ψ suppression in nuclear collisions by rescattering of secondary hadrons

Volume 243, number 1,2

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21 June 1990

-enhancement and suppression in nuclear collisions by rescattering of secondary hadrons Peter K o c h a,1, Ulrich H e i n z a,2 a n d J a n Pi~tit b a Institutj~r TheoretischePhysik, Universit~itRegensburg, Postfach 397, D-8400Regensburg, FRG b DepartmentofTheoreticalPhysics, Comenius University, MlynskdDolina, F2, CS-842 15Bratislava, Czechoslovakia Received 14 February 1990

We point out that recent indications from the NA38 Collaboration for an increase of the ¢/(to + p°) ratio in central 200A GeV O + U and S + U collisions at CERN give evidence for an approach to chemical equilibrium in these systems. Under the assumption (which is supported by previous theoretical work) that the J / ¥ suppression found in the same experiment under similar kinematic conditions is due to final state absorption via rescattering in the dense collision zone, we solve the rate equations for Oproduction and -absorption via secondary collisions in the reaction zone. Eliminating unknown geometrical parameters of the collision zone by using the J / ~ suppression data, we obtain a quantitative description of the measured Q enhancement.

I. Introduction In the search for quark-gluon plasma ( Q G P ) formation in relativistic heavy-ion collisions much excitement was created by the discovery by the NA38 Collaboration [ 1,2 ] that the production of J / ~ mesons is suppressed in central O + U and S + U collisions at 200A GeV, compared to peripheral nuclear collisions and p + U collisions. This discovery followed the prediction by Matsui and Satz [ 3 ] that such a suppression should be a clean Q G P signature. Subsequently much work was done to obtain a quantitative fit of the data assuming QGP formation in these collisions [4], but it was also found that it is not impossible to explain the experiments without resort to QGP, but by assuming the formation of a very dense "gas" of hadronic resonances in which the J/O mesons can rescatter and dissociated [ 5 ]. Also a combination of both mechanisms has been suggested [6]. Actually, the transverse m o m e n t u m dependence of the suppression effect [ 1,2] is straightforwardly explained [7] in terms of initial state interactions Supported by Bundesministerium f'tir Forschung und Technologie (BMFT), grant 06 OR 764. 2 Supported in part by Deutsche Forschungsgemeinschaft (DFG), grant He1283/3-1.

(multiple gluon scattering in the target material before formation of the ce pair) and is completely analogous to a similar effect seen in p + A collisions (see, for example, ref. [ 8 ] ). The QGP interpretation of this dependence [ 4 ] relies on the concept of a fixed classical formation time for the J/~g and fails when the problem of J/~g formation and dissolution is studied in a quantum mechanical context [ 9 ]. On the other hand, the required initial panicle densities in the hadronic scenarios of well above 1 particle/fm 3 are embarrassingly large and also stretch this interpretation to the limits of its applicability. New information from the NA38 experiment on the production of 0, pOand to mesons in p + U , O + U and S + U collisions at 200A GeV [ 10] might throw new light on this ambiguous situation. The experimental findings are as follows: After a PT cut which reduces substantially the combinatorial background from kaon and pion decay muons, the measured la+ls spectra now show also evidence for the ~, pO and to vector mesons: a clear double peak structure in the muon pair mass region from 0.6 to 1.2 GeV is seen in a restricted sample containing only muons with pT>0.7 GeV/c. (Note that this cut effectively restricts the Pr of the vector mesons to PT> 1.3 G e V / c.) By fitting it under the assumption of equal production cross sections for to and pO, a ~ / (to + pO) ratio

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is extracted. Subdividing the data into bins with different amounts of produced transverse energy ET seen in the calorimeter (which is indicative for the centrality or "violence" of the nuclear collision), one observes a systematic increase of the 0 / ( t o + p °) ratio with ET (see fig. 2), while at the same time the ( J / v ) / c o n t i n u u m ratio systematically decreases [ 1 ] (see fig. 1 ). The data presented in ref. [ 10 ] also allow to extract a 0/continuum ratio and its ET dependence. One observes qualitatively the same behaviour as for the 0/(to + pO) ratio, indicating that po and to production scales essentially in the same way as the continuum when going from peripheral to central collisions. Fig. 2 shows that with increasing centrality of the nuclear collisions the 0/(to + pO) ratio increases to up to a factor of 3 above the ratio observed by the same Collaboration in p + U collisions. Over the same ET range a suppression of J / ~ by roughly a factor 2 was observed [ 1 ]. The new observation parallels the one by the NA35 Collaboration [11,12] in S + S collisions, where an enhancement of the ratios of kaons and A's (containing strange quarks) over the total multiplicity (dominated by non-strange hadrons) as a function of centrality of the collision was seen. Both findings point towards enhanced strangeness production in central A-A collisions. In this letter we analyze whether it is possible to account for this approach towards chemical equilibrium in terms of additional 0 production by secondary collisions within a hot hadronic fireball formed in the collision. We solve the rate equations for secondary O-production and -absorption, using measured rapidity distributions from pp collisions as input to describe the initial conditions created by the superposition of primary N - N collisions in the heavyion collision. Some poorly known geometric parameters, like the relationship between volume of the collision region and produced transverse energy, or the lifetime of the fireball, are eliminated by using the data on J / ~ suppression and assuming that the latter can be explained entirely by rescattering effects, too. We find a quantitative description of the ¢ enhancement and its ET dependence, thereby linking the interpretation of the two effects. Other possible mechanisms for the 0 enhancement were also studied and will appear in a longer article [ 13]. We found that nuclear modifications of the 150

21 June 1990

primary N - N collisions cannot account for the data, but that a qualitative explanation is easily achieved by assuming that in these collisions an Er-dependent fraction of all events end up in an initial QGP phase in which strangeness is chemically equilibrated by gluon fusion into q£1 pairs. (A different version of this idea has been discussed in ref. [14].) Based on an improved version of the equilibrium 0/(to + po) ratio from a hadronizing Q G P [ 15,13 ], we argued that the observed 0 enhancement of a factor -~ 3 over the p + U result corresponds to about 50% of the maxim u m effect possible in such a model, which is again consistent with the observed J / ~ suppression which is also about 50%. Thus the combined interpretation of both effects remains ambiguous: a more detailed analysis both in theory and experiment will be necessary to decide which should be the preferred description.

2. Chemical kinetics for vector mesons

We study here the following picture for the nuclear collision process: Hadrons are produced initially in primary N - N collisions by a soft production mechanism (e.g. independent string fragmentation). In any such model most hadrons are produced close to the central rapidity on a proper time scale of approximately Zo~ 1 fro. We shall describe this centrally produced matter in terms of average densities which depend on the impact parameter of the nuclear collision, without, however, requiring that the averages should be calculated assuming thermal or chemical equilibrium. If the density of produced particles is large enough (or the mean free path is smaller than the size of the collision region), they can rescatter and absorb or produced even more hadrons. Such rescattering processes, given enough time to go on, could eventually drive the central rapidity region towards thermal and chemical equilibrium. In order to achieve a consistent description of rescattering effects on all relevant channels, we will consider the evolution of the vector mesons V=J/~, O, oJ, p in parallel. After an initial abundance has been established for each one of them by the primary collisions between projectile and target nucleons, secondary production can occur from other species i and j via processes of the type i + j ~ V+X, while losses

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arise from absorption in a collision with species l, V + l ~ X . In the central rapidity region these processes are probably dominated by meson-meson collisions, with i, j, l describing mesons which were themselves also created in primary N - N collisions. This results in the following variation of the number of vector mesons per unit volume and time, expressed as a sum of gain and loss terms:

dNv - ~ (av)~Xpi(x)&(x)&(x) d4x - ~ (av)~.~pl(x)pv(x).

( 1)

l

Here the ( o r ) o are the relevant cross sections averaged over the the momentum distribution of the colliding particles, and the Pi are the space-time-dependent particle densities. Immediately after formation, the hadron matter will begin to expand. For the collision geometry we assume that for a given impact parameter all hadrons are contained in a tube with a transverse extension given by the overlap of the the two nuclei. We use cylindrical space-time variables with the longitudinal proper time z = ~ , space-time rapidity y = ½In [ ( t + z ) / ( t - z) ], and transverse coordinates s. The space-time volume element is then given by d 4 x = z dr dy ~ , and the densities can be written as pk ( X ) = dNk ( X ) / z dy ds. For the expansion dynamics we assume longitudinal boost invariance [ 16 ], i.e. physical quantities are taken to be constant along proper-time hyperbolae and thus independent of y. Although no extended rapidity plateau is seen in the present CERN experiments we expect such a picture to be approximately valid in the most central rapidity interval 2
pi(z, y, s) =pi(ro, s)

Z_o. 12

(2)

For strange hadrons there will be additional time-dependence from secondary production and absorption processes, eq. ( 1 ). For the vector mesons, which are the focus of our interest, we keep this explicitly. The effect of other strange hadrons in eq. ( 1 ) is small,

21 June 1990

due to their small abundance compared to the nonstrange channels and their generally smaller cross sections. Thus using for them the simple law (2), too, seems to be a reasonable first approximation. The assumption in eq. (2) that the abundancies of non-strange hadrons like ~, P, 11and (o are not changed appreciably by final state interactions, i.e. that for them secondary production is balanced by absorption, crucially simplifies the problem. It can be justified by the observation that in hadronic collisions momentum spectra and absolute yields of the most abundant produced hadrons are well described by thermodynamical and hydrodynamical models assuming local thermal and chemical equilibrium [ 17 ]. (Only for strange hadrons this picture breaks down in a qualitative way, being produced at levels much below chemical saturation. ) Once particle abundancies are very close to phase-space saturation their numbers will not change anymore. In order to cast eq. ( 1 ) into a more intuitive form we define production (P) and annihilation (A) rate factors

~.~= *o Z <'rv>~Xa,aJ, r i,j

~v= Zo

7 E <~v>,.'fva,.

(3)

Here aj is the density of species j normalized to the total charged multiplicity, aj=

~j('~O, *)

peh(ZO, S)

--

dNJdyds d N c J dy da "

(4)

According to (2) this ratio is time-independent. The rate equation ( 1 ) can then be rewritten as

d[dUv\ vdNch [2 v dNeh d--z~d-~) = 2 A d - ~ ~2--~d y d s

~dNv y y ~_)

(5)

This expression shows explicitly the dependence on the charged multiplicity which itself is directly proportional to the total transverse energy produced in the collision [ 18 ]. As long as the vector mesons are rare (i.e. at a level below their saturation value), eqs. (3), (5) show that their production increases quadratically, but their absorption only linearly with charged multiplicity. If the secondary production cross sections are not too small (as will be shown to be true for ~ mesons), we can in this case have addi151

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tional production with increasing multiplicity or transverse energy production. On the other hand, we already argued that the vector mesons p and co (which constitute a large fraction of the charged particle multiplicity) are produced already in the primary collisions at a level close to saturation; thus for them both secondary production and absorption processes depend quadratically on the charged multiplicity, and we expect practically no change of their abundancies with dN¢h/dy. This seems to be consistent with the NA38 findings [ 10]. Eq. (5) can be directly integrated over time:

dNv(3) - dyds

dNv(Zo)

- - dyds

exp[-Av(3)]

dNch 2pV { 1 - e x p [ - A v ( 3 ) ] }

+ dy--

)t v dNeh = A d - ~ ln(~o).

(6)

(7)

(8)

Using eq. (3) one sees that this is simply the ratio between the gain and loss terms in eq. ( 1 ); in the form given here it relates explicitly the vector meson to total multiplicity ratio from the primary N - N collisions to the ratio between vector meson production and absorption rates in secondary collisions. In terms of Rveq. (6) can be recast into

dNv(3)/dy ds dNv(3o)/dy ds (9)

One sees that the two driving parameters of the kinetic evolution are the ratio Rv and the absorption factor A v. For large absorption cross sections or after long times (large values of Av) one approaches the limit d N v ( 3 ) / d y ds =Rv, dNv( ~o)/ dy ds

~ (aV)(va,

It should be noted that in eqs. (6), (7) dN~Jdyds is the charged multiplicity at time 30, i.e. as it was produced by the primary N - N collisions. Thus our assumptions imply that there is no additional production of multiplicity due to rescattering between the produced particles in the central rapidity region. (This does not exclude an increase of multiplicity density in the fragmentation regions due to cascading of produced particles in the cold projectile and target spectator regions. ) This feature is consistent with an analysis by Ga2dzicki et al. (NA35 Collaboration) [ 12 ] for symmetric S + S collisions which concludes that the average multiplicity of non-strange hadrons per participant nucleon is constant, and that the increase of multiplicity with centrality of the collision is entirely due to an increasing number of participant nucleons and not to rescattering effects between the produced hadrons. An analogue result has been obtained from hadron-nucleus collisions [ 19 ]. The discussion of the result (6) is further simplified by introducing the double ratio 152

(dNch/dy)2 v NN/dy)J.vv (dNch Rv= [dNv(3o)/dy]2 v = (dNl~N/dy)2AV.

=exp[-Av(O]+Rv{1-exp[-Av(3)]}.

Here dNv(3o)/dyds is the initial density of vector mesons produced in primary N - N collisions, and the quantity A v is defined by Av(r)= d--~ln

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(10)

and from the definition (8) one sees that the asymptotic number of vector mesons is proportional to the total multiplicity. As we will discuss below, this situation applies to ~ meson production. On the other hand, if the initial abundance of V is already saturated, i.e. Nv/N¢hfrom the primary collisions is identical to the ratio between the production and absorption rates, 2V/2Av, then Rv= 1 and no further changes are caused by the final state interactions. This is the case for the p and co mesons. Finally, even if both the initial vector meson abundance and the absorption rates are small (as for 0 and J/~t), additional particles can still only be produced if the product of production cross section and charged multiplicity (which enters into 2pv) is large enough. This is not the case for the J / ~ meson, because due to its high mass threshold it is only produced in hard collisions, and the available energy in secondary collisions is generally too small (leading to a nearly vanishing effective cross section (av)~,j). Thus for the J / ~ mesons the first term in eq. (9) describing absorption dominates.

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Let us denote the ~/(co+ pO) ratio normalized to its value in N - N collisions by X[ET ]:

3. T h e ET d e p e n d e n c e of the O e n h a n c e m e n t

It was observed in ref. [20] that the produced transverse energy is directly proportional to the total multiplicity and that both quantities are a direct measure of the impact parameter. The impact parameter dependence is introduced by writing dNch

dyds-

dN iN

--

dy

[Tp(b-s)+Tr(s)],

(11)

where Tp,T(S)= f + ~ d z p v , v ( ~ ) are the nuclear thickness functions for the projectile and target. As discussed above, eq. (11 ) incorporates that the charged multiplicity is proportional to the overlap region of the colliding nuclei at given impact parameter which again is proportional to the number of participants: Nva~t(b) =

fda [TT(s)+Tp(b-s)].

(12)

Consequently the ratios aj and 2p/2A v v are independent of impact parameter b and transverse position s. In order to obtain a tractable analytical result we eliminate the left-over s dependence in dNt(b, s)

pl(zo,S)- - To~

- at

dNch(b, s) Zodyds

(13)

by replacing dNt

X[Er]

=

( dN./dy ~/[ dN~N/dy - NN \ dNo,+oo/dyJ / k dN o,+oo/dy,I"

(14)

X[Er(b)]=R,+exp[-A,(b)] ( l - R , ) .

ONNN =Npa~t (b)

(17)

In this expression, A,(b) contains practically the whole space-time and impact parameter dependence; since the latter is difficult to estimate reliably, we will eliminate this quantity with the help of the measured J / ~ suppression. The procedure is based on the assumption that the J/ll/suppression observed in the same NA38 experiment is also due to final state interactions in a dense hadronic medium. Recent investigations [ 5 ] of this possibility are not yet conclusive but seem to indicate that at least a major fraction of the effect can be attributed to such a mechanism. As already mentioned, for J/V mesons absorption dominates the final state effects: dyds

-

dNv(b, %) dyds

exp[-A~,(b) ].

(18)

The ratio

where Saf(b) is the effective transverse area of the system for given impact parameter. Thereby we eliminate the space-time dependence as far as possible. Consistent with our above discussion we now assume that the relation ( 11 ) actually holds for each particle species separately. With eq. (14) the integration of eqs. (6), (9) over ds is then trivial, and we find the simple analytical result for the impact parameter dependence of the final vector meson abundancies:

dNv( b, z)

(16)

The denominator has approximately the value 1/40 [21 ]. The ET dependence of Xis implicit and due to the impact parameter dependence of dN,.,o.o/dy. The only feature we will need below is that there exists a monotonic relation between b and ET [ 22 ]. Inserting eq. (15) for V= ~, co, p0, and setting Ro,= Rp_ 1 as discussed above, we obtain our final result

dNv(b, z) dNl

Z o @ ~ - ,o dy&fr'

dy

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dy

×{Rv+exp[-Av(b,z)l ( 1 - - R v ) } .

(15)

The b dependence ofA v arises from the b dependence of the charged multiplicity in eq. (7).

dNv(b , z)/dyds S[ET] --= dNv(b, zo)/dyds

(19)

is the experimentally observed ET-dependent J / ~ suppression ratio [ l ]. Thus we can eliminate from eqs. (18), (19) A,(b) in favour of S[ET]: A¢(b) = - 7 , In S [ E T ] ,

A,

Zt (av)~o4

(20)

Y*= & - Z, < ~ v > ~ a , "

Since Y, involves only ratio of suitably weighted absorption cross sections, it does not depend on the details of the nuclear collision dynamics, and all information on the dependence on the impact parameter and collision lifetime is contained in S[ET ]. Thus our final result reads 153

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X[Er] = R , + ( SIEr] )~*( 1 - R , ) .

PHYSICSLETTERSB (21)

4. Comparison with data For a quantitative comparison of our results with the recent NA38 data [ 10], we have to estimate Ro and 7,. From nuclear photoproduction of t) and J/~¢ their total cross sections on nucleons have been determined as a 0 c N - ~ X ) ~ 2 - 3 mb [23] and a(0N-~ X ) ~ 8 - 1 0 mb [24,25]. It is also known [8,24,25] that these cross sections are dominated by absorption. Assuming the relative ratio of these cross sections to be similar for absorption on mesons, we may approximate a(t~N~X) Y*--- a ( ~ N ~ X )

3-4.

(22)

We like to remark that we consider meson-meson scattering processes at low relative momenta, i.e. small v/s, where usually cross sections are dominated by intermediate resonance formation. In the case of the (~ meson, however, resonance formation is suppressed because of the Zweig rule. Only processes like

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2~, dNr~N/dy 2'~ - dNNN/dy"

(24)

Of course, this is a crucial step since it basically determines the asymptotic enhancement factor. We consider eq. (24) as an upper bound on secondary ¢ production, since secondary processes happen at lower x/~ such that the mass threshold of the 0 mesons becomes more important, and on the other hand rescattering processes with secondary strange hadrons (which are generally not OZI suppressed) are still rare. With this assumption one obtains R,~-22/2~, i.e. the increase in the 0/(co + pO) ratio is entirely determined by the different absorption probabilities. While secondary production occurs with the same relative ratio as primary production, absorption is less effective for the ~ mesons and thus determines their net gain due to secondary processes. An upper limit for the co and p absorption cross section on nucleons is again obtained from the total o~-N and p°-N cross sections extracted from nuclear photoproduction of p and co mesons: a(c0, p°+N--,X) ~ 2 5 - 3 3 mb [24]. This is once more a factor 3-4 larger than the ~-N absorption cross section. Assuming as before similar circumstances for absorption on mesons, we approximate

K / K + meson ~ K * / l ~ ~ ~)+ meson are not OZI forbidden. Since the known kaon resonances do not show any appreciable ~)decay mode we hope that our estimate for the cross section ratio is quite reasonable. To obtain a precise estimate for R, is much more difficult since this quantity requires knowledge of the average cross sections for many processes most of which cannot be directly measured. However, a reasonable number can be obtained from the following consideration. Since we argued above that R~ ~ l, the ratio

R, Ro)

dNNS/dy )t~ 22 dNr~N/dy 2~ 2*A

(23)

can be directly used for an estimate of R,: We expect that rescattering produces c) and a) mesons with about the same relative ratio as observed in the primary N N collisions. This implies 154

22 a(o~N-.X) R*-~ 2*A -- a(t~N~X)

3-4

(25)

Again, we have to be careful when extrapolating to small x/~ where resonance contributions to the absorption cross section might be relevant, but considering the unitarity limit for the relevant meson resonances decaying into co or p mesons shows that we do not expect cross sections which are much larger than our rough estimate. For eq. (21) we need an expression for the J / ~ suppression as a function of ET. We obtain it from the NA38 data by performing a linear fit in the form S[ET] = 1 -

o

(Ex/Ex)Aiac

E ° =26.7 GeV,

-2/3

,

(26)

where Ainc is the number of projectile nucleons and has been used to renormalize the transverse energy from the most central collisions by the effective transverse overlap area Seff(b = 0). This fit is shown

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in fig. 1. The data points from NA38 [ 1,2] represent the V / c o n t i n u u m ratio as a function of Ex; our fit assumes that the limit ET--,0 corresponds to the case of N - N collisions which has so far not been experimentally verified. In fig. 1 we have used pT-integrated data while the data shown in fig. 2 are affected by a 1OW-px cut, P x > 1.3 G e V / c [ 10]. This raises a question since for ]'/~b SUPPRESSION

~zs

10 "~5 S 2.5

o Oxygen -U A Sutphur-U 200 AGeV i

i

i

i

ET/A2/) laeV) Fig. 1. Linear fit to the J / ~ suppression as a function of Ex measured by the NA38 Collaboration. The data are taken from ref. [ 2 ] where ET has been normalized by the transverse area of the incident projectile.

I

.__5

0

•p.u

(~l(w*~/') ENHANCEMENT

2

1,

6

8

10

ET/A~GeV}

Fig. 2. 4/(to + pO) enhancement as a function of transverse energy from 200A GeV O+U and S+U collisions, normalized to the ratio measured in p+U events. The data are from the NA38 Collaboration [ 10], and the Er axis is normalized in the same way as in fig. 1. The solid lines show the result eq. (21), using the linear fit shown in fig. 1.

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the J / V a strong PT dependence o f the suppression effect was observed [ 1,2 ]. However, within the existing hadronic models for the suppression [ 5 ] this PT dependence cannot be reproduced by final state absorption, but is rather understood as an initial state effect [ 7 ]. Thus it has nothing to do with the geometrical problems o f fireball lifetime and impact parameter dependence of multiplicity and particle densities which we want to eliminate from eq. ( 15 ) using eq. (20). Within the hadronic suppression scenario these are rather given by the total suppression, i.e. integrated over Pr. Using the fit from fig. l in eq. (21 ), the lines in fig. 2 show the resulting X[ET] for two values of R, ( R , = 3 and 4) and an average value o f 3.5 for 7,. Again the question about a possible PT dependence of the effect arises, this time in the context of normalization of our curves: NA38 have normalized their ¢ / ( c o + pO) ratio to p + U collisions, while eq. ( 15 ) is normalized to p + p collisions. Thus in principle one has to correct for the difference of this ratio between p + p and p + A collisions, and such a correction will in general be PT dependent. An often discussed origin for an A dependence o f this ratio is the absorption of the produced vector mesons within the cold target spectator matter. (Since the matter density is small, absorption dominates in this case over secondary production.) Since uto N~abs/~aab¢ this leads to an increase of the ¢/(co + pO) ratio ¢N as one goes from p + p to p + U collisions. Experimental evidence for this p h e n o m e n o n is provided by the slower than linear growth o f the total production cross sections in pA experiments: writing a ( p + A - , V ) / t r ( p + p - ~ V ) ~ - A °' one finds for p mesons a , _ 0.75 [ 25 ], while for ¢ mesons or, = 0.86 is much closer to 1 [ 25 ]. A straightforward evaluation of these power laws for A = 2 3 8 would imply an increase o f the ¢ / ( c o + p °) ratio by a factor = 1.8 between p + p and p + U collisions. This would mean that our theoretical curves should intersect the vertical axis near 0.6, rising with a slope reduced by a factor 1.8. However, these ot values depend strongly on the Pr of the produced vector meson, systematically increasing with Px to values > 1 for PT above - 2 G e V / c. This effect has been interpreted in terms of multiple scattering in the initial ( J / v ) a n d / o r final state (Cronin effect [ 26 ] ), but a quantitative understanding is still lacking. Since the NA38 data contain a low155

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PT cut on the vector mesons, the effective c~ values to be applied to the data in fig. 2 are expected to be much closer to 1. Indeed, preliminary results by NA38 on the A dependence of the ¢ / ( t o + p °) ratio, with the same low-pr cut, in various pA systems [ 10 ] indicate only a very slight rise with increasing A (certainly less than the factor 1.8 discussed above). Awaiting more detailed experimental information on this question, we have therefore refrained from a renormalization of our theoretical curves with respect to the data. While this may be the reason for a systematic error in our comparison shown in fig. 2, we estimate it (based on the above numbers) to be less than 30% and thus of the same order as the uncertainties involved in the estimate of R,.

5. Conclusions

Fig. 2 shows that the qualitative trend of the data is nicely explained by our simple hadronic rescattering model. If our approximations are accurate, and the observed J/V suppression is indeed entirely of hadronic origin (as we assumed), we do not see any need to invoke additional, non-hadronic mechanisms for the observed ¢ enhancement. However, we have pointed out that we consider our estimate of R~ as an upper limit, and that a quantitative account of the difference between pp and pA collisions tends to strengthen the experimental effect compared to our calculation. Therefore a stronger enhancement effect in future experiments with larger nuclei, or even the demonstration that the effect does not decrease if the full data set without a low-pa- cut is used, would put considerable strain on the hadronic rescattering scenario, while still being consistent with the QGP hypothesis [ 13 ]. Since the O / ( t z + p °) ratio is so small in pp collisions ( ~ 1/40), it is not too surprising that even very little additional production via rescattering can lead to an observable enhancement effect, without really requiring thermal equilibration. However, our analysis indicates that it will be very hard to reach an enhancement by more than a factor 3-4 (compared to pp collisions) by this mechanism. This limit could only be exceeded if the collision lifetime were so long that the collision zone effectively equilibrates. In such a case our solution of the rate equations using time156

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dependent perturbation theory breaks down (in particular the time-dependence of other strange channels has to be considered which can feed the 0 channel through OZI-unsuppressed reactions), and our result can no longer be interpreted as an upper limit which would separate ("uninteresting") hadronic physics from ("interesting") QGP physics. In chemical equilibrium a ~ enhancement by a factor 6-10 over the N - N value can be expected [ 13 ]. Should such a large value ever be observed, a detailed dynamical analysis will be required to settle the question whether the actual time scales in the collision are large enough to explain this equilibration on a purely hadronic basis, or whether a more natural explanation would be provided by the QGP hypothesis. This is beyond the scope of this paper. It should also be stressed again that our analysis strongly links the observations of~ enhancement and J / ~ suppression. Should it eventually turn out that the observed J/V suppression cannot be consistently explained by hadronic final state absorption, the consequence would very likely be that the observed ~ enhancement cannot be explained on a hadronic basis either: our analysis required the large multiplicity densities and collision times (which enter into A,) extracted from the J/~/suppression in order to be successful.

Acknowledgement

U.H. gratefully acknowledges inspiring discussions with J.M. Gago and P. Sonderegger of the NA 38 data before their publication. J.P. is indebted to L. McLerran for very useful discussions.

References [ 1 ] NA38 CoUab., M.C. Abreu et al., Z. Phys. C 38 ( 1988 ) 117; NA38 Collab., L. Kluberg et al., Nucl. Phys. A 488 (1988) 613; NA38 Collab., C. Baglin et al., Phys. Lett. B 220 (1989) 471. [2] NA38 Collab. C. Racca, et al., in: Hadronic matter in collision 1988, eds, P. Carruthers and J. Rafelski (World Scientific, Singapore, 1989) p. 552. [3] T. Matsui and H. Satz, Phys. Lett. B 178 (1986) 416.

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PHYSICS LETTERS B

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