A precise measurement of the ratios of the Drell-Yan cross section per
nucleon for an 800 GeV/c proton beam incident on Be, Fe and W targets is
reported. The behavior of the Drell-Yan ratios at small target parton momentum
fraction is well described by an existing fit to the shadowing observed in
deep-inelastic scattering. The cross section ratios as a function of the
incident parton momentum fraction set tight limits on the energy loss of quarks
passing through a cold nucleus

Beddo, M. E.

Brown, C. N.

Carey, T. A.

Chang, T. H.

Cooper, W. E.

Gagliardi, C. A.

Garvey, G. T.

Geesaman, D. F.

Hawker, E. A.

He, X. C.

Isenhower, L. D.

Kaplan, D. M.

Kaufman, S. B.

Koetke, D. D.

Lee, W. M.

Leitch, M. J.

McGaughey, P. L.

Moss, J. M.

Mueller, B. A.

Papavassiliou, V.

Peng, J. C.

Petitt, G.

Reimer, P. E.

Sadler, M. E.

Sondheim, W. E.

Stankus, P. W.

Towell, R. S.

Tribble, R. E.

Vasiliev, M. A.

Webb, J. C.

Willis, J. L.

Young, G. R.

English

arXiv

Texas A&M University

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Parton energy loss limits and shadowing in Drell-Yan dimuon production
M.A. Vasilievi∗, M.E. Beddog, C.N. Brownc, T.A. Careyf , T.H. Changg, W.E. Cooperc, C.A. Gagliardii,
G.T. Garveyf , D.F. Geesamanb, E.A. Hawkeri,f , X.C. Hed, L.D. Isenhowera, D.M. Kaplane, S.B. Kaufmanb,
D.D. Koetkej, W.M. Leed, M.J. Leitchf , P.L. McGaugheyf , J.M. Mossf , B.A. Muellerb, V. Papavassilioug,
J.C. Pengf , G. Petittd, P.E. Reimerf , M.E. Sadlera, W.E. Sondheimf , P.W. Stankush, R.S. Towella,f , R.E. Tribblei,
J.C. Webbg, J.L. Willisa, G.R. Youngh
(FNAL E866/NuSea Collaboration)
aAbilene Christian University, Abilene, TX 79699
bArgonne National Laboratory, Argonne, IL 60439
cFermi National Accelerator Laboratory, Batavia, IL 60510
dGeorgia State University, Atlanta, GA 30303
eIllinois Institute of Technology, Chicago, IL 60616
fLos Alamos National Laboratory, Los Alamos, NM 87545
gNew Mexico State University, Las Cruces, NM, 88003
hOak Ridge National Laboratory, Oak Ridge, TN 37831
iTexas A & M University, College Station, TX 77843
jValparaiso University, Valparaiso, IN 46383
(January 11, 2018)
A precise measurement of the ratios of the Drell-Yan cross section per nucleon for an 800 GeV/c
proton beam incident on Be, Fe and W targets is reported. The behavior of the Drell-Yan ratios
at small target parton momentum fraction is well described by an existing fit to the shadowing
observed in deep-inelastic scattering. The cross section ratios as a function of the incident parton
momentum fraction set tight limits on the energy loss of quarks passing through a cold nucleus.
24.85.+p; 13.85.Qk; 25.40.Ve; 25.75.q
The Drell-Yan process, where a beam quark (anti-
quark) fuses with a target antiquark (quark) producing
a muon pair, can be used to study the interactions of
fast partons penetrating through cold nuclei. Only ini-
tial state interactions are important in Drell-Yan since
the dimuon in the final state does not interact strongly
with the partons in the medium. This makes Drell-Yan
scattering an ideal tool to study energy loss of fast quarks
in nuclear matter by comparing the observed yields from
a range of nuclear targets. The dynamics of fast parton
energy loss in nuclear matter is the subject of consider-
able theoretical interest [1–4] and has significant implica-
tions for the physics of relativisitic heavy ion collisions.
Drell-Yan scattering is closely related to deep-inelastic
scattering (DIS) of leptons, but unlike DIS it can be
used specifically to probe antiquark contributions in tar-
get parton distributions. When DIS on nuclei occurs at
x < 0.08, where x is the parton momentum fraction,
the cross section per nucleon decreases with increasing
nuclear number A due to shadowing [5,6]. Shadowing
should also occur in Drell-Yan dimuon production at
small x2, the momentum fraction of the target parton,
and theoretical calculations indicate that shadowing in
the two reactions has a common origin [7,8]. This should
be particularly apparent at x < 0.06 where DIS on nuclei,
like Drell-Yan, is dominated by scattering off sea quarks.
Fermilab Experiment 866 (E866) measured the nu-
clear dependence of Drell-Yan dimuon production by 800
GeV/c protons on Be, Fe and W targets at larger values
of x1, the momentum fraction of the beam parton, larger
values of xF (≈ x1 − x2), and smaller values of x2 than
reached by the previous experiment, Fermilab E772 [9].
The extended kinematic coverage of E866 significantly
increases its sensitivity to parton energy loss and shad-
owing. This Letter reports the results.
The experiment used the same 3-dipole magnet spec-
trometer that was described in [10]. An 800 GeV/c ex-
tracted proton beam averaging 3× 1011 protons per 20 s
spill bombarded one of three solid targets or an empty
target frame. The Be, Fe and W targets were 9.4% –
19% of an interaction length thick. Their relative thick-
nesses were chosen carefully to match the background
rates present in the spectrometer. The targets were lo-
cated far upstream of the main dipole magnet to opti-
mize the acceptance at low x2 and large xF . During
a cycle, 2 beam spills were taken on each target and 1
spill was collected on an empty location. After passing
through a target, the remaining beam was intercepted by
a copper beam dump, which was followed by a thick ab-
sorber that removed hadrons produced in the target and
the dump. This ensured that only muons traversed the
spectrometer’s detectors, which consisted of four tracking
stations and a momentum analyzing magnet. The trigger
required a pair of triple hodoscope coincidences having
the topology of a muon pair from the target. Typically
1400 triggers per second were recorded with an average
live time of 93%.
Over 130,000 muon pairs with dimuon mass in the
1
FIG. 1. Ratios of the measured cross section per nucleon for Drell-Yan events versus dimuon mass (in GeV/c2), x2, xF and
x1. The upper (lower) panels show ratios of Fe/Be (W/Be) from the present experiment as solid circles and Fe/C (W/C) from
E772 as open circles. The errors are statistical only. The solid curves are the predicted cross section ratios, integrated over the
hidden variables, from leading-order calculations using EKS98 [11] and MRST [12].
range 4.0 < M < 8.4 GeV/c2 survived the data cuts.
Random pairs were subtracted from the data using sim-
ulated random dimuons constructed by mixing single
muon tracks that were obtained simultaneously from
prescaled single muon triggers. The normalization factor
for the random correction was evaluated by comparing
to the observed rate of same-charge muon pairs in the
data. The random rate was 9% of the real events, and it
occurred primarily at low dimuon mass and high pT . A
residual 3% background from the empty target was also
subtracted. The solid targets intercepted the beam at
nearly the same z location, making differences in dimuon
acceptance negligible. The overall systematic normaliza-
tion uncertainty in the cross section ratios reported here
is 1%.
The Drell-Yan events obtained by E866 extend over
the ranges 0.01 < x2 < 0.12 and 0.21 < x1 < 0.95, with
〈x2〉 = 0.038 and 〈x1〉 = 0.46. They also cover the range
0.13 < xF < 0.93 and provide good pT coverage to 4
GeV/c. Ratios of the cross section per nucleon for Fe to
Be and W to Be versus dimuon mass, x2, xF and x1 are
shown in Fig. 1, along with similar results from E772 for
Fe to C and W to C. The figure shows very good agree-
ment between the experiments for the cross section ratios
versus x2. The agreement versus other variables is also
quite good, given the much smaller 〈x2〉 and, hence, in-
creased shadowing of the present data. Note that the A
dependence observed here and in E772 implies the change
in the cross section ratios in Fig. 1 due to the choice of
Be versus C is small compared to the effect of the dif-
ference in 〈x2〉. The reduction in the cross section per
nucleon on the heavy targets, characteristic of shadow-
ing, is clearly apparent at small x2. A similar reduction,
part of which could be related to incident parton energy
loss, is apparent at large xF and x1. However, it is im-
portant to recognize that the spectrometer acceptance
coupled to the intrinsic Drell-Yan cross section leads to
a strong anti-correlation between x2 and xF for the ob-
served events. Therefore, the events that show the cross
section reduction at large xF and x1 are in general the
same events that appear in the shadowing region.
In order to identify the contributions from shadowing,
Fig. 1 also shows the predicted cross section ratios, in-
tegrated over the hidden variables, from leading-order
Drell-Yan calculations using the code EKS98 [11] to-
gether with the MRST parton distribution functions [12].
Essentially identical results are obtained using CTEQ5M
or CTEQ5L parton distributions [13] instead. EKS98
describes the ratios fA(x,Q
2)/fp(x,Q
2) of the various
quark flavors in nucleus A, compared to those in the pro-
ton. It has been tuned to fit the shadowing observed in
DIS [14] and E772 while conserving baryon number and
momentum.
EKS98 provides an unbiased way to separate the ef-
fects of shadowing and energy loss in the present data
because it uses a single shadowing function to describe
the nuclear dependence of all sea quark distributions at
its initial scale Q0
2 = 2.25 GeV2 and only DIS results are
used to constrain that function for x <∼ 0.1. The shape
and magnitude of the ratios versus x2 are well reproduced
by the shadowing predictions. Most of the A dependence
observed in the ratios versus mass, xF and x1 can also be
explained by shadowing at small x2. As a further test of
the shadowing parametrization, the events in Fig. 1 have
been separated into two sets at the median x2 value. The
cross section ratios differ by up to 6% when the events
2
FIG. 2. Ratios of the measured Drell-Yan cross section per
nucleon versus pT . Ratios of Fe/Be and W/Be from the
present experiment are shown as solid circles, and ratios of
Fe/C and W/C from E772 are shown as open circles. The
solid curves are shadowing predictions for the present exper-
iment from leading-order calculations using EKS98 [11] and
MRST [12].
at low and high x2 – but at the same mass, xF or x1
– are observed separately. EKS98 also describes these
differences well. This is the first experimental demon-
stration that the shadowing observed in Drell-Yan and
DIS is quantitatively similar.
Figure 2 shows the measured ratios of the Drell-Yan
cross section per nucleon as a function of pT . Unlike the
longitudinal variables that have strongly correlated ac-
ceptances, the pT acceptance in E866 is nearly indepen-
dent of the other kinematic variables, so the shadowing
calculations predict essentially constant cross section ra-
tios versus pT , as shown by the smooth curves in the fig-
ure. The data demonstrate a clear pT dependence which
must have an independent origin. The slight reduction
in the cross section per nucleon observed for heavy nu-
clei at small pT , coupled with the increase in the cross
section per nucleon at large pT , is characteristic of mul-
tiple scattering of the incident partons as they traverse
the nucleus.
The x1 dependence of the cross section ratios provides
the best direct measure of the energy loss of the incident
quarks in the nuclear medium. Table I gives the ratios
of the measured cross section per nucleon as a function
of x1, and the mean values of x1, x2 and dimuon mass
for each bin. However, as shown above, shadowing at
small x2 explains a substantial fraction of the apparent
variation in the cross section ratios versus x1. This must
be removed before one can isolate a nuclear dependence
due to energy loss. Figure 3 shows the same cross sec-
tion ratios versus x1 as given in Table I, but corrected
for shadowing by weighting each event with the calcu-
lated ratio of the Drell-Yan cross sections per nucleon for
TABLE I. Ratios of the cross section per nucleon for Fe
to Be and W to Be as functions of x1, without correction for
shadowing. Also given are mean values for x1, x2 and dimuon
mass (in GeV/c2) for each bin. Mean xF may be found from
〈xF 〉 = 〈x1〉 − 〈x2〉. The errors are statistical only.
x1 range 〈x1〉 〈x2〉 〈M〉 σ
Fe/σBe σW/σBe
0.21-0.3 0.279 0.055 4.76 1.059(41) 0.971(37)
0.3-0.4 0.356 0.046 4.92 0.973(16) 0.964(15)
0.4-0.5 0.448 0.039 5.07 0.959(14) 0.951(13)
0.5-0.6 0.545 0.034 5.17 0.962(17) 0.944(16)
0.6-0.7 0.642 0.030 5.24 0.979(25) 0.914(23)
0.7-0.8 0.738 0.026 5.27 0.920(42) 0.884(40)
0.8-0.95 0.836 0.023 5.28 0.960(99) 0.822(86)
FIG. 3. Ratios of the cross section per nucleon versus x1 for
Fe/Be (upper panel) and W/Be (lower panel), corrected for
shadowing. The solid curves are the best fit using the energy
loss form (1), and the dashed curves show the 1σ upper limits.
The dotted curves show the 1σ upper limits using the energy
loss form (3). The 1σ upper limit curves using the energy loss
form (2) are essentially identical to those using form (3).
deuterium and nucleus A at the same (x1, x2, Q
2), using
EKS98 and MRST.
Several groups have studied energy loss of partons in
nuclei. Their results can be expressed in terms of the
average change in the incident parton momentum frac-
tion, ∆x1, as a function of target nucleus. Gavin and
Milana [1] analyzed the E772 Drell-Yan data for energy
loss based on the parametrization
∆x1 = −κ1 x1A
1/3, (1)
where the factor κ1 may have a Q
2 dependence. They
based the form (1) on an analogy to the transverse spin
asymmetry in direct photon production. From a com-
parison to the xF dependence seen by E772 and neglect-
ing shadowing, they concluded that the fractional energy
loss of quarks passing through nuclei is ≈ 0.4%/fm. Re-
cently, other groups have assumed equivalent formula-
tions with even more rapid energy loss [15,16]. Brodsky
3
and Hoyer [2] argued that the energy loss found by Gavin
and Milana was too large since the time scale for QCD
bremsstrahlung was too short to allow for multiple con-
tributions to the energy loss. Brodsky and Hoyer used an
analogy to the photon bremsstrahlung process to obtain
a form for gluon radiation leading to an initial parton
energy loss [17]
∆x1 ≈ −
κ2
s
A1/3. (2)
They found an upper limit for the gluon radiation from
the uncertainty relation. They also noted that elastic
scattering should make a similar contribution to the en-
ergy loss. Overall, they concluded that energetic partons
should lose <∼ 0.5 GeV/fm in nuclei. The formulation de-
veloped by Brodsky and Hoyer was extended by Baier et
al. [3,4]. They found that the energy loss of sufficiently
energetic partons depends on a characteristic length and
the broadening of the squared transverse momentum of
the parton. For finite nuclei, both factors vary as A1/3,
so Baier et al. predict
∆x1 ≈ −
κ3
s
A2/3. (3)
Baier et al. predict that energy loss may be different in
hot and cold nuclear matter and that there could a large
coherent effect in relativistic heavy ion collisions. In con-
trast, tight limits have been placed on energy loss in S+S
and Pb+Pb collisions [18], but the parton momenta rel-
ative to the hadronic medium were very much smaller
in those cases than in the present experiment, making a
direct comparison difficult.
Given these energy loss expressions, it is possible to
obtain empirical values for the κ’s by performing simul-
taneous fits to the Fe/Be and W/Be Drell-Yan cross
section ratios versus x1 in Fig. 3. We assume that κ1
is Q2-independent [1,2] when using form (1) and that
our incident quarks are sufficiently energetic when us-
ing form (3). Curves corresponding to the fits are in-
cluded in Fig. 3. When assuming the form (1), we find
κ1 = 0.0004±0.0009. This implies that the observed frac-
tional energy loss of the incident quarks is < 0.14%/fm.
For the energy loss forms (2) and (3), the best fits im-
ply essentially zero energy loss. We find the 1σ upper
limits to be κ2 < 0.75 GeV
2 and κ3 < 0.10 GeV
2. The
κ2 limit indicates that the incident quarks lose energy
at a constant rate of < 0.44 GeV/fm. The κ3 limit im-
plies that the observed energy loss of the incident quarks
within the model of Baier et al. is ∆E < 0.046 GeV/fm2
× L2, where L is the quark propagation length through
the nucleus. This is very close to the lower value given by
Baier et al. for cold nuclear matter [19]. In all three cases,
the quoted errors include both statistics and the overall
normalization uncertainty, with the latter dominating.
One can also obtain an indirect estimate of the energy
loss due to gluon radiation in the model of Baier et al.
from the broadening of the 〈pT
2〉 as the incident quark
passes through the nucleus, as shown in Fig. 2. How-
ever, such an analysis involves two significant difficulties.
While the Drell-Yan cross section is very small for pT
beyond 4 GeV/c, the change in 〈pT
2〉 from nucleus to
nucleus, being the small difference of large numbers, is
quite sensitive to the yield at very large pT where our
acceptance is poor and the random background becomes
significant. Meanwhile, the pT dependence of the ratio
of the Drell-Yan cross sections per nucleon on hydrogen
and deuterium shows possible evidence for a change in
the reaction mechanism at pT ≈ 3 GeV/c [20], compli-
cating interpretation of the large pT ratio data in Fig. 2.
Further analysis of the pT dependence of the Drell-Yan
cross section will be presented in a future publication.
In summary, this Letter reports a measurement of the
ratios of the Drell-Yan cross section per nucleon for Fe
to Be and W to Be. Nuclear shadowing is found to be
important in the small x2 domain. For sufficiently small
x2, the shadowing observed in Drell-Yan has been demon-
strated to be quantitatively similar to that in DIS. Sub-
sequently, a correction for shadowing has been applied.
The cross section ratios versus x1 provide direct upper
limits on the energy loss of the incoming parton as it
traverses a cold nucleus that are tighter than previous
constraints. Shadowing and initial state energy loss are
processes that occur in both Drell-Yan production and
J/ψ formation. Hence, these results should also further
the understanding of J/ψ production, which is required
if it is to be used as a signal for the quark-gluon plasma
in relativistic heavy ion collisions.
We would like to acknowledge R. Vogt for many use-
ful discussions. We thank the Fermilab Particle Physics,
Beams and Computing Divisions for their assistance in
performing this experiment. This work was supported in
part by the U.S. Department of Energy.
∗ On leave from Kurchatov Institute, Moscow, Russia.
[1] S. Gavin and J. Milana, Phys. Rev. Lett. 68, 1834 (1992).
[2] S.J. Brodsky and P. Hoyer, Phys. Lett. B 298, 165
(1993).
[3] R. Baier et al., Nucl. Phys. B 484, 265 (1997).
[4] R. Baier et al., hep-ph/9804212.
[5] D.F. Geesaman, K. Saito and A.W. Thomas, Ann. Rev.
Nucl. Part. Sci. 45, 337 (1995).
[6] M. Arneodo et al., Nucl. Phys. B 441, 3 (1995).
[7] B. Kopeliovich, Proc. Workshop Hirschegg ’95, ed. by
H. Feldmeier and W. Norenberg, Darmstadt, 1995, 102,
hep-ph/9609385.
[8] S.J. Brodsky, A. Hebecker and E. Quack, Phys. Rev. D
55, 2584 (1997).
[9] D.M. Alde et al., Phys. Rev. Lett. 64, 2479 (1990).
4
[10] E. Hawker et al., Phys. Rev. Lett. 80, 3715 (1998).
[11] K.J. Eskola, V.J. Kolhinen and P.V. Ruuskanen, Nucl.
Phys. B 535, 351 (1998); K.J. Eskola, V.J. Kolhinen and
C.A. Salgado, hep-ph/9807297.
[12] A.D. Martin et al., Eur. Phys. J. C 4, 463 (1998).
[13] H.L. Lai et al., hep-ph/9903282.
[14] M. Arneodo et al., Nucl. Phys. B 481, 3 (1996); Nucl.
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1636 (1999).
[16] E. Marco and E. Oset, Nucl. Phys. A 645, 303 (1999).
[17] Eq. 2 and Eq. 7 of [2] differ because we define
∆x1 = ∆Eparton/Ebeam. Eq. 7 of [2] uses ∆x1 =
∆Eparton/Eparton. S.J. Brodsky, private communication
(1999).
[18] X.-N. Wang, Phys. Rev. Lett. 81, 2655 (1998).
[19] Note that [4] indicates that the estimate 0.02 GeV/fm2
given in [3] should be increased by a factor of 2.
[20] R.S. Towell et al., to be submitted.
5


Physical Review Letters

Parton Energy Loss Limits and Shadowing in Drell-Yan Dimuon Production

M. A. Vasiliev

M. E. Beddo

C. N. Brown

T. A. Carey

T. H. Chang

W. E. Cooper

C. A. Gagliardi

G. T. Garvey

D. F. Geesaman

E. A. Hawker

X. C. He

L. D. Isenhower

D. M. Kaplan

S. B. Kaufman

D. D. Koetke

W. M. Lee

M. J. Leitch

P. L. McGaughey

J. M. Moss

B. A. Mueller

V. Papavassiliou

J. C. Peng

G. Petitt

P. E. Reimer

M. E. Sadler

W. E. Sondheim

P. W. Stankus

R. S. Towell

R. E. Tribble

J. C. Webb

J. L. Willis

G. R. Young

Crossref

OAKTrust Digital Repository (Texas A&M Univ)

arXiv:hep-ex/9906010v1  4 Jun 1999Parton energy loss limits and shadowing in Drell-Yan dimuon productionM.A. Vasilievi∗, M.E. Beddog, C.N. Brownc, T.A. Careyf , T.H. Changg, W.E. Cooperc, C.A. Gagliardii,G.T. Garveyf , D.F. Geesamanb, E.A. Hawkeri,f , X.C. Hed, L.D. Isenhowera, D.M. Kaplane, S.B. Kaufmanb,D.D. Koetkej, W.M. Leed, M.J. Leitchf , P.L. McGaugheyf , J.M. Mossf , B.A. Muellerb, V. Papavassilioug,J.C. Pengf , G. Petittd, P.E. Reimerf , M.E. Sadlera, W.E. Sondheimf , P.W. Stankush, R.S. Towella,f , R.E. Tribblei,J.C. Webbg, J.L. Willisa, G.R. Youngh(FNAL E866/NuSea Collaboration)aAbilene Christian University, Abilene, TX 79699bArgonne National Laboratory, Argonne, IL 60439cFermi National Accelerator Laboratory, Batavia, IL 60510dGeorgia State University, Atlanta, GA 30303eIllinois Institute of Technology, Chicago, IL 60616fLos Alamos National Laboratory, Los Alamos, NM 87545gNew Mexico State University, Las Cruces, NM, 88003hOak Ridge National Laboratory, Oak Ridge, TN 37831iTexas A & M University, College Station, TX 77843jValparaiso University, Valparaiso, IN 46383(January 11, 2018)A precise measurement of the ratios of the Drell-Yan cross section per nucleon for an 800 GeV/cproton beam incident on Be, Fe and W targets is reported. The behavior of the Drell-Yan ratiosat small target parton momentum fraction is well described by an existing fit to the shadowingobserved in deep-inelastic scattering. The cross section ratios as a function of the incident partonmomentum fraction set tight limits on the energy loss of quarks passing through a cold nucleus.24.85.+p; 13.85.Qk; 25.40.Ve; 25.75.qThe Drell-Yan process, where a beam quark (anti-quark) fuses with a target antiquark (quark) producinga muon pair, can be used to study the interactions offast partons penetrating through cold nuclei. Only ini-tial state interactions are important in Drell-Yan sincethe dimuon in the final state does not interact stronglywith the partons in the medium. This makes Drell-Yanscattering an ideal tool to study energy loss of fast quarksin nuclear matter by comparing the observed yields froma range of nuclear targets. The dynamics of fast partonenergy loss in nuclear matter is the subject of consider-able theoretical interest [1–4] and has significant implica-tions for the physics of relativisitic heavy ion collisions.Drell-Yan scattering is closely related to deep-inelasticscattering (DIS) of leptons, but unlike DIS it can beused specifically to probe antiquark contributions in tar-get parton distributions. When DIS on nuclei occurs atx < 0.08, where x is the parton momentum fraction,the cross section per nucleon decreases with increasingnuclear number A due to shadowing [5,6]. Shadowingshould also occur in Drell-Yan dimuon production atsmall x2, the momentum fraction of the target parton,and theoretical calculations indicate that shadowing inthe two reactions has a common origin [7,8]. This shouldbe particularly apparent at x < 0.06 where DIS on nuclei,like Drell-Yan, is dominated by scattering off sea quarks.Fermilab Experiment 866 (E866) measured the nu-clear dependence of Drell-Yan dimuon production by 800GeV/c protons on Be, Fe and W targets at larger valuesof x1, the momentum fraction of the beam parton, largervalues of xF (≈ x1 − x2), and smaller values of x2 thanreached by the previous experiment, Fermilab E772 [9].The extended kinematic coverage of E866 significantlyincreases its sensitivity to parton energy loss and shad-owing. This Letter reports the results.The experiment used the same 3-dipole magnet spec-trometer that was described in [10]. An 800 GeV/c ex-tracted proton beam averaging 3× 1011 protons per 20 sspill bombarded one of three solid targets or an emptytarget frame. The Be, Fe and W targets were 9.4% –19% of an interaction length thick. Their relative thick-nesses were chosen carefully to match the backgroundrates present in the spectrometer. The targets were lo-cated far upstream of the main dipole magnet to opti-mize the acceptance at low x2 and large xF . Duringa cycle, 2 beam spills were taken on each target and 1spill was collected on an empty location. After passingthrough a target, the remaining beam was intercepted bya copper beam dump, which was followed by a thick ab-sorber that removed hadrons produced in the target andthe dump. This ensured that only muons traversed thespectrometer’s detectors, which consisted of four trackingstations and a momentum analyzing magnet. The triggerrequired a pair of triple hodoscope coincidences havingthe topology of a muon pair from the target. Typically1400 triggers per second were recorded with an averagelive time of 93%.Over 130,000 muon pairs with dimuon mass in the1FIG. 1. Ratios of the measured cross section per nucleon for Drell-Yan events versus dimuon mass (in GeV/c2), x2, xF andx1. The upper (lower) panels show ratios of Fe/Be (W/Be) from the present experiment as solid circles and Fe/C (W/C) fromE772 as open circles. The errors are statistical only. The solid curves are the predicted cross section ratios, integrated over thehidden variables, from leading-order calculations using EKS98 [11] and MRST [12].range 4.0 < M < 8.4 GeV/c2 survived the data cuts.Random pairs were subtracted from the data using sim-ulated random dimuons constructed by mixing singlemuon tracks that were obtained simultaneously fromprescaled single muon triggers. The normalization factorfor the random correction was evaluated by comparingto the observed rate of same-charge muon pairs in thedata. The random rate was 9% of the real events, and itoccurred primarily at low dimuon mass and high pT . Aresidual 3% background from the empty target was alsosubtracted. The solid targets intercepted the beam atnearly the same z location, making differences in dimuonacceptance negligible. The overall systematic normaliza-tion uncertainty in the cross section ratios reported hereis 1%.The Drell-Yan events obtained by E866 extend overthe ranges 0.01 < x2 < 0.12 and 0.21 < x1 < 0.95, with〈x2〉 = 0.038 and 〈x1〉 = 0.46. They also cover the range0.13 < xF < 0.93 and provide good pT coverage to 4GeV/c. Ratios of the cross section per nucleon for Fe toBe and W to Be versus dimuon mass, x2, xF and x1 areshown in Fig. 1, along with similar results from E772 forFe to C and W to C. The figure shows very good agree-ment between the experiments for the cross section ratiosversus x2. The agreement versus other variables is alsoquite good, given the much smaller 〈x2〉 and, hence, in-creased shadowing of the present data. Note that the Adependence observed here and in E772 implies the changein the cross section ratios in Fig. 1 due to the choice ofBe versus C is small compared to the effect of the dif-ference in 〈x2〉. The reduction in the cross section pernucleon on the heavy targets, characteristic of shadow-ing, is clearly apparent at small x2. A similar reduction,part of which could be related to incident parton energyloss, is apparent at large xF and x1. However, it is im-portant to recognize that the spectrometer acceptancecoupled to the intrinsic Drell-Yan cross section leads toa strong anti-correlation between x2 and xF for the ob-served events. Therefore, the events that show the crosssection reduction at large xF and x1 are in general thesame events that appear in the shadowing region.In order to identify the contributions from shadowing,Fig. 1 also shows the predicted cross section ratios, in-tegrated over the hidden variables, from leading-orderDrell-Yan calculations using the code EKS98 [11] to-gether with the MRST parton distribution functions [12].Essentially identical results are obtained using CTEQ5Mor CTEQ5L parton distributions [13] instead. EKS98describes the ratios fA(x,Q2)/fp(x,Q2) of the variousquark flavors in nucleus A, compared to those in the pro-ton. It has been tuned to fit the shadowing observed inDIS [14] and E772 while conserving baryon number andmomentum.EKS98 provides an unbiased way to separate the ef-fects of shadowing and energy loss in the present databecause it uses a single shadowing function to describethe nuclear dependence of all sea quark distributions atits initial scale Q02 = 2.25 GeV2 and only DIS results areused to constrain that function for x <∼ 0.1. The shapeand magnitude of the ratios versus x2 are well reproducedby the shadowing predictions. Most of the A dependenceobserved in the ratios versus mass, xF and x1 can also beexplained by shadowing at small x2. As a further test ofthe shadowing parametrization, the events in Fig. 1 havebeen separated into two sets at the median x2 value. Thecross section ratios differ by up to 6% when the events2FIG. 2. Ratios of the measured Drell-Yan cross section pernucleon versus pT . Ratios of Fe/Be and W/Be from thepresent experiment are shown as solid circles, and ratios ofFe/C and W/C from E772 are shown as open circles. Thesolid curves are shadowing predictions for the present exper-iment from leading-order calculations using EKS98 [11] andMRST [12].at low and high x2 – but at the same mass, xF or x1– are observed separately. EKS98 also describes thesedifferences well. This is the first experimental demon-stration that the shadowing observed in Drell-Yan andDIS is quantitatively similar.Figure 2 shows the measured ratios of the Drell-Yancross section per nucleon as a function of pT . Unlike thelongitudinal variables that have strongly correlated ac-ceptances, the pT acceptance in E866 is nearly indepen-dent of the other kinematic variables, so the shadowingcalculations predict essentially constant cross section ra-tios versus pT , as shown by the smooth curves in the fig-ure. The data demonstrate a clear pT dependence whichmust have an independent origin. The slight reductionin the cross section per nucleon observed for heavy nu-clei at small pT , coupled with the increase in the crosssection per nucleon at large pT , is characteristic of mul-tiple scattering of the incident partons as they traversethe nucleus.The x1 dependence of the cross section ratios providesthe best direct measure of the energy loss of the incidentquarks in the nuclear medium. Table I gives the ratiosof the measured cross section per nucleon as a functionof x1, and the mean values of x1, x2 and dimuon massfor each bin. However, as shown above, shadowing atsmall x2 explains a substantial fraction of the apparentvariation in the cross section ratios versus x1. This mustbe removed before one can isolate a nuclear dependencedue to energy loss. Figure 3 shows the same cross sec-tion ratios versus x1 as given in Table I, but correctedfor shadowing by weighting each event with the calcu-lated ratio of the Drell-Yan cross sections per nucleon forTABLE I. Ratios of the cross section per nucleon for Feto Be and W to Be as functions of x1, without correction forshadowing. Also given are mean values for x1, x2 and dimuonmass (in GeV/c2) for each bin. Mean xF may be found from〈xF 〉 = 〈x1〉 − 〈x2〉. The errors are statistical only.x1 range 〈x1〉 〈x2〉 〈M〉 σFe/σBe σW/σBe0.21-0.3 0.279 0.055 4.76 1.059(41) 0.971(37)0.3-0.4 0.356 0.046 4.92 0.973(16) 0.964(15)0.4-0.5 0.448 0.039 5.07 0.959(14) 0.951(13)0.5-0.6 0.545 0.034 5.17 0.962(17) 0.944(16)0.6-0.7 0.642 0.030 5.24 0.979(25) 0.914(23)0.7-0.8 0.738 0.026 5.27 0.920(42) 0.884(40)0.8-0.95 0.836 0.023 5.28 0.960(99) 0.822(86)FIG. 3. Ratios of the cross section per nucleon versus x1 forFe/Be (upper panel) and W/Be (lower panel), corrected forshadowing. The solid curves are the best fit using the energyloss form (1), and the dashed curves show the 1σ upper limits.The dotted curves show the 1σ upper limits using the energyloss form (3). The 1σ upper limit curves using the energy lossform (2) are essentially identical to those using form (3).deuterium and nucleus A at the same (x1, x2, Q2), usingEKS98 and MRST.Several groups have studied energy loss of partons innuclei. Their results can be expressed in terms of theaverage change in the incident parton momentum frac-tion, ∆x1, as a function of target nucleus. Gavin andMilana [1] analyzed the E772 Drell-Yan data for energyloss based on the parametrization∆x1 = −κ1 x1A1/3, (1)where the factor κ1 may have a Q2 dependence. Theybased the form (1) on an analogy to the transverse spinasymmetry in direct photon production. From a com-parison to the xF dependence seen by E772 and neglect-ing shadowing, they concluded that the fractional energyloss of quarks passing through nuclei is ≈ 0.4%/fm. Re-cently, other groups have assumed equivalent formula-tions with even more rapid energy loss [15,16]. Brodsky3and Hoyer [2] argued that the energy loss found by Gavinand Milana was too large since the time scale for QCDbremsstrahlung was too short to allow for multiple con-tributions to the energy loss. Brodsky and Hoyer used ananalogy to the photon bremsstrahlung process to obtaina form for gluon radiation leading to an initial partonenergy loss [17]∆x1 ≈ −κ2sA1/3. (2)They found an upper limit for the gluon radiation fromthe uncertainty relation. They also noted that elasticscattering should make a similar contribution to the en-ergy loss. Overall, they concluded that energetic partonsshould lose <∼ 0.5 GeV/fm in nuclei. The formulation de-veloped by Brodsky and Hoyer was extended by Baier etal. [3,4]. They found that the energy loss of sufficientlyenergetic partons depends on a characteristic length andthe broadening of the squared transverse momentum ofthe parton. For finite nuclei, both factors vary as A1/3,so Baier et al. predict∆x1 ≈ −κ3sA2/3. (3)Baier et al. predict that energy loss may be different inhot and cold nuclear matter and that there could a largecoherent effect in relativistic heavy ion collisions. In con-trast, tight limits have been placed on energy loss in S+Sand Pb+Pb collisions [18], but the parton momenta rel-ative to the hadronic medium were very much smallerin those cases than in the present experiment, making adirect comparison difficult.Given these energy loss expressions, it is possible toobtain empirical values for the κ’s by performing simul-taneous fits to the Fe/Be and W/Be Drell-Yan crosssection ratios versus x1 in Fig. 3. We assume that κ1is Q2-independent [1,2] when using form (1) and thatour incident quarks are sufficiently energetic when us-ing form (3). Curves corresponding to the fits are in-cluded in Fig. 3. When assuming the form (1), we findκ1 = 0.0004±0.0009. This implies that the observed frac-tional energy loss of the incident quarks is < 0.14%/fm.For the energy loss forms (2) and (3), the best fits im-ply essentially zero energy loss. We find the 1σ upperlimits to be κ2 < 0.75 GeV2 and κ3 < 0.10 GeV2. Theκ2 limit indicates that the incident quarks lose energyat a constant rate of < 0.44 GeV/fm. The κ3 limit im-plies that the observed energy loss of the incident quarkswithin the model of Baier et al. is ∆E < 0.046 GeV/fm2× L2, where L is the quark propagation length throughthe nucleus. This is very close to the lower value given byBaier et al. for cold nuclear matter [19]. In all three cases,the quoted errors include both statistics and the overallnormalization uncertainty, with the latter dominating.One can also obtain an indirect estimate of the energyloss due to gluon radiation in the model of Baier et al.from the broadening of the 〈pT2〉 as the incident quarkpasses through the nucleus, as shown in Fig. 2. How-ever, such an analysis involves two significant difficulties.While the Drell-Yan cross section is very small for pTbeyond 4 GeV/c, the change in 〈pT2〉 from nucleus tonucleus, being the small difference of large numbers, isquite sensitive to the yield at very large pT where ouracceptance is poor and the random background becomessignificant. Meanwhile, the pT dependence of the ratioof the Drell-Yan cross sections per nucleon on hydrogenand deuterium shows possible evidence for a change inthe reaction mechanism at pT ≈ 3 GeV/c [20], compli-cating interpretation of the large pT ratio data in Fig. 2.Further analysis of the pT dependence of the Drell-Yancross section will be presented in a future publication.In summary, this Letter reports a measurement of theratios of the Drell-Yan cross section per nucleon for Feto Be and W to Be. Nuclear shadowing is found to beimportant in the small x2 domain. For sufficiently smallx2, the shadowing observed in Drell-Yan has been demon-strated to be quantitatively similar to that in DIS. Sub-sequently, a correction for shadowing has been applied.The cross section ratios versus x1 provide direct upperlimits on the energy loss of the incoming parton as ittraverses a cold nucleus that are tighter than previousconstraints. Shadowing and initial state energy loss areprocesses that occur in both Drell-Yan production andJ/ψ formation. Hence, these results should also furtherthe understanding of J/ψ production, which is requiredif it is to be used as a signal for the quark-gluon plasmain relativistic heavy ion collisions.We would like to acknowledge R. Vogt for many use-ful discussions. We thank the Fermilab Particle Physics,Beams and Computing Divisions for their assistance inperforming this experiment. This work was supported inpart by the U.S. Department of Energy.∗ On leave from Kurchatov Institute, Moscow, Russia.[1] S. Gavin and J. Milana, Phys. Rev. Lett. 68, 1834 (1992).[2] S.J. Brodsky and P. Hoyer, Phys. Lett. B 298, 165(1993).[3] R. Baier et al., Nucl. Phys. B 484, 265 (1997).[4] R. Baier et al., hep-ph/9804212.[5] D.F. Geesaman, K. Saito and A.W. Thomas, Ann. Rev.Nucl. Part. Sci. 45, 337 (1995).[6] M. Arneodo et al., Nucl. Phys. B 441, 3 (1995).[7] B. Kopeliovich, Proc. Workshop Hirschegg ’95, ed. byH. Feldmeier and W. Norenberg, Darmstadt, 1995, 102,hep-ph/9609385.[8] S.J. Brodsky, A. Hebecker and E. Quack, Phys. Rev. D55, 2584 (1997).[9] D.M. Alde et al., Phys. Rev. Lett. 64, 2479 (1990).4[10] E. Hawker et al., Phys. Rev. Lett. 80, 3715 (1998).[11] K.J. Eskola, V.J. Kolhinen and P.V. Ruuskanen, Nucl.Phys. B 535, 351 (1998); K.J. Eskola, V.J. Kolhinen andC.A. Salgado, hep-ph/9807297.[12] A.D. Martin et al., Eur. Phys. J. C 4, 463 (1998).[13] H.L. Lai et al., hep-ph/9903282.[14] M. Arneodo et al., Nucl. Phys. B 481, 3 (1996); Nucl.Phys. B 481, 23 (1996).[15] C. Gale, S. Jeon, and J. Kapusta, Phys. Rev. Lett. 82,1636 (1999).[16] E. Marco and E. Oset, Nucl. Phys. A 645, 303 (1999).[17] Eq. 2 and Eq. 7 of [2] differ because we define∆x1 = ∆Eparton/Ebeam. Eq. 7 of [2] uses ∆x1 =∆Eparton/Eparton. S.J. Brodsky, private communication(1999).[18] X.-N. Wang, Phys. Rev. Lett. 81, 2655 (1998).[19] Note that [4] indicates that the estimate 0.02 GeV/fm2given in [3] should be increased by a factor of 2.[20] R.S. Towell et al., to be submitted.5

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Parton energy loss limits and shadowing in Drell-Yan dimuon production

Parton energy loss limits and shadowing in Drell-Yan dimuon production

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