lier NA50 data [3] or 7.1 Â± 3.0 mb obtained from a fit to. NA38 S+U data [2]. Within error, the S+U cross sections are compatible with pA cross secti...

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arXiv:nucl-th/0302044v2 19 May 2003

Variable Energy Cyclotron Centre 1/AF,Bidhan Nagar, Calcutta - 700 064

are absorbed in nuclear medium could explain the data [9,11,12]. Parameters of the model were obtain from a fit to then existing pp/pA/AA total J/ψ cross section data [3]. Preliminary analysis of high statistics pA data [1] with the implication of less absorption of J/ψ in nuclear medium, along with the changed suppression pattern observed in the preliminary analysis of NA50 2000 Pb+Pb run [4], necessitated the re-examination of the QCD based nuclear absorption model [9]. In the present brief report, we have analyzed the latest NA50 data on pA/SU total J/ψ cross section [1] to obtain the parameters of the QCD based nuclear absorption model. The model was then used to explain the centrality dependence of J/ψ over Drell-Yan ratio in 200 GeV/c S+U collisions and in 158 GeV/c Pb+Pb collisions (preliminary data). As will be shown in the following, once the model parameters are fixed from J/ψ total cross sectional data, the QCD based nuclear absorption model give a consistent description of the centrality dependence of J/ψ suppression in S+U collisions as well as in Pb+Pb collisions. The plan of the paper is as follows: in section 2, we will briefly describe the model and obtained the model parameters from the new high statistics pA/AA NA50 data. In section 3, the NA50 data on ET dependence of J/ψ over Drell-Yan ratio in S+U and in Pb+Pb collisions are analyzed. Summary and conclusions are drawn in section 4.

We have analyzed the latest NA50 data on J/ψ production in pA and AA collisions. The J/ψ production is assumed to be a two step process, (i) formation of c¯ c pairs, perturbatively calculable, and (ii) formation of J/ψ from the pair, a non-perturbative process, which is conveniently parameterized. In a nuclear medium, as the c¯ c pair passes through the nuclear medium, it gain relative square momentum and some of the pairs can gain enough square momentum to cross the threshold for open charm meson, leading to suppression in nuclear medium. Few parameters of the model were fixed from the latest high statistics NA50 pA and NA38 SU total J/ψ cross sectional data. The model then reproduces the centrality dependence of J/ψ over Drell-Yan ration in 200 GeV/c S+U and 158 GeV/c Pb+Pb collisions.

I. INTRODUCTION

Recently, in Quark Matter 2002, NA50 collaboration presented their analysis of the nuclear absorption of J/ψ in high statistics 450 GeV pA collisions [1]. They estiJ/ψN mated the J/ψ nucleon absorption cross section (σabs ) in the framework of Glauber model. High statistics 450 J/ψN GeV pA data yield σabs = 4.4 ± 1.0 mb [1]. They also J/ψN estimate a common σabs from latest pA and NA38 200 J/ψN GeV/c S+U data [2], σabs =4.4 ± 0.5 mb. The extracted absorption cross section is much smaller than the earlier value of 6.4 ± 0.8 mb extracted from fit to earlier NA50 data [3] or 7.1 ± 3.0 mb obtained from a fit to NA38 S+U data [2]. Within error, the S+U cross sections are compatible with pA cross sections. In Quark matter 2002, NA50 collaboration also presented their preliminary analysis of 2000 Pb+Pb run [4]. ET dependence of the J/ψ over Drell-Yan ratio, in the rapidity range of 2.94.5 was presented. Compared to 1998 run [5], 2000 data are flatter, suppression being more at low ET and less at high ET . The difference may be attributed to the difference in method of analysis. In 1998, NA50 collaboration presented combined result of standard as well minimum bias analysis. In the 2000 run, only the standard analysis was performed. Centrality dependence of J/ψ absorption is still anomalous in the sense that Glauber model of nuclear absorption fails to explain the data. The 1998 data of NA50 collaboration [5] were analyzed in a variety of models, with and without assumption of QGP [6–9,11]. We have shown that a QCD based model, where J/ψ’s

II. J/ψ PRODUCTION AND SUPPRESSION

In the QCD based nuclear absorption model [9,12], J/ψ production is assumed to be a two step process, (a) formation of a c¯ c pair, which is accurately calculable in QCD and (b) formation of a J/ψ meson from the c¯ c pair, which is non-perturbative but can be conveniently parameterized. The J/ψ √cross section in AB collisions, at center of mass energy s is written as, Z XZ σ ˆab→cc J/ψ 2 dxF φa/A (xa , Q2 ) (1) σ (s)= K dq Q2 a,b

φb/B (xb , Q2 )

xa xb × Fc¯c→J/ψ (q 2 ), xa + xb

P where a,b runs over all parton flavors, and Q2 = q 2 + 4m2c . The K factor takes into account the higher order corrections. The incoming parton momentum fractions p 2 + 4Q2 /s + are fixed by kinematics and are x = ( x a F p ˆab→c¯c are xF )/2 and xb = ( x2F + 4Q2 /s − xF )/2. σ 1

square momentum gain factor, ε2 = 0.1875 GeV 2 /f m, a value 20% lower than the value obtained earlier [9]. Lowering of ε2 indicate less absorption of J/ψ’s in nuclear medium, in agreement with the Glauber model calculations. While the square momentum gain factor do not show energy dependence, the evident energy dependence of the cross section ratios shows up in the other parameter of the model Nnorm . We obtain Nnorm = 10.18 at 200 GeV/c and Nnorm = 4.43 at 450 GeV/c. The energy dependence of J/ψ cross section being taken care of in the model (Eq.1), the energy dependence of Nnorm is due to the Drell-Yan cross sections only. In the mass range, 2.9 > M > 4.5 GeV, the Craigie parameterization [15], of √ −14.9M/ s the Drell-Yan cross section, σ(DY ) ∝ e , gives for the ratio σ(DY )450GeV /σ(DY )200GeV = 2.1 -3.1, consistent with the presently obtained ratio of 2.29.

the sub process cross section and are given in [14]. Fc¯c→J/ψ (q 2 ) is the transition probability that a c¯ c pair with relative momentum square q 2 evolve into a physical J/ψ meson. It is parameterized as, 2

Fc¯c→J/ψ (q 2 ) = NJ/ψ θ(q 2 )θ(4m′ − 4m2c − q 2 )

(2)

2

(1 −

q )αF . 4m′ 2 − 4m2c

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Bµµ σ(J/Ψ)/σ(DY)

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III. ET DEPENDENCE OF J/ψ/DY RATIO

pp,pd 450 GeV pA 450 GeV pA 200 GeV

In the present section, we analyzed the ET dependence of J/ψ over Drell-Yan ratio in 200 GeV/c S+U collisions and in 158 GeV/c Pb+Pb collisions. Details of the calculation can be found in ref. [9].

SU 200 GeV 20 -1

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FIG. 1. The experimental ratio of total J/ψ cross section and Drell-Yan cross sections in proton-proton, proton-nucleus and nucleus-nucleus collisions. The fit to the data obtained in the QCD based nuclear absorption model is shown as solid lines. σ(J/ψ)/σ(DY)

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In a nucleon-nucleus/nucleus-nucleus collision, the produced c¯ c pairs interact with nuclear medium before they exit. It is argued [12] that the interaction of a c¯ c pair with nuclear environment increases the square of the relative momentum between the c¯ c pair. As a result, some of the c¯ c pairs can gain enough relative square momentum to cross the threshold to become an open charm meson. Consequently, the cross section for J/ψ production is reduced in comparison with nucleon-nucleon cross section. If the J/ψ meson travel a distance L, q 2 in the transition probability is replaced to q 2 → q 2 + ε2 L, ε2 being the relative square momentum gain per unit length. Parameters of the model (αF ,KNJ/ψ and ε2 ) can be fixed from experimental data on total J/ψ cross section in pA/AA collisions. Earlier NA50 data [3] are well described with KNJ/ψ =0.458, ε2 = 0.225GeV 2 /f m and αF = 1.0 [9]. As mentioned in the beginning, NA50 collaboration presented high statistics pA data on J/ψ cross section. They have measured Bµµ σ(J/ψ)/σ(DY ). In Fig.1, experimental data are shown as a function of nuclear length. The Drell-Yan cross sections donot have any A or alternately any L-dependence. The observed L dependence is then due to J/ψ’s only. We fit the data with two parameters, DY Nnorm = KNJ/psi /σN N (nb) and square momentum gain 2 factor ε (αF being kept fixed at 1). In Fig.1, the fit obtained to the data is shown. The two sets of data at 200 GeV/c and 450 GeV/c could be fitted with a common

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FIG. 2. The transverse energy dependence of J/ψ over Drell-Yan ratio in 200 GeV/c S+U collisions. The dashed and dotted lines are the fit obtained in the Glauber model J/ψN of nuclear absorption with σabs =7.1mb and 4.4 mb respectively. The solid line is the fit obtained in the QCD based nuclear absorption model.

In Fig.2, NA38 experimental ratio of Bµµ σ(J/ψ)/σ(DY ) for 200 GeV/c S+U collisions [2] is compared with the present model calculation (solid line). The data are well described in the model. For comparison purpose, we have also shown the fit obtained to the data in the Glauber model. The dashed line is the J/ψN Glauber model calculations with σabs = 7.1 mb. However, quality of fit gets poorer if we use lower value (4.4 J/ψN mb) for σabs as extracted from the most recent data (the dotted line). It is evident that in the Glauber model

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of nuclear absorption, the transverse energy dependence of J/ψ’s prefer larger absorption of J/ψ in S+U collisions than indicated in pA/AA total J/ψ cross section data. The QCD based nuclear absorption model, on the other hand, give consistent description of the data.

IV. SUMMARY AND CONCLUSIONS

To summarize, we have analyzed the latest NA50 data [4] on J/ψ suppression obtained in 2000 Pb+Pb run. The data were analyzed in the QCD based nuclear absorption model. The J/ψ production is assumed to be two step process, (i) production of c¯ c pair, purturbatively calculable and (ii) formation of J/ψ from the c¯ c pair. In a nuclear medium, due to random collisions with medium, relative square momentum of the c¯ c increases and some of the pair may gain enough square momentum to cross the threshold for open charm meson. We obtain the parameter, square momentum gain factor per unit length, ε2 , from a fit to the latest NA50 data [1], and obtain ε2 =0.1875 GeV 2 /f m. The value is lower than the value ε2 = 0.225 GeV 2 /f m, obtained in our earlier work [9]. There, we had fitted the earlier version of the NA50 data [3]. Reduction in ε2 indicate that the J/ψ’s are less absorbed in nuclear medium. This is in accordance with the J/ψ-nucleon absorption cross section, extracted from J/ψN the data [1,3]. σabs extracted from the earlier version J/ψN of the NA50 data [3] was large, σabs = 6.4 ± 0.8 mb, compared to the value extracted from the latest data set J/ψN [1], σabs = 4.4 ± 1.0 mb. With the new model parameter, the model could explain the centrality dependence of J/ψ over Drell-Yan ratio in 200 GeV/c S+U collisions as well as the latest NA50 data on the centrality dependence of J/ψ over Drell-Yan ratio in 158 GeV/c Pb+Pb collisions.

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σ(J/Ψ)/σ(DY)

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FIG. 3. NA50 preliminary transverse energy dependence of J/ψ over Drell-Yan ratio in 158 GeV/c Pb+Pb collisions. The dotted line is the Glauber model calculation. The dashed line is the QCD based nuclear absorption model calculation without including the effect of ET fluctuations. The solid line is obtained with including the effect of ET fluctuations.

Transverse energy dependence of the ratio, Bµµ σ(J/ψ)/σ(DY ) in 158 GeV/c Pb+Pb collisions could not be explained in the Glauber model of nuclear absorption. The preliminary NA50 data [4]obtained in 2000, are flatter compared to 1996/1998 data [5], still the usual Glauber model of nuclear absorption fails to describe the data. In Fig.3 the experimental data are shown along with the Glauber model fit to it obtained J/ψ with σabs =4.4 mb. The Glauber model calculation (the dotted line) agree only for the peripheral collisions. For more central collisions, the model predict less absorption than in experiment. Also the Glauber model shows saturation at more central collisions, in contrast to experiment. The 2nd drop in the ratio is mainly due to transverse energy fluctuations at a fixed impact parameter [6,10]. In the present model, we take into account ET fluctuations at a fixed impact parameter b, by the replacement: L(b, s) → L(b, s)ET / < ET > (b). In Fig.3, the dashed is obtained in the QCD based nuclear absorption model, without incorporating the ET fluctuation effect. It explains the data up to 100 GeV, the knee of the ET distribution, beyond which only, ET fluctuations are important. If ET fluctuation is included, the data are explained throughout the ET range (the solid line). Consistent description of ET dependence of J/ψ over DrellYan ratio in 200 GeV/c S+U and 158 GeV/c Pb+Pb collisions clearly demonstrate that the QCD based nuclear absorption model, together with transverse energy fluctuation could explain consistently the J/ψ absorption data at SPS energy.

e-mail:[email protected] [1] NA50 collaboration, P. Cortese et al, in Quark Matter 2002, Nantes, France (unpublished). [2] NA38 Collaboration, M. C. Abreu at. al., Phys. Lett. B449, 128 (1999). [3] NA50 collaboration, M.C. Abreu et. al., Phys. Lett. B410, 337 (1997). [4] NA50 collaboration, L. Ramello et al, in Quark Matter 2002, Nantes, France (unpublished). [5] NA50 collaboration, M. C. Abreu et al. Phys. Lett. B 477,28(2000). [6] J. P. Blaizot, P. M. Dinh and J.Y. Ollitrault, Phys. Rev. Lett. 85,4012(2000). [7] A. K. Chaudhuri, Phys.Rev. C64,054903(2001), Phys. Lett. B527,80(2002) [8] A. Capella, E. G. Ferreiro and A. B. Kaidalov, hepph/0002300, Phys. Rev. Lett. 85,2080 (2000). [9] A. K. Chaudhuri, Phys. Rev. Lett.88,232302(2002). [10] A. K. Chaudhuri, Phys. Rev.C66,021902 (2002). [11] A. K. Chaudhuri, nucl-th/0207082. [12] J. Qiu, J. P. Vary and X. Zhang, hep-ph/9809442, Nucl. Phys. A698, 57w1 (2002). ∗

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[13] NA50 collaboration, M.C. Abreu et al, Phys. Lett. B410,337 (1997). [14] C. J. Benesh, J. Qiu and J. P. Vary, Phys. Rev. C50, 1015 (1994). [15] N.S. Craigie, Phys. Reports, 47 (1978) 1.

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