Charmonium composition and nuclear suppression

11 January

1996

PHYSICS

LETTERS

B

Physics Letters B 366 (1996) 316-322

Charmonium composition and nuclear suppression D. Kharzeev, H. Satz Theory Division,

CERN, CH-1211 Geneva, Switzerland

and Fakultiit fiir Physik, Universitiit Bielefeld. D-33501 Bielejkld, Germany Received

13 August

1995; revised manuscript received 20 September Editor: R. Gatto

1995

Abstract

We study charmonium production in hadron-nucleus collisions through the intermediate next-to-leading Fock space component 1(cZ.)sg), formed by a colour octet cE pair and a gluon. We estimate the size of this state and show that its interaction

with nucleons accounts for the observed charmonium

Charmonium production in hadronic collisions inherently involves different energy and time scales; for an extensive recent treatment, see [ 11. The first step is the creation of a heavy cE pair, e.g., by gluon fusion; this takes place in a very short time, rpert II 1/2m,. The pair is in a colour octet state; to neutralize its colour and yield a resonance state of J/I// quantum numbers, it has to absorb or emit an additional gluon (Fig. 1) . The time 7s associated to this process is determined by the virtuality of the intermediate ci; state. In the rest frame of the CC,it is approximately [ 21 (1)

c

suppression

in nuclear interactions.

where A = [ (p + k)’ - m,‘] = 2pk. For massless quarks, this gives the familiar l/k~ for the time uncertainty associated with gluon emission/absorption; for charm quarks of (large) mass m,, we get

(2)

rs=&

where k0 is the energy of the additional gluon . In a confining medium, k 2 hwc~, with AQCD 0.20-0.25 GeV. We thus encounter a new scale (2m,Aqco)‘/*, with Aqco << (2mdiQCD) ‘I2 << m,; it makes 7s >> rpert ’ . For J/t,b production at midrapidity of a nucleon-nucleon collision, the colour neutralisation time becomes ts N 7s [ 1 + (PA/%&)*]

J/V

“*

(3)

in the rest frame of target or projectile nucleon, with denoting the momentum of the CZpair in this frame. As seen from the nucleon, colour neutralisation of fast PA

Fig.

1. J/e production through gluon fusion.

0370-2693/96/$12.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0370-2693(95)01328-8

’ Such a “hybrid” first introduced in

scale, depending

on both m, and AQco, was quark mesons.

[ 31 in the study of heavy-light

317

D. Kharzeev, H. Satz/Physics Letters B 366 (1996) 316-322

cE pairs will thus take a long time. Equivalently, a fast CEtravels in the time fs a long distance, (4)

ds 11 r8(P0/%)

in the rest frame of the nucleon. On the basis of the process shown in Fig. 1, this seems to imply the existence of a coloured CE state of well-defined quantum numbers over times or distances much greater than the confinement scale of 0.8-l .O fm (corresponding to A&). This problem is particularly evident for J/(/I production at low transverse momentum, for which the additional gluon can be quite soft; in this case, however, perturbative arguments become in any case questionable. The problem seems avoidable for productionat sufficiently high pr, i.e., for large enough k~,.Hence the colour singlet model [ 4,5], which treats the complete colour singlet formation process in Fig. 1 within perturbative QCD, was usually restricted to high pr production. The low pr problem was until now usually “solved” by noting that inclusive J/e production occurs in the colour field of the collision, leaving the form of the colour neutralisation unspecified (“colour evaporation” [ 6,7] ) . Recent data [8] have shown, however, that also at high pr non-perturbative features seem to be essential for charmonium production [ 1,9]. The most important outcome of these studies (see [ IO] for a recent review) is that higher Fock space components of charmonium states play a dominant role in their production. We thus decompose the J/$ state I@) I@,)-aOI(c + a2)(@1@)

+alI(c‘?8&+ + a;/(@8&?)

+ ...

(5)

into a pure cE colour singlet component ( 3Sr ), into a component consisting of CScolour octet ( ‘& or 3PJ) plus a gluon, and so on. The higher Fock space coefficients correspond to an expansion in the relative velocity u of the charm quarks. As we shall see below, this corresponds in coordinate space to an expansion in terms of components of decreasing spatial extension. For the wave function of the J/e, the higher components correspond to (generally small) relativistic corrections. In high energy J/G production, however, the short time available before confinement constraints appear favours colour neutralisation of the (05) 8 by gluons already present (Fig. 2). Since (CC) prduction at high energies occurs at small X, the density of

Fig. 2. J/q? production via (c@) colour singlet.

L

Fig. 3. Transition

from (CR)

colour singlet to CC colour singlet.

such comoving gluons is in fact high. Hence the higher Fock space components become dominant. Analogous Fock space decompositions hold for the other charmonium states [ 1,9]. In all cases, the first higher state consists of a colour octet cc plus a gluon. For the @‘, the next-to-leading terms again contain a colour octet (3P, or ’ SOCC) plus a gluon; for the x’s, a 3S1 colour octet cc is combined with a gluon. This sheds some light onto the unspecified colour evaporation process. When the colour octet cc leaves the field of the nucleon in which it was produced, it will in general neutralize its colour by combining nonperturbatively with an additional collinear gluon, thus producing the (cc) 8g component of the J/t,b or the other charmonium states (Fig. 2). After the “relaxation time” 78, the (cc) sg will then absorb the accompanying gluon to revert to the dominant (cc) I charmonium mode (Fig. 3). Note that we are here considering those cE pairs which will later on form charmoma. The (cc) 8 could as well neutralize its colour by combining with a light quark-antiquark pair, but this would result predominantly in open charm production. The production of high energy charmonia thus implies the production of composite and hence extensive states (cCg)i E 1(cC)8g)i; here the subscript i refers to the specific charmonium state in question (J/t++, xc, I/‘). Although the intrinsic transverse size of the (cEg) i depends in principle on the quantum numbers of the state i, confinement constraints on the gluon lead to a universal (c?g) size rs. Let us consider this in more detail. The formation process of the cE pair in the (cc’g)

D. Kharzeev, H. Sarz / Physics Letters B 366 (1996) 3 16-322

318

state (see Fig. 2) makes this pair very compact, with a spatial extension of about 1/2m,. The size of the (c?g) is thus essentially determined by the softness of the gluon, which is restricted by k > Aqc~. The effect of this can be estimated by noting that in the time 7s obtained above, a gluon can propagate over a distance rs !? (kkAQc~)-~‘~. Equivalently, we can consider energy conservation in the passage from (c?g) to the leading Fock space component (cc) I (Fig. 3); the non-relativistic form for heavy quarks leads to

p2 Tip

k.

(6)

’

where p is the quark three-momentum in the charmonium ems. From the lowest allowed gluon energy ko = AQCD we thus obtain the intrinsic size rg % $ 2! d&

2/ 0.20-0.25 fm .

(7)

Since this size is determined only by the (cc) gg composition of the next-to-leading Fock space state, the compactness of the produced (cE) 8 in this state and the gluon momentum cut-off in confined systems, it is essentially the same for the different charmonium states. The Fock space state (c?g) thus constitutes something Iike a gluonic hard core present in all charmonium states. Its size is seen to be approximately that of the ground state charmonium J/I+, while the higher excited charmonium states are larger. The hard gluon core in these just corresponds to the fact that in extended bound states the emission (or absorption) of gluons with momenta bigger than hwo can occur Only in a sufficiently small inner region. In other words: while the basic (CC), state gives for different quantum numbers quite different spatial distributions, the much more localized higher Fock space states are of universal size 2 (2m,&o) -‘j2. It would be interesting to confirm our result (7) by explicit calculation of the the spatial extension associated to the higher Fock space components of different charmonium states. We now want to study the effect of these considerations on J/(cr production in proton-nucleus collisions. For low PT production, with ko ISI&CD in Eq. (2), tg would exceed the size of the even heavy nuclei for 2 In the large quark mass limit, however, the bound state radii become smaller than (hQil~D)-‘/~,

so that the universality

would then be lost. For a related discussion, see

[ 1I].

J/#‘s of sufficiently high lab momenta (see Eq. (3) ). Maintaining an approach based on the colour singlet model would thus require a colour octet CC to pass through the entire nuclear medium [ 2,12-151. The composition of the colour-neutralizing cloud needed for this was so far undetermined, and hence estimates for the resulting cross sections were generally obtained by assuming such a dressed (c@s to be of hadronic size [ 2,12,16]. It was also left open why interactions with the surrounding cloud would not destroy the spatial and quantum number structure of the (cc) 8. Quarkonium production through higher Fock space components now provides a specific description of the (cc) 8 passage through the nucleus. The system leaves the nucleon in whose field it was formed as the colour singlet (c?g) and continues as such through the nuclear medium. Since the size of the common gluonic core, given by Eq. (7)) is approximately that of the J/I,+, we expect the cross section for its interaction with light hadrons to be comparable, apart from colour factor differences. Short distance QCD leads for high energy quarkonium-nucleon interactions to the geometric cross section [ 171 (8)

where reG is the quarkonium radius. The strong coupling constant LY.~ (at the scale corresponding to rcegj ) arises from the coupling of an exchanged gluon to one of the heavy quarks. For J/$-nucleon interactions, Eq. (8) gives 2.5-3 mb. To extend this result to (cEg) -nucleon interactions, we therefore have to take into account that the gluon exchanged between the two colliding systems will now couple predominantly to the gluon or to the ( CE)s component of the (c@) . Since both are colour octets, in contrast to the colour triplet heavy quarks, the coupling is correspondingly enhanced by a factor $. Note that since Eq. (8) includes interference terms between the different contributions, this enhancement does not imply an incoherent sum of gluon and (cc)8 interactions; it is just a resealing of the coupling strength. A (ci;g) -nucleon interaction by gluon exchange will make the system coloured. Due to the repulsive onegluon exchange interaction, the colour octet (cc)8 iS not bound, in contrast to the colour singlet (cc) I. Moreover, the probability of the (~2)s encountering another collinear gluon to again form a colour singlet

D. Khurzeeu, H. Satz/ Physics Lerrers B 366 (1996) 316-322

319

Moreover, since the cE combines with an already existing collinear gluon, there is no coherence length associated with any (cCg) formation. Hence shadowing through destructive quantum-mechanical interference [ 18,191 is excluded as dominant quarkonium suppression mechanism in p-A collisions. In passing through the nucleus, the small physical state (cCg) will interact incoherently with the nucleons along its trajectory. The charmonium production probability on nuclei relative to that on nucleons, valid for J/t,b. ,y and @’ production, thus becomes (10)

l

J/y

NA38

.

J/I+I

E 772

c

A

0.5

0

r

\

E 772

I

I

/

I

I

I

1

2

3

4

5

6

7

LA [fml Fig. 4. J/+ and Y suppression in p-A collisions; data [22,24] are compared to (c@) suppression (Eq. ( IO) ) in nuclear matter and to the corresponding form for (hbg).

system of J/# quantum numbers is minimal. Hence any (c?g) interaction will generally lead to its breakup, so that there is no threshold factor and the whole geometric (cCg) -nucleon cross section corresponds to (c?g) break-up. Eq. (8) gives u(,?~)N 2: 6 - 7mb

(9)

for the value of this cross section with LY,at the charmonium scale. The cross section (9) thus describes the common “pre-resonance” break-up of J/$, xc and (jl’ by hadrons. This cross section, while larger than the high energy J/e--hadron cross section by about a factor two, is very much smaller than the hadronic value of 20-50 mb previously assumed for the colour octet CF passing through the nucleus [ 2,12,16]. This has immediate consequences. The mean free path of the (c?g) in nuclear matter, A(+) = l/ne~~,~~,~ II 10 fm is larger than the radius of even the heaviest nuclei.

where L denotes the length of the path through nuclear matter of standard density no = 0.17 fmP3, and g(fzg)N rv 6-7 mb is the inelastic (cCg) -nucleon cross section obtained above. With Eq. ( 10) we have derived the Gerschel-Hiifner fit [ 201, introduced as a phenomenological description of hadron-nucleus data on J/(/I production. In [ 201, it was attempted to interpret the cross section entering in Eq. ( 10) as the physical J/+hadron cross section, which led to theoretical as well as experimental problems. The fit value was 5-7 mb; both short distance QCD [ 171 and photoproduction experiments [ 211 give a J/&hadron cross section smaller by at least a factor two. Moreover, p-A data [ 22,231 lead to exactly the same suppression of I,# and J/S production for all A, with an A-independent production ratio $‘l (J/t++>cv 0.15. Since the geometric cross section of the ground state J/$ and the next radial excitation differ by more than a factor four, an equal suppression contradicts the interaction of fully formed physical resonances. We find here that all aspects of the observed suppression arise naturally in charmonium production through the next higher Fock space component (ccg) . A composite hard core state (cEg) of the same size for all charmonia passes through the nuclear medium and hence leads to equal r,Vand J/G suppression. The value of the cross section ‘+ccEg)~thus obtained is in good agreement with that obtained from a fit to the data [20]. The same argumentation also provides the suppression of bottomium production in p-A collisions. The radius of the (b6)sg state is smaller by a factor dx = 1/J?; than that of the (ccg) (see Eq. (7)); combined with the reduction of (Y.~,this

D. Kharzeev. H. Satz/Physics Letters B 366 (1996) 316-322

320

0.2

0

ill~~““‘llA

E 772 Y

0

NA38

I+’

2

4

6

8

10

12

L Pm1

Fig. 5. J/t+b, 9

and Y suppression

in p-A and S-U collisions,

leads to aCbbgjN2 1S-2 mb. To illustrate how well both J/$ and Y production in p-A collisions are described by this scenario, we show in Fig. 4 recent high energy data at fi N 20 [ 23],30 [ 241 and 40 GeV [ 221. With an average path length 1)/A][1.12A’/3] weobtainexcellent LA - :[(Aagreement for (T(,~~)NN_6 mb and u(,~~)~ N 1.5 mb. In [ 201 it was shown that J/t,b production data from T-A collisions lead to very similar values for the cross section in Eq. (9). With quarkonium suppression in hadron-nucleus collisions thus accounted for in terms of interaction between (QQ)sg states and nucleons, we can now also consider nucleus-nucleus interactions. For collision energies of fi 21 20 GeV, the centers of the two colliding nuclei have at time tg separated in the ems by about 0.5 fm. With the nuclei Lorentz-contracted to a thickness of about 0.5 fm or less, this means that a J/t,13produced at mid-rapidity in the ems has experienced in its early phase an effect corresponding to that obtained by superimposing the passages through the two nuclei [ 201. Hence the charmonium suppression now is given by S(A-B)

‘exp[-~~(&+4(LA

f

LB)]

(

(11)

again in accord with the phenomenological fit of [ 201.

nonnalised

to (cCg) and (l&g) suppression

in nuclear matter.

The path length L = LA + LB in Eq. (11) varies with impact parameter and hence with the associated transverse energy ET produced in the collision. A relation between L and ET can thus be obtained through a detailed study of the collision geometry [ 251. An alternative is given by determining f. through the broadening of the average transverse momentum of J/q or Drell-Yan dileptons, since this broadening also depends on the average path length [ 261. In Fig. 5 we show the resulting values [ 231, normalised to the (c?g) suppression of Eqs. ( 10) and ( 11)) for both p-A and S-U data. We conclude that also the J/I) suppression observed so far in S-U collisions is completely accounted for by (cCg) suppression in standard nuclear matter. The comparison of J/I) and $’ production in nucleus-nucleus collisions provides a test for the presence of a medium in the later stages. As long as the interaction leading to charmonium suppression is determined by the (ci’g) state, J/S and (jl’ must be equally suppressed. To make J/S and $’ suppression different, the medium must see the fully formed resonances and distinguish between them. In Fig. 5 we have included also the $’ suppression divided by the (ccg) suppression [ 27,231. It is evident that in S-U collisions J/e and 9’ are not affected equally, the

D. Kharzeeu, H. Satz/Physics Letters B 366 (1996) 316-322

1+3’ being much stronger suppressed. This establishes the presence of a medium at a time late enough for fully formed charmonium resonances to exist. On the other hand, this medium breaks up only the $‘, leaving the J/I/ unaffected. It was shown [ 171 that interactions with hadrons in the range of present collision energies cannot dissociate a J/I)/, while for the much more loosely bound $’ this is readily possible. We therefore conclude that the medium probed by charmonium production in present S-U collisions is of hadronic nature, i.e., confined; it could consist of stopped nucleons and/or of secondary hadrons produced in the collision [ 281. Note that we include the I,,+’data as function of L in Fig. 5 simply to show the additional suppression present in this case. It is not at all clear that L is a meaningful variable for the effect of such a confined environment on charmonia. We also note that the apparent absence of any effect of this medium on the observed J/S, even though this is to about 40% produced through x decay, is in accord with the short distance QCD form of the x-hadron cross section [ 291. To establish colour deconfinement, either in equilibrium or pre-equilibrium systems, nucleus-nucleus collisions have to produce a J/I) suppression beyond that given by Eq. (lo), i.e., beyond that found in pA collisions [ 201, and different from I,&’suppression. If such an additional suppression were found, the results for inelastic J/+hadron collisions obtained from short distance QCD [ 171 would rule out a confined medium, and the difference in J/t) and (jl’ suppression would exclude (c?g) interactions as a source. In summary: we study quarkonium production in hadron-nucleus collisions through the intermediate next-to-leading Fock space state consisting of a colour octet cc and a gluon. We estimate the inelastic (cEg) -nucleon cross section and use this to show the same pre-resonance suppression in nucIear matter for all charmonium states; exclude shadowing based on destructive interference as main origin for the quarkonium suppression observed in hadron-nucleus interactions; derive the Gerschel-Htifner fit describing such suppression, both for cE and bb states; conclude that the J/S suppression observed in SU collisions is fully accounted for by early (CQ) interactions with standard nuclear matter; conclude that the stronger 9’ suppression found

321

in S-U collisions is due to an additional confined medium present at a later stage. It will be interesting to see if the results of forthcoming Pb-Pb collisions can provide first indications for deconfinement - in particular, if they show a stronger J/I) dissociation than accounted for by (ci’g) interactions. We thank A. Capella, C. Gerschel, A. Kaidalov, C. Lourenco and M. Mangano for stimulating and helpful discussions. The support of the German Research Ministry BMFT under contract 06 BI 721 is gratefully acknowledged. References

[II

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