

 2 Jun 93

Studying minijets via the pT dependence of two-particle correlation in azimuthal angle OE

Xin-Nian Wang Nuclear Science Division, Mailstop 70A-3307, Lawrence Berkeley Laboratory

University of California, Berkeley, California 94720y

and Physics Department, Duke University, Durham, NC 27706.

(Received )

Following my previous proposal that two-particle correlation functions can be used to resolve the minijet contribution to particle production in minimum biased events of high energy hadronic interactions, I study the pT and energy dependence of the correlation. Using HIJING Monte Carlo model, it is found that the correlation c(OE1; OE2) in azimuthal angle OE between two particles with pT ? pcutT resembles much like two back-to-back jets as pcutT increases at high colliding energies due to minijet production. It is shown that c(0; 0)\Gamma c(0; ss), which is related to the relative fraction of particles from minijets, increases with energy. The background of the correlation for fixed pcutT also grows with energy due to the increase of multiple minijet production. Application of this analysis to the study of jet quenching in ultrarelativistic heavy ion collisions is also discussed.

13.87.Ce, 12.38.Bx, 12.38.Qk, 13.85.Hd

Typeset Using REVTEX

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I. INTRODUCTION Minijets with pT ?, few GeV/c are commonly believed to become increasingly important in hadronic interactions for energies beyond the CERN Intersecting Storage Ring (ISR) energy range. It has been suggested by many authors that they are responsible for not only the global properties, like the rapid increase of the total cross sections[1]-[7] and the average charged multiplicity[7, 10], but also the local correlation and fluctuations[6]-[10] of multiparticle production in high energy pp and p_p collisions. They have also been estimated to play an important role in ultrarelativistic heavy ion collisions[11].

Another particularly interesting feature of minijets is that they seem to give a natural explaination[12] to the apparent "flow" effect in high energy p_p collisions. This "flow" effect is the observation in experiments[13] at Fermilab Tevatron Collider energy that the average transverse momentum of charged particles increases with the total multiplicity of the events and the increase is stronger for heavy particles than the light ones. However, this observation is surprisingly in coincident with the results of an equilibrated quark gluon plasma (QGP)[14] in which the common transverse flow velocity from the collective expansion gives heavy particles larger transverse momentum than the pions. The speculation was made even more plausible by L'evai and M"uller's finding[15] that there is no time for the baryons to equilibrate with the pions during the expansion of a hadronic fireball. Other models such as the string fusion model[16] can also explain the observed phenomenon. In order to differentiate the minijet picture from the other scenarios, one must find a way to confirm the influence of minijets on particle production.

Although minijets are anticipated from the prediction of perturbative QCD (PQCD) and many efforts have been made to investigate their phenomenological consequences, there exists little direct experimental evidence of their presence in hadronic collisions. The only experimental attempt to find minijets is by UA1 experiments[17] at CERN where hadronic clusters with transverse energy ET ?, 5 GeV have been identified as minijets and the cross sections are found to be consistent with the PQCD prediction. However, this kind of cluster-finding method even for intermediate ET values is complicated by the background of random fluctuations[18]. For smaller ET , minijet clusters are overwhelmed by the background fluctuation. Therefore, because of their small transverse momenta, minijets with relatively small pT ?, 2 GeV/c can never be resolved as distinct jets from the large soft background in minimum biased events. To avoid the experimental difficulties of reconstructing jets with the huge background in high energy AA collisions, it has been suggested[19] that

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single inclusive spectra of produced particles can be used to study the properties of jet production. Similarly, I have proposed in a previous paper[20] that two particle correlation functions is useful to study the content of minijets in minimum biased events of hadronic interactions. In this paper, I report the detailed study of the pT and energy dependence of the two-particle correlation in the azimuthal angle OE and the influence of finite rapidity cuts.

Since particles from jet fragmentation are correlated in both directions of the minijets, they have been found[21] to dominate both the short and forward-backward two-particle correlations in pseudorapidity. For two-particle correlation in the azimuthal angle OE, contribution from back-to-back minijets should be strongly peaked at both forward (\Delta OE = 0) and backward (\Delta OE = ss) directions. If we calculate the same correlation, but for some selected particles whose transverse momenta are larger than a certain pT cut, the two peaks should be more prominent because these particles are more likely to come from minijets. The energy and pT dependence of such correlations of charged particles must depend on the relative fraction of minijet events and minijet multiplicity, thus shedding some light on minijet content in these events. On the contrary, particles from soft production of fused strings or an expanding quark gluon plasma are isotropical in the transverse plane and would only have some nominal correlation in the backward direction due to momentum conservation.

The experimental study of the two-particle correlations is important to clarify the controversial issue whether the observed flavor dependence of the correlation between the multiplicity and average transverse momentum at Fermilab Tevatron energy[13] is due to minijet production[12], or string interaction[16], or the formation of a quark gluon plasma[14]. On the other hand, it can also provide constraints on theoretical models as how to combine PQCD hard scatterings with nonperturbative soft interactions, how to parametrize the soft processes, and what is the appropriate fragmentation scheme of multiple minijets. In the light of the study on intermittency in particle production[22], it also helps us to have a better understanding of the intermittent fluctuations in hadronic collisions at collider energies as particles from jet fragmentation indeed have been shown to have strong intermittent behavior[23].

This study is based on the Monte Carlo model, HIJING[24], which combines a simple two-string phenomenology for low pT processes together with PQCD for high pT processes. Since HIJING is a model with a very specific scheme of minijet fragmentation, the results we get are only a qualitative estimate of the effects of minijets on the two-particle correlation functions. Though the correlations in pseudorapidity j and azimuthal angle OE are both important, we limit our discussions only to the

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latter case. The remaining of this paper is organized as follows. In Sec. II we briefly review the HIJING model as discussed in detailed in Ref.[24]. In Sec. III we study the pT dependence of the two-particle correlations in OE and their resemblance to large pT jet profiles. Special emphasis is given to the effects of minijets on the back-to-back differences of the correlation, c(0; 0) \Gamma c(0; ss). In Sec. IV, the energy dependence of the background of the correlation and its implication on multiple minijet production are discussed. The effect of finite rapidity cut is also discussed. Finally, Sec. V concludes with a summary and remarks.

II. THE HIJING MODEL The HIJING model[24] has been developed mainly for multiple jet and particle production in pp, pA, and AA collisions at energies ps ?, 5 AGeV. The formulation of HIJING was guided by the successful implementation of PQCD in the PYTHIA model[25] and the need to incorporate a consistent model of soft processes. It thus provides a link between the dominant nonperturbative fragmentation physics at intermediate energies and the perturbative physics at higher collider energies. A detailed description of the HIJING model can be found in Ref.[24]. It includes multiple jet production with initial and final state radiation along the lines of the PYTHIA model[25] and soft beam jets are modeled by quark-diquark strings with gluon kinks along the lines of the DPM[26] and FRITIOF[27] models. For nucleus induced reactions, nuclear shadowing of parton structure functions and final state interaction of produced jets are also considered[19].

In the eikonal formalism, the inelastic cross section of pp or p_p collisions is given by

oein = Z d2b[1 \Gamma e\Gamma (oesoft+oejet)TN(b;s)]; (1) where TN (b; s) is the partonic overlap function between two nucleons at impact parameter b, oejet(p0; s) is the total inclusive jet cross section calculated from PQCD with pT ? p0, and oesoft(s) is the corresponding phenomenological inclusive cross section of soft interactions. The cross sections for no and j * 1 number of hard or semihard parton scatterings are,

oe0 = Z d2b[1 \Gamma e\Gamma oesoftTN(b;s)]e\Gamma oejetTN(b;s) ; (2)

oej = Z d2b [oejetTN (b; s)]

j

j! e

\Gamma oejetTN (b;s) ; (3)

with their sum giving rise to the total inelastic cross section, oein. Following the above

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formulas, the cross section with at least one hard parton scattering, defined as oehard, is then

oehard = Z d2b[1 \Gamma e\Gamma oejetTN(b;s)]e\Gamma oesoftTN (b;s); (4) and the average number of parton scatterings per inelastic event is

hnjeti = oejet(p0; s)=oein: (5) Shown in Fig. 1 are the energy dependence of hnjeti and the fractional cross section of hard processes, oehard=oein for p0 = 2 GeV/c and oesoft = 57 mb. We see that as energy increases inelastic events contain more and more hard processes and finally are dominated by minijet production. The probabilities for multiple minijet production also become prominent at energies above 1 TeV as hnjeti ?, 1.

Once again, we emphasize here that p0 and oesoft in HIJING model are phenomenological and model dependent parameters separating PQCD at high pT from the nonperturbative low pT regime. Our guideline for choosing the value of p0 is that it should be much larger than \Lambda QCD , 200 MeV/c in order to apply PQCD but low enough to permit the simplest possible model for the nonperturbative dynamics. Choosing p0 = 2 GeV/c allows us to use a constant oesoft = 57 mb to reproduce the observed energy dependence of the total, elastic and inelastic cross sections in pp and p_p collisions[10, 21]. With these parameters, it has been shown[21] that a simple two-string model suffices to account for the soft dynamics. A complete test of the HIJING model has been reported in Ref. [21]. The model has been successful to provide a consistent explanation of not only the energy dependence of pseudorapidity distributions, moderate pT inclusive spectra, and the violation of Koba-Nielsen-Olesen (KNO) scaling, but also the flavor and multiplicity dependence of the average transverse momentum[12] in pp and p_p collisions in a wide energy range ps = 50-1800 GeV. In addition, it is also consistent with the available data on pA and AA collisions at moderate energies ps !, 20 AGeV[24].

III. TWO-PARTICLE CORRELATION Experimental study of particles from the fragmentation of high pT jets has shown that particles with larger average transverse momenta are much concentrated in both directions of the back-to-back jets. The widths of these jet profiles are about 1 in both pseudorapidity j and azimuthal angle OE as has been determined from the calorimetric study of high pT jets. It is apparent that similar trends should also hold for particles from minijets and they must influence the two-particle correlation functions. It has

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already been shown in Ref. [21] that minijets are the dominant mechanism underlying both the enhanced short range and forward-backward correlations in j. In this paper I demonstrate that the energy and pT dependence of two-particle correlations in the azimuthal angle OE can be used to study minijets in minimum biased events. One can expect that with higher pcutT , the correlation must look similar to the high pT jet profiles. Moreover, the energy dependence of the correlation for fixed pcutT should be related to the increase of the fraction of minijet events and the average number of minijets as shown in Fig. 1.

The normalized two-particle correlation functions are defined as,

c(OE1; OE2) j ae(OE1; OE2)ae(OE

1)ae(OE2) \Gamma 1; (6)

where ae(OE) is the averaged particle density in OE and ae(OE1; OE2) is the two-particle density which is proportional to the probability of joint particle production at OE1 and OE2. Both ae(OE) and ae(OE1; OE2) are integrated over the whole rapidity range. The limitation of a restricted rapidity range will be discussed in the next section. In actual calculations, one direction in the transverse plane is randomly selected as OE1 = 0 for all the events and then both the averaged single inclusive density ae(\Delta OE) and the two-particle joint density ae(0; \Delta OE) are calculated. Because the collisions are symmetrical in the transverse plane perpendicular to the beam direction, ae(\Delta OE) should be a constant equal to the total averaged multiplicity of the selected particles divided by 2ss. Similarly, ae(0; \Delta OE) is also independent of the direction which is chosen as OE1 = 0. In fact, one can even choose the direction of each particle as OE1 = 0 to calculate c(0; \Delta OE) and then average it over all particles in each event. In this case one can get better statistics for a limited number of events. Since I have the luxury to produce many events through the Monte Carlo simulation, I instead try to average over as many events as we can to achieve the best statistics possible over global quantities such as the number of jets per event with relative large pT .

Shown in Figs. 2-5 are calculated results on two-particle correlation functions in pp and p_p collisions at different energies. To study the pT dependence, the correlations are obtained for selected particles with different transverse momentum cut pT ? pcutT =0 (long-dash-short-dashed histograms), 0.5 (dotted histograms), 1.0 (solid histograms), 1.5 (short-dashed histograms), and 2.0 (dot-dashed histograms). At low energy ps = 50 GeV (Fig. 2) where minijet production is not very important as seen from Fig. 1, there is very little correlation between two particles with \Delta OE !, 2ss=3 except some small increase at \Delta OE , 0 for the case of pT ? 1:0 GeV/c. The correlation at \Delta OE , ss is totally due to the momentum conservation which increases with larger

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pT cuts. As was pointed out in Ref. [21], minijet contribution to particle production at the highest CERN ISR energies ps ss 50 GeV is just beginning to emerge. This is again illustrated here by the slight increase of the correlation at \Delta OE , 0 for particles with pT ? 1:0 GeV/c.

As we can see from Fig. 1, minijet production increases very fast with energy and becomes a significant part of the hadronic interactions above ps ?, 100 GeV. Therefore, the two-particle correlation functions in Fig. 3 for ps = 200 GeV are very different from those at ps = 50 GeV in Fig. 2. We observe that there is apparently strong correlation between two particles with pT ? 0:5 GeV/c at both \Delta OE , 0 and ss forming a valley at \Delta OE , ss=3. This feature is very similar to the high pT jet profiles as functions of OE relative to the triggered jet axis[28]. However, due to the relative large fraction of particles from soft interactions where momentum conservation dictates the two-particle correlation at \Delta OE , ss, the resultant c(0; \Delta OE) at \Delta OE , ss is still larger than at \Delta OE , 0. Whereas in high pT jet profiles, the peak of particle flow toward the triggered jet (\Delta OE = 0) is always narrower but the height is about the same as in the backward direction(\Delta OE = ss). The dominance of particles from soft interactions at this energy is clearly demonstrated in the case of pcutT = 0 where c(0; \Delta OE) monotonically increases from 0.2 at \Delta OE = 0 to 0.3 at \Delta OE = ss.

As we increase the energy to 1.8 and 6 TeV (Figs. 4, 5), the correlation functions with no pT cut become flatter over the whole angular range due to the increasing fraction of particles from minijets relative to the soft processes. The correlation functions with higher pT cuts look more and more similar to the high pT jet profiles with c(0; 0) ss c(0; ss) and narrower peaks at \Delta OE , 0. We know from Fig. 2 that particles from soft production have some strong correlation only at \Delta OE , ss due to momentum conservation while particles from minijets, on the other hand, have enhanced correlation both at \Delta OE , 0 and ss. The actual shape of the correlation function then depends on the relative fractions of particles from minijets and soft processes. Looking through Figs. 2-5, we can clearly see that the height of the correlation functions at \Delta OE , ss gradually becomes equal to that at \Delta OE , 0 as shown in Fig. 6 by the increase of the difference c(0; 0) \Gamma c(0; ss) with energy. It approaches zero for any fixed pcutT at higher energies. This energy dependence of c(0; 0) \Gamma c(0; ss) is a direct consequence of the increase of minijet production with energy in pp and p_p collisions. Thus, it has been demonstrated that the study of the energy and pT dependence of two-particle correlation function c(0; \Delta OE) can provide us with information about the minijet content in minimum biased events.

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IV. EFFECTS OF MULTIPLE MINIJETS AND FINITE RAPIDITY CUT When the average number of produced minijets is larger than one (Fig. 1) at high colliding energies, multiple minijet production becomes important[10, 24]. Since these minijets are independently produced, they should increase the background to the twoparticle correlation. The very extreme cases are central events of high energy heavy ion collisions where hundreds of minijets are produced. The two-particle correlation will be completely flat when the valleys we see in Figs. 2-5 for pp and p_p collisions are filled up by the increased background. In hadronic collisions this rarely happens and the increase of the background can be considered as an implication of multiple minijet production.

Plotted in Fig. 7 is the difference c(0; 0) \Gamma c(0; ss=3) between the correlation at \Delta OE = 0 and the background in the valley \Delta OE = ss=3 for each fixed pcutT as a function of ps. It grows first with energy due to the increase of minijet events and the relative small number of minijets per event. However, as the probabilities of multiple minijet production become increasingly important, the difference then decreases with energy. The larger the pcutT , the sooner the decrease begins.

Unlike high pT back-to-back jets which are both kinematically bounded to the central rapidity region, a pair of minijets can be easily produced with large rapidity gap between them. When we trigger one minijet in a limited rapidity window, the other one which is produced in the same parton scattering often falls outside the rapidity window. Therefore, if we calculate two-particle correlation for particles in a limited rapidity range, minijet contribution to the backward correlation (\Delta OE = ss) will mostly drop out while the contribution to forward correlation (\Delta OE = 0) still remains. Indeed, as shown in Fig. 8, the forward correlation at \Delta OE = 0 for particles in jjj ! 1 is very strong, but the backward correlation at \Delta OE = ss is drastically reduced as compared to the correlation pattern in the full rapidity range in Fig. 2-5. Furthermore, due to strong short range two-particle correlation in rapidity[21], the forward correlation at \Delta OE = 0 is enhanced by restricting particles to jjj ! 1. Atp

s = 1:8 TeV, I find that the enhancement of backward correlation at \Delta OE = ss due to minijets becomes important only when the rapidity window is jjj ?, 2.

V. SUMMARY AND REMARKS It is demonstrated in detail in this paper that two-particle correlation functions in the azimuthal angle OE are useful for the study of minijets and their contribution to particle production in the minimum biased events of hadronic interactions. Because

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particles from jet fragmentation are more concentrated along the jet axes, they result in enhanced two-particle correlation in both the triggered (\Delta OE = 0) and the backward (\Delta OE = ss) direction. On the other hand, particles from isotropic soft production only have some nominal correlation in the backward direction due to momentum conservation. Therefore, the energy dependence of the relative height c(0; 0) \Gamma c(0; ss) of the correlation in the two opposite directions is directly related to the minijet content in the particle production and increases with the colliding energy. Furthermore, multiple minijet production becomes important at high energies and they increase the background relative to the enhanced correlation at \Delta OE = 0 and ss.

It is important to keep in mind that the results we obtained via HIJING are only intended to show qualitatively the effects of multiple minijets on the energy and pT dependence of two-particle correlation in OE. The quantitative magnitudes of the correlations must depend on the specific scheme of minijet fragmentation and the color flow of multiple minijets[24] in HIJING. It is important to study in the future the sensativity of two-particle correlation functions to the schemes of minijet fragmentation and the color flow structure of multiple minijets. The final schemes which survive the tests on single inclusive spectra have also to be constrained by the experimental measurements of the energy and pT dependence of two-particle correlation functions.

I have emphasized the implications of the energy and pT dependence of the twoparticle correlation functions on minijet production. For experiments at a fixed energy, one can also investigate the contribution of minijets to the two-particle correlation function by comparing the direct measurements to the calculation from the same data sample but with randomized azimuthal angle OE for each particle. Due to this randomization of OE, the correlation calculated from the manipulated data should be much flatter than the real one for any given pcutT . It is also important and interesting to study the pT dependence of two-particle correlation functions in pseudorapidity j and the correlation relative to a triggered particle which has the highest pT in each event[20].

As discussed in Sec. IV, the two-particle correlation in OE in ultrarelativistic heavy ion collisions should be much flatter than in pp and p_p collisions for any fixed pcutT due to the huge number of minijet production. However, if we increase pcutT to a much larger value (e.g. 4-6 GeV/c), the background to the correlation becomes smaller due to small cross sections of large pT jets. Since the single inclusive spectrum at large and moderate pT has been shown to be sensative to jet quenching[19], twoparticle correlation is apparently more relevant to the study of jet quenching and the

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implication on energy loss mechanism it conveys.

ACKNOWLEDGMENTS I would like to thank A. Goshaw, M. Gyulassy, B. M"uller, and S. Oh for their helpful comments and encouraging discussions. This work was supported by the Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098 and DE-FG05-90ER40592.

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FIGURES FIG. 1. Fractional cross section oehard=oein for at least one hard scattering and average number of minijet production hnjeti per event as functions of ps.

FIG. 2. The correlation functions c(0; \Delta OE) between two particles with fixed pT cutoff vs \Delta OE in pp collisions at ps = 50 GeV.

FIG. 3. The same as Fig. 2, except for p_p collisions at ps = 200 GeV. FIG. 4. The same as Fig. 2, except for p_p collisions at ps = 1:8 TeV. FIG. 5. The same as Fig. 2, except for ps = 6 TeV. FIG. 6. The energy dependence of the difference c(0; 0) \Gamma c(0; ss) between the correlation at \Delta OE = 0 and ss for each fixed pT cutoff.

FIG. 7. The energy dependence of the difference c(0; 0) \Gamma c(0; ss=3) between the correlation at \Delta OE = 0 and the background at ss=3 for each fixed pT cutoff.

FIG. 8. The same as Fig. 4, except for charged particles in a limited rapidity range of jjj ! 1.

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