Energy and system size dependence of \phi meson production in Cu+Cu and Au+Au collisions

We study the beam-energy and system-size dependence of \phi meson production (using the hadronic decay mode \phi -- K+K-) by comparing the new results from Cu+Cu collisions and previously reported Au+Au collisions at \sqrt{s_NN} = 62.4 and 200 GeV measured in the STAR experiment at RHIC. Data presented are from mid-rapidity (|y|<0.5) for 0.4<pT<5 GeV/c. At a given beam energy, the transverse momentum distributions for \phi mesons are observed to be similar in yield and shape for Cu+Cu and Au+Au colliding systems with similar average numbers of participating nucleons. The \phi meson yields in nucleus-nucleus collisions, normalised by the average number of participating nucleons, are found to be enhanced relative to those from p+p collisions with a different trend compared to strange baryons. The enhancement for \phi mesons is observed to be higher at \sqrt{s_NN} = 200 GeV compared to 62.4 GeV. These observations for the produced \phi(s\bar{s}) mesons clearly suggest that, at these collision energies, the source of enhancement of strange hadrons is related to the formation of a dense partonic medium in high energy nucleus-nucleus collisions and cannot be alone due to canonical suppression of their production in smaller systems.

c Brookhaven National Laboratory, Upton, New York 11973

Introduction
Experimental results from the Relativistic Heavy Ion Collider (RHIC) have confirmed the formation of a hot and dense medium in the initial stages of high-energy heavy-ion collisions [1]. Thus one of the prerequisites for the formation of a Quark Gluon Plasma (QGP) [2] in such collisions has been established. High statistics data on φ meson elliptic flow and yields as a function of transverse momentum (p T ) have been used to support the picture of formation of a hot and dense medium with partonic collectivity at RHIC [3]. Evidence of φ mesons being formed by the coalescence of seemingly thermalized ss-quarks in central Au+Au collisions has also been presented [3].
Several interesting features were also observed in the centrality dependence of φ meson production in Au+Au collisions at 200 GeV. As one goes from central collisions (average number of participants, N part , > 166) to peripheral collisions ( N part < 77), the p T spectra showed a gradual evolution from an exponential shape to a shape which requires an additional power law type of behavior at higher p T (> 3 GeV/c) [3,4]. At the same time, the average transverse momentum ( p T ) of φ mesons, dominated by the transverse momentum distribution at low p T , showed no significant collision centrality dependence in Au+Au collisions, unlike what has been seen for other particles of similar mass such as anti-protons (p) [4]. The N(φ)/N(K − ) ratio was observed to be independent of collision centrality in Au+Au collisions, in contrast to predictions from microscopic transport models like RQMD and UrQMD [5]. Both of these results led to the conclusion that φ meson production may not be from KK coalescence and φ mesons may have decoupled early on in the collisions [4].
The linear increase of the N(Ω)/N(φ) ratio with p T was proposed as an observable to test the recombination picture and hence also provided a test for thermalization in heavy-ion collisions [6]. A distinct trend was observed in the centrality dependence of this ratio vs. p T in Au+Au collisions [3]. With decreasing centrality, the observed N(Ω)/N(φ) ratio seems to turn over at successively lower values of p T indicating a smaller contribution from thermal quark coalescence in more peripheral collisions. Furthermore, in lower energy collisions at the SPS [7] and AGS [8], it was observed that the relative strangeness production increases with N part . For similar N part , the increase was found to be slower for larger colliding ions. The possible reason was related to variations of space-time density of the participating nucleons and the increase in collision density (interactions per fm 3 ) towards the center of the reaction volume [7,8]. The measurement of φ production in Cu+Cu collisions, in which systems with N part < 128 are created, is therefore expected to provide more precise data to further probe these centrality and colliding ion size dependent features.
In this letter we report the first results of φ meson production for rapidities |y| < 0.5 and 0.4 < p T < 5 GeV/c in Cu+Cu collisions at √ s NN = 62.4 and 200 GeV. The data were taken by the STAR experiment at RHIC [9]. A detailed comparative study of the energy and system size dependence of φ meson production (p T spectra, rapidity density and p T ) is carried out using both the Cu+Cu and Au+Au data.
Several possible mechanisms of φ meson production in nucleus-nucleus collisions have been reported in the literature [6,[10][11][12]. Some of these are supported by the experimental data [3] which is not true with others [3]. In a QGP, thermal s ands quarks can be produced by gluon-gluon interactions [10]. These interactions could occur very rapidly and the s-quark abundance would equilibriate. During hadronisation, the s ands quarks from the plasma coalesce to form φ mesons. Production by this process is not suppressed as per the OZI (Okubo-Zweig-Izuka) rule [13]. This, coupled with large abundances of strange quarks in the plasma, may lead to a dramatic increase in the production of φ mesons and other strange hadrons relative to non-QGP p+p collisions [14]. Alternative ideas of canonical suppression of strangeness in small systems as a source of strangeness enhancement in high energy heavy-ion collisions have been proposed for other strange hadrons (e.g Λ, Ξ and Ω) [15]. The strangeness conservation laws require the production of ans-quark for each s-quark in the strong interaction. The main argument in such canonical models is that the energy and space time extensions in smaller systems may not be sufficiently large. This leads to a suppression of strange hadron production in small collision systems. These statistical models fit the data reasonably well [16]. According to these models, strangeness enhancement in nucleusnucleus collisions, relative to p+p collisions, should increase with the strange quark content of the hadrons. This enhancement is predicted to decrease with increasing beam energy [17]. So far, discriminating between the two scenarios (strange hadron enhancement being due to dense partonic medium formed in heavy-ion collisions or due to canonical supression of their production in p+p collisions) using the available experimental data has been, to some extent, ambiguous. Enhancement of φ(ss) production (zero net strangeness) in Cu+Cu and Au+Au relative to p+p collisions would clearly indicate the formation of a dense partonic medium in these collisions. This would then rule out canonical suppression effects being the most likely cause for the observed enhancement in other strange hadrons [18] in high energy heavy-ion collisions.

Experiment and analysis
The data presented here were taken at RHIC in 2004 (Au+Au) and 2005 (Cu+Cu) using the STAR detector [9]. The analysis presented is from the data taken by the Time Projection Chamber (TPC) [19]. The TPC magnetic    Au+Au collisions at 200 GeV using these data sets have been presented elsewhere. [3]. Centrality selection for the Au+Au and Cu+Cu collisions utilized the uncorrected charged particle multiplicity for pseudorapidities |η| < 0.5, measured by the TPC.  [20].
The φ meson yield in each p T bin was extracted from the invariant mass (M inv ) distributions of K + K − candidates after the subtraction of the combinatorial background estimated using the event mixing technique [3,4,21]. The charged kaons were identified through their ionization energy loss in the TPC. Figure 1 shows a typical, background subtracted, K + K − M inv distribution as obtained for 200 GeV Cu+Cu collisions. The resultant distribution is well described by a Breit-Wigner function (solid line) plus a linear background function (dashed line). The form of the Breit-Wigner function is dN , where C is the area under the mass peak, Γ is the full width at half maximum for the distribution in GeV/c 2 and m φ is the mass of the φ meson. Figure 1 also shows that for p T > 0.7 GeV/c, the mass peak position of the φ meson agrees well with the PDG value of 1.0194 GeV [22]. For p T < 1.2 GeV/c there is a monotonic drop in the value of the fitted mass value with decreasing p T , reaching (mass φ fitted -mass φ PDG) = -2.5 MeV at p T = 0.5 GeV/c. The reconstructed invariant mass distribution of the φ meson is wider than the PDG value (4.26 MeV/c 2 ), decreasing from 9 MeV/c 2 to 4.26 MeV/c 2 with increasing p T [23]. The variations in the position of the φ invariant mass peak and its width, at low p T , are consistent with the simulation values and are understood within the scope of the detector resolution effects [21]. To understand these effects, φ decays to K + K − and detector response were studied within the STAR GEANT framework [24]. The resulting simulated signals were then embedded into real events before being processed by the standard STAR event reconstruction. These data were then processed like real data and analyzed to reconstruct the embedded φ [3,4,21,23]. Embedding simulations were also used to obtain the φ meson acceptance and reconstruction efficiency [21,23]. The product of the acceptance and reconstruction efficiency was found to increase from 3% at p T = 0.5 GeV/c to about 40% at p T = 3 GeV/c for central Cu+Cu collisions. The centrality dependence of these values were found to be small for Cu+Cu collisions. At higher p T (3-5 GeV/c), the efficiency was found to remain constant. The other important corrections applied to the data were related to the vertex finding efficiency which was ∼ 92.5% and the correction for branching ratio of 49.2% for the channel φ → K + K − . A more detailed description of the φ meson mass peak position, width of the φ meson invariant mass distribution, variation of the reconstruction efficiency with collision centrality and p T , and the general procedure for obtaining the signal and constructing mixed events are discussed elsewhere [23].
Systematic errors for the φ meson spectral measurements in Cu+Cu collisions include uncertainties from the following sources: Uncertainties in φ meson reconstruction efficiency (∼ 8-14%), Kaon identification from dE/dx (8%), Kaon energy loss corrections (∼ 3-4%), Residual background shape (4%) and magnetic field configuration (∼ 3%). The systematic errors from all the above sources have been added in quadrature. Systematic errors for the φ meson spectra are similar at both energies (62.4 and 200 GeV). The total systematic errors for φ yields at both energies are estimated to be < ∼ 18% over the entire p T range studied. A discussion on systematic errors for Au+Au collisions, dN/dy, and p T can be found in Ref. [3,4,23].  To study the system size dependence, comparison of 40-50% Au+Au spectra to 10-20% Cu+Cu spectra at 200 GeV, and 40-60% Au+Au spectra to 20-30% Cu+Cu spectra at 62.4 GeV are shown. These centralities for the two colliding systems have similar N part values as outlined in Table 2. The errors represent the statistical and systematic errors added in quadrature. They are found to be within the symbol size. The spectra are fitted to a Lévy function discussed in the text.  also shown in the same figure on the right panel. The ratios of the φ meson p T spectra for Au+Au and Cu+Cu systems with similar N part agree within ∼ 10%. This is further quantified by studying their rapidity density (dN/dy) and p T for both colliding systems.  Table 3. Both at 62.4 and 200 GeV, all three quantities viz dN/dy, dN/dy/ N part and p T scale with N part . These findings seem to indicate that the general features of φ meson production characterized in terms of dN/dy and p T at a given energy (62.4 or 200 GeV) do not depend on the colliding ion species studied, but depend on the N part of the collision. It will be interesting to see whether the same is true for other produced hadrons at RHIC. However, for a given N part , both dN/dy and p T are observed to be lower for 62.4 GeV when compared to 200 GeV. This is in contrast to what has been seen at lower energies at AGS and SPS with smaller colliding systems [7,8]. At those lower energies, for similar N part , the strange hadron production was higher while at RHIC, due to higher center of mass energy, a hotter and denser medium is expected to form with a very low net baryon density at midrapidity [1], leading to the observed differences.

Nuclear modification factor
Now we look at the p T dependences of the nuclear modification factor, for the φ meson, both in terms of N part and N bin . For N part , this factor is given by To get the corresponding R N bin AA (p T ), one needs to replace N part by N bin in the above expression. The results, as shown in Fig. 2 and Fig. 3   . This is reflected in the R N bin AA . As one can see from Fig. 4, R N bin AA for 0-10% Cu+Cu is higher than that of Au+Au collisions, for p T < 3 GeV/c. Both the modification factors at p T > 3.5 GeV/c are below unity, showing the characteristics of parton energy loss in hot and dense medium formed in central heavy-ion collisions. For 20-30% central collisions, the similarity between R N bin AA for Cu+Cu and Au+Au collisions seems to extend to lower p T (∼ 1.5 GeV/c). It may be interesting to use the nuclear modification factor of φ mesons to investigate the differences in energy loss of quarks and gluons in the medium formed in heavy-ion collisions [26]. This is because φ mesons in central collisions are formed from coalescence of s ands quarks [3], which presumably are formed by gluon interactions in the initial stages of the collision.

φ meson production and strangeness enhancement
The ratio of strange hadron production normalized to N part in nucleusnucleus collisions relative to corresponding results from p+p collisions at 200 GeV are shown in the upper panel of Fig. 5. The results are plotted as a function of N part . K − [27],Λ and Ξ +Ξ [18] are seen to show an enhancement (value > 1) that increases with the number of strange valence quarks. Furthermore, the observed enhancement in these open-strange hadrons increases with collision centrality, reaching a maximum for the most central collisions. However, the enhancement of φ meson production from Cu+Cu and Au+Au collisions shows a deviation in ordering in terms of the number of strange constituent quarks. More explicitly, this enhancement is larger than for K − and Λ, at the same time being smaller than in case of Ξ +Ξ. Despite being different particle types (meson-baryon) and having different masses, the results for K − andΛ are very similar in the entire centrality region studied. This rules out a baryon-meson effect as being the reason for the deviation of φ mesons from the number of strange quark ordering seen in Fig. 5 (upper panel). The observed deviation is also not a mass effect as the enhancement in φ meson production is larger than that inΛ (which has mass close to that of the φ).
In heavy-ion collisions, the production of φ mesons is not canonically suppressed due to its ss structure. In low energy p+p collisions at √ s = 3.6 GeV, φ meson production is suppressed due to the OZI rule [28]. In p+p collisions at √ s = 6.84 GeV violation of this rule has been reported [29]. At this higher energies φ production through channels accompanied by non-strange hadrons was found to dominate strongly over its production in channels accompanied with strange hadrons. Measurements of φ production in protonnucleus collisions at √ s N N = 27.4 GeV have also shown that it takes place primarily by other than OZI allowed processes [30]. Experiments studying inclusive φ production off protons by hadrons at incident momenta 63 and 93 GeV/c also show that the production of φ mesons are from OZI allowed processes [31]. Experiments on the production of φ mesons in p+p collisions near threshold have shown a large enhancement of the cross section ratio σ(pp → ppφ)/σ(pp → ppω) [32] compared to that predicted by the OZI rule [33]. This ratio is sensitive to the basic feature of the rule, which states that proceses with disconnected quark lines between initial and final states are suppressed compared to those where the incident quarks continue through to the exit channel. The p+p collisions at RHIC are at an energy which is ∼ 25 times higher than energies where violations of the OZI rule were reported [29]. The φ meson enhancement in heavy-ion collisions shows an increasing trend with centrality (Fig. 5). From this, we conclude that the observed enhancement of φ production in heavy-ion collisions may not be due to OZI suppression of φ production in p+p collisions.
The observed enhancement of φ meson production then is a clear indication for the formation of a dense partonic medium being responsible for the strangeness enhancement in Au+Au collisions at 200 GeV. Furthermore, φ mesons do not follow the strange quark ordering as expected in the canonical picture for the production of other strange hadrons. The observed enhancement in φ meson production being related to medium density is further supported by the energy dependence shown in the lower panel of Fig. 5 . The φ meson production relative to p+p collisions is larger at higher beam energy, a trend opposite to that predicted in canonical models for other strange hadrons. Earlier measurements have indicated that φ meson production is not from coalescence of KK and minimally affected by re-scattering effects in the medium [4]. Recent measurements indicate that φ mesons are formed from the coalescence of seemingly thermalized strange quarks [3]. All these observations put together along with the observed centrality and energy dependence of φ meson production (shown in Fig. 5) indicate the formation of a dense partonic medium in heavy-ion collisions where strange quark production is enhanced (possible mechanisms could be as discussed in Refs. [10,14]). This in turn suggests that the observed centrality dependence of the enhancement for other strange hadrons (shown in Fig. 5) is likely to be related to the same reasons as in the case of the φ meson, that it is due to the formation of a dense partonic medium in the collisions. These experimental data rule out the possibility of canonical suppression being the only source of the observed strangeness enhancement at beam energies of 200 GeV.

Summary
We have presented a study of the energy and system size dependence of φ meson production using the p+p, Cu+Cu and Au+Au data at √ s NN = 62.4 and 200 GeV. The p T spectra are measured at midrapidity (|y| < 0.5) over the range 0.4 < p T < 5 GeV/c. These measurements provide new experimental results showing that at a given beam energy the transverse momentum spectra in both shape ( p T ) and yields (dN/dy) are similar in Cu+Cu and Au+Au for collisions with similar N part . In addition to observing similarity in the φ meson distributions for Cu+Cu and Au+Au collisions with similar N part , the N part scaled nuclear modification factors are observed to be similar for the 0-10% central Cu+Cu and Au+Au collisions at 200 GeV. However, such a similarity is not seen for other collision centralities. The corresponding results for the nuclear modification factor, scaled by the number of binary collisions, are in general found to be higher for Cu+Cu compared to Au+Au collisions.
The enhancement in the φ meson production has been studied through the ratio of the yields normalized to N part in nucleus-nucleus collisions to corresponding yields in p+p collisions as a function of N part . The centrality and energy dependence of the enhancement in φ meson production clearly reflects the enhanced production of s-quarks in a dense medium formed in high energy heavy-ion collisions. This then indicates that the observed enhancements in other strange hadron (K − ,Λ and Ξ +Ξ) production in the same collision system are likely to be due to the similar effects and not only due to canonical suppression of strangeness production. At RHIC the colliding beam energy is high, so it is very unlikely that the observed enhancement in heavy-ion collisions is due to OZI suppression of φ production in p+p collisions.
The enhancement in the φ meson production deviates from the number of valence s-quark dependence observed for other strange hadrons. The results from φ mesons lie in between those from single valence s-quark carrying hadrons K − andΛ, and double valence s-quark carrying hadrons Ξ +Ξ. Comparisons with other strange hadrons rule out the possibility of this being a baryon-meson or mass effect. The exact reason for the observed deviation of the enhancement factor for the φ meson from the valence strange quark dependence observed for other strange hadrons is not clear. It could be due to the effect of light-flavor valence quarks in the other strange hadrons or due to the net strangeness being zero in φ mesons.