Volume 243, number 1,2 PHYSICS LETTERS B 21 June 1990

-enhancement and suppression in nuclear collisions by rescattering of secondary hadrons

Peter Koch a,1, Ulrich He inz a,2 and Jan 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 assump- tion (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 O- production 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 (QGP) for- mation in relativistic heavy-ion collisions much ex- citement was created by the discovery by the NA38 Collaboration [ 1,2 ] that the production of J / ~ me- sons is suppressed in central O + U and S + U colli- sions at 200A GeV, compared to peripheral nuclear collisions and p + U collisions. This discovery fol- lowed the prediction by Matsui and Satz [ 3 ] that such a suppression should be a clean QGP signature. Sub- sequently much work was done to obtain a quantita- tive fit of the data assuming QGP formation in these collisions [4], but it was also found that it is not im- possible 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 me- sons can rescatter and dissociated [ 5 ]. Also a com- bination of both mechanisms has been suggested [6]. Actually, the transverse momentum dependence of the suppression effect [ 1,2] is straightforwardly ex- plained [7] in terms of initial state interactions

Supported by Bundesministerium f'tir Forschung und Tech- nologie (BMFT), grant 06 OR 764.

2 Supported in part by Deutsche Forschungsgemeinschaft (DFG), grant He1283/3-1.

(multiple gluon scattering in the target material be- fore formation of the ce pair) and is completely anal- ogous 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 clas- sical 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 interpreta- tion to the limits of its applicability.

New information from the NA38 experiment on the production of 0, pO and 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 re- stricts the Pr of the vector mesons to PT> 1.3 GeV/ c.) By fitting it under the assumption of equal pro- duction cross sections for to and pO, a ~ / (to + pO ) ratio

0370-2693/90/$ 03.50 © 1990 - Elsevier Science Publishers B.V. ( North-Holland ) 149

Volume 243, number 1,2 PHYSICS LETTERS B 21 June 1990

is extracted. Subdividing the data into bins with dif- ferent amounts of produced transverse energy ET seen in the calorimeter (which is indicative for the cen- trality or "violence" of the nuclear collision), one ob- serves a systematic increase of the 0 / ( t o + p °) ratio with ET (see fig. 2), while at the same time the ( J / v ) / con t inuum ratio systematically decreases [ 1 ] (see fig. 1 ). The data presented in ref. [ 10 ] also al- low to extract a 0/continuum ratio and its ET depen- dence. One observes qualitatively the same behav- iour 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 colli- sions, 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 produc- tion in central A-A collisions.

In this letter we analyze whether it is possible to account for this approach towards chemical equilib- rium in terms of additional 0 production by second- ary collisions within a hot hadronic fireball formed in the collision. We solve the rate equations for sec- ondary O-production and -absorption, using mea- sured rapidity distributions from pp collisions as in- put to describe the initial conditions created by the superposition of primary N - N collisions in the heavy- ion collision. Some poorly known geometric param- eters, like the relationship between volume of the col- lision 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 ¢ enhance- ment 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

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) ra- tio from a hadronizing QGP [ 15,13 ], we argued that the observed 0 enhancement of a factor -~ 3 over the p + U result corresponds to about 50% of the maxi- mum 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 nec- essary 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 mecha- nism (e.g. independent string fragmentation). In any such model most hadrons are produced close to the central rapidity on a proper time scale of approxi- mately Zo ~ 1 fro. We shall describe this centrally pro- duced matter in terms of average densities which de- pend on the impact parameter of the nuclear collision, without, however, requiring that the averages should be calculated assuming thermal or chemical equilib- rium. 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 eventu- ally drive the central rapidity region towards thermal and chemical equilibrium.

In order to achieve a consistent description of res- cattering effects on all relevant channels, we will con- sider 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 col- lisions between projectile and target nucleons, sec- ondary 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 pro- cesses are probably dominated by meson-meson col- lisions, 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, ex- pressed as a sum of gain and loss terms:

dNv - ~ ( a v ) ~ X p i ( x ) & ( x ) & ( x ) d4x

- ~ (av)~.~pl(x)pv(x) . ( 1 ) l

Here the ( o r ) o are the relevant cross sections aver- aged over the the momentum distribution of the col- liding particles, and the Pi are the space-t ime-depen- dent 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 longitudi- nal proper time z = ~ , space-time rapidity y = ½ In [ ( t + z ) / ( t - z) ], and transverse coordinates s. The space-time volume element is then given by d4x= 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 rapid- ity interval 2 <Y~ab< 4. Assuming that, apart from particle creation and annihilation processes, the den- sity of hadrons is diluted primarily due to the strong longitudinal motion of the matter constituents, and completely neglecting collective transverse expan- sion, we can write for all non-strange hadrons

pi(z, y, s) =pi(ro, s) Z_o. (2) 12

For strange hadrons there will be additional time-de- pendence from secondary production and absorp- tion 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,

due to their small abundance compared to the non- strange 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, 11 and (o are not changed appreciably by final state interactions, i.e. that for them secondary production is balanced by absorp- tion, crucially simplifies the problem. It can be justi- fied 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 as- suming 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 abundan- cies 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,

a j = ~j('~O, *) - - d N J d y d s (4) peh(ZO, S) dNcJ dy da "

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

dNv d [ d U v \ vdNch [2 v dNeh ~yy~) _ d--z~d-~) = 2 A d - ~ ~2--~ dyds (5)

This expression shows explicitly the dependence on the charged multiplicity which itself is directly pro- portional 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 quad- ratically, but their absorption only linearly with charged multiplicity. I f the secondary production cross sections are not too small (as will be shown to be true for ~ mesons), we can in this case have addi-

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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) dNv(Zo) - - - - - e x p [ - A v ( 3 ) ]

dyds dyds

dNch 2pV { 1 - e x p [ - A v ( 3 ) ] } (6) + dy--

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

A v ( r ) = d - - ~ l n ~ (aV)(va,

)t v dNeh = A d - ~ ln(~o) . (7)

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 pro- duction 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 in- crease 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 ob- tained from hadron-nucleus collisions [ 19 ].

The discussion of the result (6) is further simpli- fied by introducing the double ratio

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

(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 to- tal multiplicity ratio from the primary N - N colli- sions 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

=exp[-Av(O]+Rv{1-exp[-Av(3)]}. (9)

One sees that the two driving parameters of the ki- netic 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

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

=Rv, (10)

and from the definition (8) one sees that the asymp- totic number of vector mesons is proportional to the total multiplicity. As we will discuss below, this situ- ation applies to ~ meson production. On the other hand, if the initial abundance of V is already satu- rated, i.e. Nv/N¢h from the primary collisions is iden- tical to the ratio between the production and absorp- tion rates, 2V/2A v, 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 parti- cles can still only be produced if the product of pro- duction cross section and charged multiplicity (which enters into 2p v) 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 gener- ally 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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3. T h e ET dependence 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 pa- rameter dependence is introduced by writing

dNch dN iN - - [Tp(b-s)+Tr(s)] , (11)

dyds - dy

where Tp,T(S)= f + ~ d z p v , v ( ~ ) are the nu- clear thickness functions for the projectile and target. As discussed above, eq. (11 ) incorporates that the charged multiplicity is proportional to the overlap re- gion 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)

2p/2A are indepen- Consequently the ratios aj and v v dent 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) dNch (b, s) pl(zo,S)- - - - at (13)

T o ~

by replacing

dNt dNl

Z o @ ~ - ,o dy&fr'

Zo dyds

(14)

where Saf(b) is the effective transverse area of the system for given impact parameter. Thereby we elim- inate the space-time dependence as far as possible.

Consistent with our above discussion we now as- sume that the relation ( 11 ) actually holds for each particle species separately. With eq. (14) the integra- tion of eqs. (6), (9) over ds is then trivial, and we find the simple analytical result for the impact pa- rameter dependence of the final vector meson abundancies:

dNv( b, z) ON NN dy =Npa~t (b) dy

×{Rv+exp[-Av(b,z)l (1 - -Rv)} . (15)

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

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

X[Er] ( dN./dy ~/[ dN~N/dy = - - - NN ( 1 6 ) \ dNo,+oo/ dyJ / k dN o,+oo/ dy, I"

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

X[Er(b)]=R,+exp[-A,(b)] ( l - R , ) . (17)

In this expression, A,(b) contains practically the whole space-time and impact parameter depen- dence; 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 in- vestigations [ 5 ] of this possibility are not yet conclu- sive 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:

dNv(b, z) dNv(b, %) - exp[-A~,(b) ] . (18)

dyds dyds

The ratio

dNv(b , z)/dyds (19) S[ET] --= dNv(b, zo)/dyds

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 [ET] ,

A, Zt (av)~o4 (20) Y*= & - Z, <~v>~a, "

Since Y, involves only ratio of suitably weighted ab- sorption cross sections, it does not depend on the de- tails of the nuclear collision dynamics, and all infor- mation on the dependence on the impact parameter and collision lifetime is contained in S[ET ]. Thus our final result reads

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X[Er] = R , + ( SIEr] )~*( 1 - R , ) . (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 de- termined 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 absorp- tion. Assuming the relative ratio of these cross sec- tions to be similar for absorption on mesons, we may approximate

a(t~N~X) 3-4 . (22) Y*--- a ( ~ N ~ X )

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 sup- pressed because of the Zweig rule. Only processes like

K/K + meson ~ K * / l ~ ~ ~) + meson

are not OZI forbidden. Since the known kaon reso- nances 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 rea- sonable number can be obtained from the following consideration. Since we argued above that R~ ~ l, the ratio

R, dNNS/dy )t~ 22 (23)

Ro) dNr~N/dy 2~ 2*A

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

2~, dNr~N/dy 2'~ - dNNN/dy" (24)

Of course, this is a crucial step since it basically de- termines 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 me- sons becomes more important, and on the other hand rescattering processes with secondary strange had- rons (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 deter- mined by the different absorption probabilities. While secondary production occurs with the same relative ratio as primary production, absorption is less effec- tive 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) ~25-33 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

22 a(o~N-.X) 3-4 (25) R*-~ 2*A -- a(t~N~X)

Again, we have to be careful when extrapolating to small x/~ where resonance contributions to the ab- sorption cross section might be relevant, but consid- ering the unitarity limit for the relevant meson reso- nances 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

- ( E x / E x ) A i a c , S[ET] = 1 o -2/3

E ° =26.7 GeV, (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 f rom NA38 [ 1,2] represent the V/con t inuum ratio as a function of Ex; our fit as- sumes that the limit ET--,0 corresponds to the case of N - N collisions which has so far not been experimen- tally 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 GeV/c [ 10]. This raises a question since for

~zs

10

"~5

S

2.5

]'/~b SUPPRESSION

o Oxygen - U A Sutphur -U

200 A GeV i i i i

E T/A 2/) laeV)

Fig. 1. Linear fit to the J / ~ suppression as a function of Ex mea- sured 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 (~l(w*~/') . _ _ 5 •p.u

ENHANCEMENT

0 2 1, 6 8 10 ET/A~GeV}

Fig. 2. 4/(to + pO) enhancement as a function of transverse en- ergy 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.

the J /V a strong PT dependence o f the suppression effect was observed [ 1,2 ]. However, within the exist- ing hadronic models for the suppression [ 5 ] this PT dependence cannot be reproduced by final state ab- sorption, but is rather understood as an initial state effect [ 7 ]. Thus it has nothing to do with the geo- metrical problems of fireball lifetime and impact pa- rameter dependence of multiplicity and particle den- sities which we want to eliminate f rom 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 nor- malization of our curves: NA38 have normalized their ¢ / ( co+ 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. Experi- mental evidence for this phenomenon is provided by the slower than linear growth of 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 the- oretical 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 in- creasing with Px to values > 1 for PT above -2 GeV/ c. This effect has been interpreted in terms of multi- ple scattering in the initial ( J / v ) and /o r final state (Cronin effect [ 26 ] ), but a quantitative understand- ing is still lacking. Since the NA38 data contain a low-

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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 in- volved in the estimate of R,.

5. Conclusions

Fig. 2 shows that the qualitative trend of the data is nicely explained by our simple hadronic rescatter- ing model. I f 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 mecha- nisms 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 sce- nario, while still being consistent with the QGP hy- pothesis [ 13 ].

Since the O/ ( t z+p °) ratio is so small in pp colli- sions ( ~ 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 anal- ysis indicates that it will be very hard to reach an en- hancement 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 time-

dependent perturbation theory breaks down (in par- ticular the time-dependence of other strange chan- nels has to be considered which can feed the 0 chan- nel 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 chem- ical 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 dy- namical analysis will be required to settle the ques- tion 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 explana- tion 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 con- sequence would very likely be that the observed ~ en- hancement 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 discus- sions 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.

156

Volume 243, number 1,2 PHYSICS LETTERS B 21 June 1990

[4] F. Karsch and R. Petronzio, Phys. Lett. B 193 (1987) 105; Z. Phys. C 37 (1988) 627; J.-P. Blaizot and J.-Y. OUitrault, Phys. Lett. B 199 ( 1987 ) 499; M. Chu and T. Matsui, Phys. Rev. D 37 (1988) 1851; F. Karsch, M.-T. Mehr and H. Satz, Z. Phys. C 37 (1988) 617.

[ 5 ] J. Ftakcnik, P. Lichard and J. Pi~tlt, Phys. Lett. B 207 (1988) 194; S. Gavin, M. Gyulassy and A. Jackson, Phys. Lett. B 207 (1988) 257; R. Vogt, M. Prakash, P. Koch and H. Hansson, Phys. Lett. B207 (1988) 263.

[6] D. Blaschke, G. R6pke and H. Schulz, Phys. Lett. B 233 (1989) 434.

[7] S. Gavin and M. Gyulassy, Phys. Lett. B 214 (1988) 241; J. Hiifner, Y. Kurihara and H.-J. Pirner, Phys. Lett. B 215 (1988) 218; J.-P. Blaizot and J.-Y. OUitrault, Phys. Lett. B 217 (1989) 392; K.S. Lee and U. Heinz, unpublished (1988).

[8] J. Badier et al., Z. Phys. C 20 (1983) 101. [9] T. Matsui, Ann. Phys. (NY) 196 (1989) 182;

J. Hiifner, B. Povh and S. Gardner, Phys. Lett. B, in press; V. (~ern~, I. Horv@h, R. Lietava, A. Nogov~i and J. Pi~tit, Z. Phys. C, in press.

[ 10] NA38 Collab. A. Baldisseri et al., Annecy preprint LAPP- EXP-89-15, in: Proc. Intern. Europhys. Conf. on High energy physics (Madrid, September 1989) to appear; private communication.

[11 ] NA35 Collab., M. Ga~dzicki et al., Nucl. Phys. A 498 (1989) 375c.

[ 12 ] NA35 Collab., M. Ga~dzieki et al., in: the nuclear equation of state, ed., W. Greiner NATO ASI Series B (Plenum Press, New York, 1990), to appear.

[ 13 ] P. Koch, U. Heinz, and J. Pi~tit, Regensburg preprint TPR- 90-7, submitted to Z. Phys. C.

[ 14] I. Lovas, K. Sailer and Z. Tr6cs~inyi, J. Phys. G 15 (1989) 1709.

[ 15 ] A. Shor, Phys. Rev. Lett. 54 ( 1985 ) 1122. [ 16 ] J,D. Bjorken, Phys. Rev. D 27 (1983) 140. [ 17] R. Hagedorn, Nuovo Cimeuto Suppl. 3 (1965) 147;

R. Hagedorn and J. Ranft, Nuovo Cimento Suppl. 6 (1968) 169; Y.P. Nikitin and I.L. Rozental, Theory of multiparticle production processes, Studies in High Energy Physics, Vol. 6 (Harwood Academic, Chur, 1988 ).

[ 18 ] WAS0 Collab., R. Albrecht et al., Phys. Lett. B 199 ( 1987 ) 297.

[ 19] W. Bell et al., Z. Phys. C 27 (1985) 191; I. Otterlund, Nucl. Phys. A 461 (1987) 113c.

[20] WAS0 CoUab., R. Albrecht et al., Z. Phys. C 38 (1988) 3. [21 ] H. Behrend et al., Phys. Lett. B 56 (1975) 408;

K.J. Anderson et al., Phys. Rev. Lett. 27 (1976) 799. [ 22 ] B. Anderson, G. Gustafson and B. Nielsson-Almqvist, Nucl.

Phys. B 281 (1987) 289; J. Ranft and S. Ritter, Z. Phys. C 27 (1985) 413; T.P. Pansart, NucL Phys. A 461 (1987) 521c; K. Werner, Phys. Lett. B 197 (1987) 225.

[23 ] S.D. Holmes, W. Lee and J.E. Wiss, Annu. Rev. Nucl. Part. Sci. 35 (1985) 397.

[24] T.H. Bauer; R.D. Spiral and D.R. Yennie, Rev. Mod. Phys. 50 (1978) 261.

[ 25 ] R. Bailey et al., Z. Phys. C 22 (1984) 125. [ 26 ] J.W. Cronin et al., Phys. Rev. D 11 ( 1975 ) 3105;

D. Antreasyan et al., Phys. Rev. D 19 (1979) 764.

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