Cold Nuclear Matter Effects on J/ψ Production
By Ramona Vogt
PHENIX has some very interesting results on the J/ψ nuclear
modification factor, RAA, in Au+Au collisions, as
nicely described by Tony Frawley in the September 25, 2007 issue
of RHIC News. Complicating the interpretation of RAA
are the effects of color screening on the J/ψ as well as
stronger effects on the higher charmonium resonances, the χcJ
and ψ′ states. In addition, in AA collisions, where multiple
charm-anticharm pairs can be produced at RHIC, the J/ψ has been
predicted to be formed by coalescence of uncorrelated charm and
anticharm quarks within the collision region. These effects are
in addition to effects already observed in fixed-target pA
interactions: modifications of the parton densities in the
nuclear medium and absorption of the J/ψ in nuclear matter by
interaction with nucleons. The cold nuclear matter effects can
best be studied in d+Au interactions which were the focus of
RHIC Run 3 and will be a major part of the current run. This
report will describe these cold nuclear matter effects on J/ψ
production.
The J/ψ (or a precursor charm-anticharm state) can interact with nucleons as it moves through the target after the pair has been produced. The larger the target, the greater the distance the J/ψ has to travel before escaping the nucleus. Thus the effect increases with nuclear mass A. This effect is known as nuclear absorption and is numerically calculated in terms of a survival probability, SA = exp(−ρA σabsψ z) where z is the distance traveled through nuclear matter and σabs is the J/ψ absorption cross section, typically fit to the data. Early data from fixed-target experiments at CERN and at Fermilab suggested that the J/ψ and ψ′ absorption cross sections were the same within errors but more recent, higher statistics data now show that the ψ′ absorption cross section is larger than that of the J/ψ. To a first approximation, the relative absorption cross sections depend on the ratios of radii squared, e.g. σabsψ′ = σabsψ(rψ′/rψ)2. The data also suggest that the absorption cross section, a few millibarns at center of mass energies of 23−29 GeV, decreases with nucleon-nucleon center-of-mass energy. Thus, at RHIC, the absorption cross section may be rather small.
The other cold nuclear matter effect relevant for the rapidity region covered by J/ψ production at RHIC is the modification of the parton densities in the nucleus, the gluon density in particular. If the deuteron beam is going from negative to positive rapidity and the gold beam is traveling from positive to negative rapidity, the parton momentum fractions in the gold nucleus, x2, are small at forward rapidity and large at negative rapidity. The x2 range covered in √sNN = 200 GeV collisions at RHIC is shown on the left-hand side of Fig. 1. At y = −1.7, 0, and 1.7, x2 ~ 0.11, 0.02, and 0.0035 respectively.
Figure 1: Left-hand side: The average value of the momentum fraction x2 in the gold nucleus as a function of rapidity for √sNN = 200 GeV. Right-hand side: The EKS98 (red) and nDSg (blue) modifications of the gluon density in the gold nucleus as a function of x2 at the scale for J/ψ production.
If one looks at the ratio of the gluon density in the gold nucleus relative to that in the proton, Rg, as a function of x2, the ratio is less than one for x2 < 0.01, larger than one for 0.01 < x2 < 0.2, and less than one again for x2 > 0.2. At PHENIX the backward rapidity region corresponds to the region where Rg > 1 and moves to smaller x2 toward forward rapidity where Rg < 1, as shown on the right-hand side of Fig. 1 for the EKS98 and nDSg parameterizations of Rg. This shadowing effect becomes larger with increasing A and increasing center-of-mass energy since x2 ~ mψ exp(−y)/√sNN. The shape of the shadowing ratio Rg is very model dependent and not all available parameterizations of Rg agree with the shape of the current d+Au PHENIX data.
Including both effects, the d+Au modification factor, RdAu, is the product RdAu = SA Rg. The characteristic shapes in Fig. 2 are those of Rg for the EKS98 and nDSg parameterizations with the positive rapidity region corresponding to low x2 and negative rapidity to large x2. Since the absorption cross section is a rather weak function of rapidity, the shape of RdAu at RHIC is due to the parton density modifications while the absolute value of the ratio is determined by the absorption cross section, as demonstrated in Fig. 2. The effect of changing the proton parton density is also shown. When the different relative values of the J/ψ, χcJ, and ψ′ absorption cross sections are taken into account, the published Run 3 data are compatible with σabsψ ~ 1 mb. However, the uncertainties in the data are still large and the shape and magnitude of the effect may change with more precise data and with reduced systematic uncertainties.
Figure 2: The d+Au modification factor as a function of rapidity for the EKS98 (left) and nDSg (right) parameterizations. The top plots vary the J/ψ absorption cross section with the MRST2001 parton distributions while the bottom plots show the differences due to the choice of parton distribution functions for a fixed absorption cross section. The PHENIX Run 3 data are also shown in the top plots.
The impact parameter dependence of RdAu
has also been studied by PHENIX. The J/ψ production cross
section should scale with the number of binary nucleon-nucleon
collisions since its production can be described by perturbative
QCD. While neither the EKS98 or nDSg parameterizations include
any impact parameter dependence, it has been implemented by
assuming that the modifications of the parton distributions in
the gold nucleus are proportional to the path length of the
parton through the nucleus. The comparison with the published
PHENIX Run 3 d+Au data is shown in Fig. 3 for both EKS98 and
nDSg for two different values of σabsψ
= 0.5 and 1.75 mb. While the two parameterizations give similar
results at forward rapidity, the differences between the two
seen as a function of rapidity in Figs. 1 and 2 at mid- and
forward rapidity are apparent in the Ncoll
dependence in Fig. 3. A more precise determination of RdAu(Ncoll)
is needed to draw further conclusions.
Figure 3: The d+Au modification factor as a function of the number of binary nucleon-nucleon collisions calculated with EKS98 (left) and nDSg (right) with the MRST2001 parton distribution functions and J/ψ absorption cross sections of 0.5 and 1.75 mb. The PHENIX Run 3 data are also shown for y = −1.7 (top), 0 (middle) and 1.7 (bottom). (An additional 12% overall normalization error is not shown.)
Figure 4. The author photographed with the PHENIX detector by PHENIX Run Coordinator Mike Leitch.
References
PHENIX collaboration, "J/ψ Production and Nuclear Effects for d+Au and p+p Collisions at √sNN = 200 GeV", Phys. Rev. Lett. 96, 012304 (2006). (arXiv:nucl-ex/0507032)
R. Vogt, C. Lourenco and M. J. Leitch, "Cold Nuclear Matter Effects on J/ψ and ψ′ Production", J. Phys. G 34, S759 (2007)
R. Vogt, "Shadowing and Absorption Effects on J/ψ Production in dA Collisions", Phys. Rev. C 71, 054902 (2005). (arXiv:hep-ph/0411378)
Acknowledgement
This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (http://www.llnl.gov/disclaimer.html). The author also acknowledges the NSF grant PHY-0555660.
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