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arXiv:hep-ph/0210105v1 7 Oct 2002

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Tomography of nuclear matter:

Comparing Drell-Yan with deep inelastic scattering data

Fran¸ cois Arleoa

aECT* and INFN, G.C. di Trento,

Strada delle Tabarelle, 286

38050 Villazzano (Trento), Italy

We set tight constraints on the energy loss of hard quarks in nuclear matter from

NA3 Drell-Yan measurements. Our estimate then allows for the description of HERMES

preliminary deep inelastic scattering data on hadron production.

A lot of new exciting data indicating a significant depletion of large p⊥hadron production

in central Au-Au collisions (√sNN= 200 GeV) have been presented at this conference [

1]. This observed jet quenching can naturally be interpreted as coming from the large

energy loss of hard quarks traveling through a quark-gluon plasma [ 2]. Therefore, it

becomes of first importance to determine (and contrast) what is the quark energy loss in

a cold QCD medium such as nuclear matter. This question is addressed in the present

proceedings.

The induced gluon spectrum radiated by a high energy quark propagating through a

medium of length L is characterized by the energy scale, ωc= 1/2 ˆ qL2. As a consequence,

the mean energy loss suffered by the hard parton is given by the so-called transport

coefficient ˆ q, proportional to the number of scattering centers in the medium. While

perturbative estimates have been given [ 2], we would like here to set some constraints

on its absolute value from experimental data. What would be the best processes to do

so ? Not only sensitive to the rescattering of high energy partons in the medium, an ideal

candidate should furthermore be independent of any other nuclear effect, such as nuclear

absorption or shadowing. We shall discuss here two mechanisms that appear promising

to achieve such a goal:

• Drell-Yan process (DY). It proves indeed particularly suited as the lepton pair does

not strongly interact with the surrounding medium. The only caveat comes from

the unknown shadowing corrections that might affect significantly the DY yield in

nuclei.

• Hadron production in deep inelastic scattering (DIS) data. The virtual photon

couples to a quark which subsequently suffers energy loss while escaping the nuclear

medium. This process will however be sensitive to the nuclear absorption of the

hadron produced inside the medium when the quark energy is not large enough.

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While the former is sensitive to the multiple scatterings of a quark approaching the nu-

cleus, the latter rather probes the energy loss experienced by hard quarks produced in

the medium (see schematic illustration below). These two mechanisms prove therefore

complementary for the study of quark energy loss in nuclear matter. We shall first dis-

cuss how DY data in π−-A collisions allow for a determination of quark energy loss in a

large nucleus. Taking this estimate, the quenching of hadron spectra in electron-nucleus

collisions is computed and compared to HERMES preliminary data [ 3].

γ

q

h

g

−

l

l

−

+

−

γ

g

q

h

l

l

( a )( b )

Figure 1. Two processes sensitive to quark energy loss in nuclear matter: (a) Drell-Yan

process in h-A collisions, (b) hadron production in deep inelastic scattering on nuclei.

Drell-Yan process

In the absence of nuclear effects, the leading-order (LO) DY production cross section

in hadron-nucleus reactions is given by

dσ(hA)

dx1

=8πα2

9x1s

?

q

e2

q

?dM

M

?

Z

?

fh

q(x1)fp

¯ q(x2) + fh

¯ q(x1)fp

q(x2)

?

+(A − Z)

?

fh

q(x1)fn

¯ q(x2) + fh

¯ q(x1)fn

q(x2)

??

(1)

where x1(resp. x2) is the momentum fraction carried by the beam (resp. target) parton,

√s the center-of-mass energy of the hadronic collision, and M = x1x2s the invariant mass.

As long as the parton densities do not show any isospin dependence (fp

DY cross section (1) is proportional to the atomic mass number A. Hence the measured

ratio in a heavy over a light nucleus

i(x2) = fn

i(x2)), the

Rh(A/B,x1) =B

A

?dσ(hA)

dx1

?

×

?dσ(hB)

dx1

?−1

(2)

is equal to one. However, the multiple scatterings encountered by the incoming (anti-)

quark reduce its momentum fraction from x1+ ǫ/Ehto x1at the point of fusion, ǫ being

the energy loss and Ehthe beam energy in the nucleus rest frame. As a consequence, the

projectile parton distribution function should be evaluated at (x1+ ∆x1) in the nuclear

cross section (1). Because the parton densities dramatically drop at large x1, even a tiny

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shift ∆x1may substantially suppress the DY yield in large nuclei. In the general case,

the DY cross section reads

dσ(hA)

dx1

=

8πα2

9x1s

?

q

e2

q

?dM

M

?

dǫDin(ǫ,x1Eh) ×

?

+Zfh

Zfh

q(x1+ ∆x1)fp/A

¯ q

(x2) + (A − Z)fh

(x2) + (A − Z)fh

q(x1+ ∆x1)fn/A

¯ q

(x2)

¯ q(x1+ ∆x1)fp/A

q

¯ q(x1+ ∆x1)fn/A

q

(x2)

?

,(3)

where Din(ǫ,Eq) is the probability that an incoming quark (with energy Eq) suffers an

energy loss ǫ [ 4]. Furthermore, the effects of shadowing are taken into account through the

nuclear parton densities of the target parton, fp/A

been fitted to NA3 data in Eπ− = 150 and 280 GeV pion induced reactions on hydrogen

and platinum targets, with the mean energy loss per unit length (hence, the transport

coefficient) being the only free parameter in the calculation. We found

i

(x2) ?= fp

i(x2). The cross section (3) has

−dE

dz

[GeV/fm] = −ωc

9L= (0.4 ± 0.3) ×

?

L

10fm

?

(4)

which corresponds to a transport coefficient1ˆ q = 0.72 ± 0.54 GeV/fm2. Moreover, it is

worth emphasizing that this fitted value does not depend much on shadowing corrections [

5]. Taking this estimate, we now investigate the effect of quark energy loss on the hadron

spectra measured in deep inelastic scattering.

Hadron production in deep inelastic scattering

The HERMES collaboration at DESY recently reported on hadron yields measured in

electron-nucleus collisions [ 3]. They measured the production ratio

Rh

A(z,ν) =

1

Ne

A(ν)

Nh

A(z,ν)

dν dz

?

1

Ne

D(ν)

Nh

D(z,ν)

dν dz

(5)

in a “heavy” (N and Kr) over a light (D) nucleus for a given hadron species h. Here, ν

denotes the virtual photon energy in the lab frame, z the momentum fraction carried by

the produced hadron, and where the multiplicity of produced electrons Ne

hadron yield Nh

Assuming for simplicity only the valence up quark to contribute when x is not too small,

Eq. (5) will approximately be given by the ratio of the u → h fragmentation functions

?

Therefore, the nuclear dependence of the fragmentation functions might be revealed

through the measure of Rh. Because of the shift in the quark energy from Eq ≃ ν to

1Note that in [ 5] we used the BDMPS mean energy loss ?ǫ? = ωc/3 (valid for outgoing quarks), while we

take here the correct Eq. (48) of [ 6] for incoming quarks, hence the discrepancy between the transport

coefficient. The energy loss per unit length, fitted to the data, remaining of course unchanged.

Anormalizes the

A. The hadron multiplicity in (5) can be computed in perturbation theory.

Rh

A(z,ν) ≃ Dh

u(z,Q2,A)Dh

u(z,Q2,D).(6)

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Eq≃ ν − ǫ at the time of the hadronization, the nuclear fragmentation functions may be

modeled according to [ 7]

z Dh

f(z,Q2,A) =

?ν−Eh

0

dǫ Dout(ǫ,ν − ǫ) z∗Dh

f(z∗,Q2).(7)

with z∗= z/(1−ǫ/ν). Taking the transport coefficient previously extracted from DY data,

the ν dependence of Rh(ν) in a krypton over a deuterium target is computed2(Figure 2).

The trend is well reproduced for all hadron species, although the calculation for the pions

(π++ π−) somehow underpredicts the effect.

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

h

Rh(ν)

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

π+

π-

0.4

0.5

0.6

0.7

0.8

0.9

1

101520

ν (GeV)

Rh(ν)

K+

PRELIMINARY

0.4

0.5

0.6

0.7

0.8

0.9

1

101520

ν (GeV)

K-

PRELIMINARY

Figure 2.

uation

for various hadron

species

to HERMES pre-

liminary data.

Atten-

ratio (5)

compared

We showed that both the DY process as well as hadron production in DIS turn out to

be very sensitive to the energy loss of fast quarks traveling through nuclear matter. Using

the transport coefficient previously extracted from NA3 DY measurements, the quenching

of hadron spectra proved in good agreement with HERMES preliminary data.

REFERENCES

1. Contributions by PHENIX, PHOBOS, and STAR collaborations, these proceedings.

2. R. Baier, (2002), these proceedings (hep-ph/0209038) and references therein.

3. HERMES, V. Muccifora et al., (2001), hep-ex/0106088.

4. F. Arleo, (2002), hep-ph/0210104.

2We use the GRV98 LO parton densities [ 8] with the Kretzer parameterization for the fragmentation

functions [ 9].

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5. F. Arleo, Phys. Lett. B532 (2002) 231.

6. R. Baier, Yu.L. Dokshitzer, A.H. Mueller and D. Schiff, Nucl. Phys. B531 (1998) 403.

7. X.N. Wang, Z. Huang and I. Sarcevic, Phys. Rev. Lett. 77 (1996) 231.

8. M. Gl¨ uck, E. Reya and A. Vogt, Eur. Phys. J. C5 (1998) 461.

9. S. Kretzer, Phys. Rev. D62 (2000) 054001.