Tribble,9M.A. Vasiliev,9, §J.C. Webb,7, ¶J.L. Willis,1and G.R. Young8
(FNAL E866/NuSea Collaboration)
1Abilene Christian University, Abilene, TX 79699
2Argonne National Laboratory, Argonne, IL 60439
3Fermi National Accelerator Laboratory, Batavia, IL 60510
4Georgia State University, Atlanta, GA 30303
5Illinois Institute of Technology, Chicago, IL 60616
6Los Alamos National Laboratory, Los Alamos, NM 87545
7New Mexico State University, Las Cruces, NM, 88003
8Oak Ridge National Laboratory, Oak Ridge, TN 37831
9Texas A&M University, College Station, TX 77843
10Valparaiso University, Valparaiso, IN 46383
(Dated: February 4, 2008)
We present measurements of the polarization of the J/ψ produced in 800-GeV proton interactions
with a copper target. Polarization of the J/ψ is sensitive to the cc production and hadronization
processes. A longitudinal polarization is observed at large xF, while at small xF the state is produced
essentially unpolarized or slightly transversely polarized. No significant variation of the polarization
is observed versus pT.
PACS numbers: 13.88.+e, 14.40.Nd
A detailed understanding of the production mecha-
nism of charmonium is important for ongoing research at
the Relativistic Heavy Ion Collider, where this process
can play an important role in the search for quark-gluon
plasma formation , as well as for the investigation of
the gluon contribution to the proton spin structure [2, 3].
In the non-relativistic QCD formalism (NRQCD), char-
monium polarization can probe  details of the produc-
tion process  that are perturbatively calculable.
NRQCD is an effective field theory that approximates
the full QCD Lagrangian for large quark masses. Un-
calculable matrix elements for the production of various
Fock-space components of the quarkonium wavefunction
are ranked, using simple scaling rules, according to their
order in v, the relative quark-antiquark velocity in the
quarkonium rest frame; for charmonium, this has a value
of ∼ 0.5. The leading matrix elements can then be ex-
tracted from fits to experimental data and used in calcu-
lating other processes.
A determination  of the various matrix elements
from available high-energy data defines to a large ex-
tent the expected production properties of charmonium,
one of which is the polarization.
cle, given the fraction ξ of particles produced in the
jz = 0 (“longitudinal”) state, we can define the polar-
ization λ = (1 − 3ξ)/(1 + ξ); λ is positive (negative) for
transverse (longitudinal) polarization. While several of
the intermediate cc states are color-octet states and must
be followed by multiple gluon emission before a physical
For a spin-1 parti-
charmonium state is produced, heavy-quark symmetry
implies that gluon radiation leaves the quark spins un-
changed, providing definite predictions for the spin state
of the final charmonium .
The polarization of the J/ψ has been measured with
relatively high statistical precision only in fixed-target
experiments, in pion  and proton [8, 9] interactions
with solid nuclear targets. No significant polarization has
been seen in either, with the exception of an intriguing
large longitudinal polarization at the highest xF value of
the pion-induced data. Measurements in collider exper-
iments, at energies and transverse momenta where the-
oretical calculations should be more robust and which
are free of potential complications from nuclear effects,
suffer from low statistics . Finally, in a recent study
of fixed-target bottomonium production , the Υ(1S)
was found to be largely unpolarized, while the Υ(2S,3S)
states had strong transverse polarization.
In this experiment, we accumulated  a much larger
sample — approximately 9 million — of reconstructed
J/ψ than any previous study, in interactions of an 800-
GeV/c proton beam with a copper target. J/ψ decays
were measured using the Fermilab Meson-East dimuon
spectrometer , which consisted of three dipole mag-
nets, SM0, SM12, and SM3, and three stations of drift
chambers and trigger scintillator hodoscopes. Data were
collected during a month-long dedicated run in which
the copper beam dump inside SM12 was used in place
of a target; the first dipole was switched off during this
run. A copper absorber filtered out all hadrons and elec-
trons produced in the interactions, allowing only muons
to enter the spectrometer.
tion was obtained using a muon identifier, consisting of
proportional tubes and scintillator hodoscopes behind a
thick absorber at the downstream end of the apparatus.
Events were recorded when the trigger condition of two
oppositely-charged muons was satisfied.
Events were reconstructed offline from the recorded
hits in the drift chambers.
through the magnetic fields to the dump/target, where
a vertex was formed, consistent with the beam position.
Energy losses and multiple Coulomb scattering in the
absorber and the dump were taken into account in the
traceback. The momentum of the muons was determined
by their bending in SM3 and this was used to calculate
their trajectories in SM12.
The invariant mass of the muon pair was calculated
from the muon momenta and opening angle at the vertex.
Since the energy loss and multiple scattering are only
known on average and not on an event-by-event basis,
the mass resolution, typically ≈ 500 MeV (FWHM), was
not sufficient to separate the J/ψ and ψ′peaks in this run
using this extended target. While the two charmonium
states cannot be separated, it is estimated that the ψ′
contributes only about 1% to the total event count, based
on the relative production cross sections and branching
ratios into muons. Therefore, the ψ′is not considered in
the following discussion.
The mass distributions were plotted in bins in the
Feynman-x variable xF, transverse momentum pT, and
the dimuon polar angle ϑ in the dimuon rest frame. We
use the Collins-Soper frame . This is identical to the
Gottfried-Jackson frame , used in several earlier ex-
periments, for pT= 0, and to a very good approximation
equivalent even at the highest pT values in this experi-
The invariant mass distribution in each (xF,pT)-bin
were fitted to a Gaussian peak plus an exponential or
polynomial background. All of the parameters, including
the mass, were determined by the fit. The number of
events under the peak gave the combined J/ψ and ψ′
triple-differential, unnormalized cross section in xF, pT,
and ϑ. Distributions as a function of ϑ were then formed
in each xF and pT bin.
The spectrometer and trigger acceptance was calcu-
lated with the help of a Monte Carlo simulation of the
J/ψ production process, which included all the measured
magnetic fields and detector efficiencies and geometry.
The known properties of J/ψ production from previous
experiments were used.However, because of the bin-
ning in xF and pT, exact knowledge of the form of the
cross section as a function of these two variables was
not crucial. Events were generated with a flat ϑ distri-
bution, corresponding to unpolarized production. Simu-
lated data were passed through the same analysis chain
Additional hadron rejec-
Tracks were traced back
as the real data. The Monte Carlo reproduced quite ac-
curately the main features of the data, including the mass
and vertex resolutions.
The azimuthal-angle (φ) dependence of the produc-
tion cross section was assumed to be flat in the Monte
Carlo, since the two interacting hadrons were unpolar-
ized. The corresponding measured acceptance-corrected
distribution was essentially flat, consistent with a 2% un-
certainty in the direction of the incoming beam. The
decay distribution was also assumed to be flat in φ, con-
sistent with previous results . No attempt was made
to extract the φ dependence of the decay in this analysis.
FIG. 1: J/Ψ polarization parameter λ versus xF in pT bins.
Solid dots are the results obtained with the 2800 A magnet
setting, open triangles with the 2040 A setting. Only statis-
tical errors are shown.
The ϑ distributions of the data in all bins were divided
by the corresponding ones of the simulation, resulting in
acceptance-corrected ϑ distributions. These were then
used to calculate the polarization in xF and pT bins,
according to the formula dσ/dcosϑ = A(1 + λcos2ϑ),
where the normalization constants A were left free. Re-
sults were obtained separately for two experimental runs
with the current in the SM12 magnet set to 2040 and
2800 A respectively, resulting in substantially different
Figure 1 shows the polarization parameter λ as a func-
tion of xFin four pTbins; it can be seen that results from
the two magnet settings are in reasonable agreement, giv-
ing some confidence that the acceptance is understood
and providing an estimate for the magnitude of the rel-
evant systematic uncertainties. The xF dependence of λ
appears to be independent of pT.
FIG. 2: J/Ψ polarization parameter λ versus pT for two xF
ranges: xF < 0.45 (solid circles) and xF > 0.45 (open tri-
angles). Statistical errors are smaller than the data points.
Systematic errors for the small xF data are shown as a dark
band; those for large xF (not shown) are slightly smaller.
Systematic errors from various sources were consid-
ered. Inexact knowledge of the pT dependence of the
production cross section, coupled with a strong pT de-
pendence of the acceptance versus decay angle ϑ, led to
an uncertainty of ±0.06 in λ, independent of xF. Ad-
ditional contributions included mass-peak fitting errors
(0.04–0.08, depending on the xF bin) and uncertainties
in the exact position (0.02) and angle (0.02–0.04) of the
incoming beam and in the fields in the analyzing magnets
(0.01). Uncertainties from various sources are largely un-
correlated; they were added in quadrature for the overall
Figure 2 presents the polarization parameter λ as a
function of pTfor two xFranges, where the two data sets
have been statistically combined. The two intervals in
xF approximately correspond to regions were the gluon-
gluon and quark-antiquark processes are dominant. No
significant pT dependence is seen in either region after
the systematic errors are taken into account. At large pT,
charmonium production is understood  to be domi-
nated by gluon bremsstrahlung with subsequent fragmen-
tation into a cc pair. In this case, the charmonium state is
expected [5, 17] to retain to a large degree the transverse
polarization of the high-pT, on-shell gluon. However, the
pTrange of the experiment, extending to 4 GeV, may not
be sufficient to see clearly such an effect. It must be noted
that this effect is also not observed at the high pT val-
ues available at collider energies , where, if anything,
polarization appears to be longitudinal. In the following,
we assume there is no significant pT dependence and the
results are presented integrated over all pT.
Figure 3 shows the polarization λ as a function of
xF for the combined data set. The one-sigma system-
atic uncertainty is shown as a dark band. Also shown
are the results previously obtained by the Chicago-Iowa-
FIG. 3: J/ψ polarization parameter λ versus xF from this
experiment (solid circles). Statistical errors are shown as error
bars, systematic as a dark band. Data values are tabulated
in . The CIP  results are also shown (open triangles).
Princeton collaboration , which used a 252-GeV pion
beam and a tungsten target. Our results suggest that the
J/ψ is produced slightly transversely polarized at small-
to-intermediate xF. Within the systematic uncertainties
the results are consistent with the CIP experiment ,
which saw no polarization in this range, albeit with much
larger statistical uncertainties. It should be noted that
in this range the qq annihilation process is expected to
play a more important role with a pion beam than with a
proton beam, where gg fusion dominates. For xF > 0.6,
the polarization turns to longitudinal, outside the mar-
gins of the systematic error. This is similar to a pattern
seen in the CIP experiment, although the behavior ap-
pears smoother as a function of xF and begins at smaller
xF than the sudden turn-over near xF ≈ 0.85 in the lat-
ter. However, the results are not incompatible. It is also
interesting to note that the clear change in polarization
in this experiment roughly coincides with the transition
from gluon-fusion dominance to quark-annihilation dom-
Integrated over the entire xF range, the measured po-
larization is λ = 0.069±0.004±0.08 (statistical and sys-
tematic errors). This small value, consistent with no po-
larization if systematic errors are taken into account, is in
agreement with previous proton-beam experiments [8, 9],
which had insufficient statistics to study the xF depen-
As a cross-check of the analysis, the polarization of
the Drell-Yan continuum was also studied using the same
technique. This can be done only for dimuon invariant
masses greater than 4 GeV, since the J/ψ peak domi-
nates the spectrum at lower masses. An additional com-
plication arises from random coincidences of uncorrelated
pairs of muons, which in the case of the J/ψ were re-
moved by the fitting procedure. These were estimated
and subtracted from the Drell-Yan sample by studying
the distributions of same-charge muon pairs. A fit to
the formula 1 + λcos2ϑ for dimuon masses from 4 to 7
GeV gave λ = 0.98 ± 0.04, in good agreement with the
100% transverse polarization expected and previously ob-
served  in the Drell-Yan process. While the kinematic
range is not the same as for the J/ψ measurement, this
agreement with expectations increases confidence in the
soundness of the J/ψ analysis. The level of statistics
were not adequate to investigate any xF dependence of
the Drell-Yan polarization.
The results are not in agreement with published pre-
dictions for J/ψ polarization based on NRQCD, which
are in the range 0.31 < λ < 0.63 , or with similar
predictions  based on an early model that considers
only color-singlet intermediate states. The small positive
values at xF<
∼0.5 are very similar to the results obtained
for Υ(1S) by this experiment in a similar pTrange, and in
sharp contrast to the essentially 100% transverse polar-
ization of the (unresolved) Υ(2S) and Υ(3S) states .
To understand the behavior of the polarization, all
sources of J/ψ production must be considered. While
b-quark production is not a major source at these en-
ergies, almost half of the produced J/ψ’s are the decay
products of higher-mass charmonium resonances, mainly
the3PJstates χcJ. Feed-down from χc2, produced exclu-
sively in the Jz= 2 state from gluon-gluon fusion, results
in 100% transverse J/ψ’s, increasing the observed values
of λ. The turn-over at high xF may reflect the transi-
tion, at xF ≃ 0.6, to the quark-annihilation graph ,
which produces a mix of χc2spin states. As for the overall
level, it cannot be explained without a substantial contri-
bution from χc1, which in general produces longitudinal
J/ψ’s. Beneke and Rothstein  originally estimated
the χc1contribution to be about 10 times smaller than
that from χc2, but it was later found experimentally 
to be of comparable size. NRQCD calculations which
retain higher orders in v can also accommodate substan-
tial χc1contributions . It would probably require a
contribution near the experimental and theoretical upper
limits in order to obtain λ values as small as experimen-
tally measured, within the context of NRQCD.
In addition, it must be noted that no existing calcu-
lation takes into account nuclear effects, which strongly
affect the production cross section . The formation
length of the J/ψ at these energies is generally longer
than the nuclear size  and it is conceivable that color-
singlet and -octet components of the wavefunction are
absorbed differently while propagating through the nu-
clear medium, resulting in a different mix of Fock states
compared to the free-nucleon production, thus altering
the polarization. Furthermore, the polarization of the χc
states themselves is predicted to have a nuclear depen-
dence  which would feed down to the J/ψ polariza-
tion. Finally, at the highest values of xF, higher-twist
effects may become important .
This work was supported in part by the U.S. Depart-
ment of Energy.
∗Present address: University of Illinois, Urbana, IL 61801
†Present address: University of Cincinnati, Cincinnati,
‡Present address: Florida State University, Tallahassee,
§On leave from Kurchatov Institute, Moscow, Russia
¶Present address: Indiana University, Bloomington, IN
 T. Matsui and H. Satz, Phys. Lett. B178, 416 (1986).
 R. W. Robinett, Phys. Rev. D43, 113 (1991).
 O. Teryaev and A. Tkabladze, Phys. Rev. D56, 7331
 G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev.
D51, 1125 (1995).
 P. L. Cho and M. B. Wise, Phys. Lett. B346, 129 (1995).
 B. A. Kniehl and G. Kramer, Eur. Phys. J. C6, 493
 C. Biino et al., Phys. Rev. Lett. 58, 2523 (1987).
 T. Alexopoulos et al. (E771), Phys. Rev. D55, 3927
 A. Gribushin et al. (E672/E706), Phys. Rev. D62,
 T. Affolder et al. (CDF), Phys. Rev. Lett. 85, 2886
 C. N. Brown et al. (E866), Phys. Rev. Lett. 86, 2529
 T.-H. Chang, Ph.D. thesis, New Mexico State University
 G. Moreno et al. (E605), Phys. Rev. D43, 2815 (1991).
 J. C. Collins and D. E. Soper, Phys. Rev. D16, 2219
 K. Gottfried and J. D. Jackson, Nuovo Cim. 33, 309
 E. Braaten and T. C. Yuan, Phys. Rev. Lett. 71, 1673
 E. Braaten, B. A. Kniehl, and J. Lee, Phys. Rev. D62,
 M. Beneke and I. Z. Rothstein, Phys. Rev. D54, 2005
 M. Vanttinen, P. Hoyer, S. J. Brodsky, and W.-K. Tang,
Phys. Rev. D51, 3332 (1995).
 M. S. Kowitt et al. (E789), Phys. Rev. Lett. 72, 1318
 T. Alexopoulos et al. (E771), Phys. Rev. D62, 032006
 M. Beneke (1997), hep-ph/9703429.
 M. J. Leitch et al. (E866), Phys. Rev. Lett. 84, 3256
 G. R. Farrar, L. L. Frankfurt, M. I. Strikman, and H. Liu,
Phys. Rev. Lett. 64, 2996 (1990).
 L. Gerland, L. Frankfurt, M. Strikman, H. Stocker, and
W. Greiner, Phys. Rev. Lett. 81, 762 (1998).