(N-1)/2 + (M-1)/2
's
§
Suppression and the Quark-Gluon Plasma
S. Frankel and W. Frati
Physics Department, University of Pennsylvania
October, 1997
Abstract
All measured Feynman distributions of the ratio, R, of production in nuclei relative to production on protons fall off with . They show [2] that absorption of charmonium cannot be the only source of suppression and that energy loss of the incident proton prior to the production, because of the exponential § dependence of the charmonium cross section, should not be neglected. Including energy loss in recent nucleus-nucleus collisions, we find that the latest measured Pb-Pb cross sections do not provide any evidence for deconfinement.
Over a decade has passed since it was proposed that suppression in p-nucleus collisions was evidence for creation of a quark-gluon plasma. [1] It was soon shown [2] from studies of the Feynman x distributions of relative p-A and p-p production of the
that initial state and final state interactions could account for the data. It is now claimed that recent measurements show an anomalous depression in the total cross section for J/Psi production in Pb-Pb interactions. No Feynman x distributions of these data have been reported.
This note gives results of the full analysis taking into account both initial state energy loss and final state absorption. Fig. 1 shows the data for two of the many examples of the ratio, R, of the nuclear to hadronic distributions of the cross sections in pion and proton interactions.
The pion data are from ref. [3] and proton data from ref. [4].
The fact that the ratio is not independent of rules out independent absorption as the sole mechanism for suppression, and the difference in the suppression in pion- and proton induced reactions mirrors the experimentally measured difference in energy loss in the initial state soft interactions.
(Theoretical fits, superimposed on Fig 1., and reproduced from early
work
[5] [6], include
an energy loss per collision, = 0.4. These fits showed
the effect of a final
state -nucleon interaction with
a + n 
+X inelastic cross section of about
ten millibarns, and a final state energy loss of 10 % per collision.
The fits are only illustrative since trade-off between them can also
account for the data. Fortunately,
the suppression in the total cross section is simpler to understand
than that
seen in the distributions since it is unaffected by the
inelastic scattering cross-section and energy loss
of charmonium in the final state, only by the initial state
energy loss and the
open-charm absorption cross section.)
The energy loss of the particular nucleon constituents that finally form charmonium cannot be calculated because of the non-perturbative nature of the prior soft collisions. One can only estimate the prior energy loss per collision, . The energy loss distributions for soft minimum bias collisions can be determined from the experimental event structures at a particular §. The ISAJET program of Frank Paige reproduces that data and allows for interpolations between different §. It allows one to estimate the relative values of a and b in the expression, = a + b§., This relationship has been well tested in studies of low interactions in nuclei [7] [8]. Nevertheless for different high final states a and b should be taken as parameters that can be extracted by studying data for widely varying A.
(Another equivalent method is to assign an energy loss to the quarks or gluons that are responsible for the production of the particular final state that is being studied, e.g, or Drell-Yan pairs, again assuming some energy loss parameter. This was the approach of the work of Gavin and Milana.[9]. Naturally will be different for different final states. (Their ratio of energy loss for Drell-Yan relative to production, (4/9), is actually close to the values obtained in refs.[5], [6], and [15].
To constrain the new analysis we have made use of the independent determination of the absorption cross section from photoproduction since that reaction has no initial state interactions. That value is = 6.6 +/- 2.2 mb, as obtained in reference [5].
To calculate the suppression we have again used a full Monte Carlo
calculation, generating nucleons according to the 3 component
Woods-Saxon distribution, 
with 
, and 
= .545.
Protons are then scattered off the nucleons in
the nuclei, to count the number of nucleon collisions prior to the
production, (which determine
the energy loss), and to count the number of
succeeding collisions of the charmonium,
(which determines the absorption).
This method removes the struck nucleon from the counting [10].
(This differs from
calculations [11]
which integrate the paths through a continuous
nucleus matter distribution.
Not taking into account the finite nucleon
size underestimates determination of an absorption cross section and may
account for differences in an extracted .)
Unlike charmonium, produced in a high 
reaction, the low
pairs (e.g., off-shell pions), produced in the soft
nucleon-nucleon collisions
have a longer evolution time. This is in fact the basis for the
difference between counting participants (``wounded nucleons'')
in predicting minimum bias event
structures [12],
rather than the number of scatters as needed for high
charmonium production.
Thus pions produced in the final state
should not contribute significantly to charmonium
absorption, are not included in the calculation, and, as we shall see,
are not needed to account for the new nucleus-nucleus data.
We also do not distinguish between charmonium absorption by unstruck
nucleons, as in the p-A
case, and on absorption on previously struck protons,
as in the B-A case.
The parameterization[13]
of the production cross section,
proportional to 
, (
),
is used. It is responsible for the
§dependence of the suppression, with 
, where n is the number of prior collisions.
We show in Fig. 2
our calculations for both the mean obtained from our prior
photoproduction analysis and a
somewhat larger value, using our estimate of the energy loss,
.
One can
make small trade-offs of
with to get other suitable fits to the
data. The filled points show the data for §= 38.8 GeV
(circles), §= 19.4 GeV
(triangles) and §= 17.4 GeV
(squares) which are the results of different
experiments [14].
The open squares are the calculations for
= 6.3 mb., while the open circles are for 7.9 mb.
In Fig. 2 we have drawn a straight line, obtained by fitting only the low higher accuracy points, which appear to show an exponential behavior. It extrapolates to a value well above the value for Pb-Pb. However there is no theoretical reason for an exponential extrapolation procedure to be valid out to large , even if absorption were the only mechanism. In fact it is shown [15] that, even with pure absorption, analytic calculations and the functional dependence of prior and subsequent scatters as a function of should cause a small enhancement of R above experiment at very high .
The suppression is a valuable tool for studying many features of
reactions that have simultaneously
both low and high interactions. We need
to know more about the time evolution of charmonium into the on-shell
, the changes in nucleon structure functions resulting from the prior
soft interactions, and the possible variation of the absorption
cross section with outgoing
energy. This requires more data and analysis of photoproduction
as well as Drell-Yan production, especially the small, but not zero,
energy losses that occur in the latter reaction. The Drell-Yan
distribution measurements
should be extended to = 1, to verify that 
depends only on the Glauber probability that the dimuon is made
in the first collision [16].
Conclusion: Incorporating the presence of energy loss in the soft interactions prior to production, we find no evidence for effects of deconfinement.