Hydrodynamical Beam Jets in High Energy Hadronic Collisions∗
연구팀의 연구 결과는 1차원적인 확장(stage of expansion)만 고려할 때 고에너지 충돌을 설명할 수 있다는 것을 보여준다. 이 결과는 Landau Hydrodynamical Model(LHM)을 사용하여 고에너지 충돌을 설명하기 위한 새로운 접근법을 제시한다.
연구팀은 1차원적인 확장과 3차원적인 확장이 모두 고려한 모델을 만들었지만, 1차원적인 확장을 제외하고는 데이터를 잘 설명할 수 없었다. 연구팀은 또한 고에너지 충돌에서 지역적 열역동적 평형(local thermal equilibrium, l.e.)가 깨진다는 것을 보여주었다.
고에너지 충돌에서 3차원적인 확장이 시작되는 시점을 표현한식으로 1차원적인 확장의 지속 시간은 증가할 수록, 전방방향 확장의 폭은 좁아지는 것을 나타내었다. 연구팀은 또한 고에너지 충돌에서 1차원적인 확장을 고려하지 않을 경우, 데이터를 설명하기가 어렵다는 결론을 얻었다.
연구팀은 고에너지 충돌에서 지역적 열역동적 평형(local thermal equilibrium, l.e.)이 깨진다는 것을 보여주었고, 이러한 현상을 설명하기 위한 새로운 접근법을 제시하였다. 연구팀은 또한 고에너지 충돌에서 1차원적인 확장을 고려하는 것이 중요하다는 결론을 얻었다.
한글 요약 끝
Hydrodynamical Beam Jets in High Energy Hadronic Collisions∗
arXiv:hep-ph/9308300v2 26 Aug 19931Hydrodynamical Beam Jets in High Energy Hadronic Collisions∗U. Ornik a †, R. M. Weiner b ‡ and G.Wilk c §a GSI Darmstadt, Darmstadt, F.R.Germanyb Physics Department, University of Marburg, F.R.Germanyc SINS, Nuclear Theory Department, Warsaw, PolandA study of hadronic data up to TEVATRON energies in terms of relativistic hydrody-namics indicates an extended 1-dimensional stage of the expansion which suggests a jetlike behaviour of the fireball along the collision axis.The Landau Hydrodynamical Model (LHM) exists already for 40 years but there hasbeen little progress in understanding its successes.
Hydrodynamics assumes in generallocal thermal equilibrium (l.e. ), a condition difficult to realize in small and short livedhadronic systems with a typical size of 10−13 cm and a corresponding lifetime of ∼10−23sec.The discovery of subentities of hadrons (quarks and gluons) with the associatedproliferation of degrees of freedom has facilitated the believe in l.e.
[1], nevertheless thephenomenological success of the LHM has not been understood so far. The situation isbetter for heavy ion reactions which are larger systems, and where it is easier to get l.e.We want to suggest that one possible reason for the success of LHM in hadronic reactionsis the fact that Landau [2] and most of his followers used only a 1-dimensional (1d) solutionwhich corrects for the possible absence of l.e.
in these reactions. This conclusion followsfrom a comparison of 1d and 3d solutions to be reported below.
The 1d approach assumesthat the strongly compressed initial fireball expands at first mainly in the longitudinaldirection (the width of the rapidity distribution is directly connected with the strengthof this flow). Then a conical (3d) correction follows.
A reasonable estimation for themoment τ3d when the conical expansion starts (R denotes the transverse radius of thefireball) is:τ3d =√t2 −x2 = a3dR(1)∗to appear in the Proceeding of Quark Matter 93†E. Mail: ORNIK@TPRI6B.GSI.DE‡E.
Mail: WEINER@VAX.HRZ.UNI-MARBURG.DE§E. Mail: WILK@FUW.EDU.PL
2where a3d is a phenomenological parameter (determined by Landau from simple geome-trical considerations [2] to be equal to a3d ≡aL = (1 + c20)/c20; c0 is the speed of sound).In Fig. 1 we present rapidity distributions calculated for “conical” 1d and 3d [3] solutionscompared with ¯pp data at SPS (√s = 20 GeV) and ISR (√s = 53 GeV) energies.
The 3dsolution uses c0 as given by lattice QCD [3] and K =0.35 at √s = 20 GeV and K = 0.176at √s = 53 GeV. More realistic values of K lead even to a worsening of the agreementwith data.
The 1d solution uses c20 = 0.18 at √s = 20 GeV and c20 = 0.195 at √s = 53GeV and K = 0.5.It turns out that only the 1d solution is able to fit the data with reasonable values forc0 and inelasticity K. The transverse expansion (present only in the 3d case) develops atthe expense of the longitudinal expansion and therefore reduces the width of the rapiditydistribution. However, going to still higher energies we have found that one has to increasethe duration of the 1d stage even further (by increasing a3d above the limit aL given byLandau).In Fig.2 we show fits to different pseudorapidity distributions which areobtained with a3d increasing from√2aL at √s = 53 GeV to√10aL at 1800 GeV.
Wehave checked that these results hold (almost) independently of the concrete variant ofinitial conditions and equation of state (EOS) provided they are physically reasonable.This observation poses a serious problem for LHM because the corresponding extended1d stage is not present in the “real” 3d dynamics (which is based on the assumptionthat each fluid cell has in its rest frame an isotropic pressure - a result of the assumedisotropic momentum distribution corresponding to local equilibrium (l.e.)). One mighttherefore argue that because of the breakdown of l.e.
conventional hydrodynamics is notvalid anymore. On the other hand, the success of 1d LHM in describing data, illustratedabove, allows also a different interpretation.
In the following we shall argue that at highenergies a “new” physical effect occurs, namely a strong anisotropy in the flow caused bysome physical processes acting on top of the conventional hydrodynamical description.The simplest “model” for such an anisotropy would be to postulate the existence ofbeam jets associated e.g. with the leading particles.
This would make necessary a re-formulation of the inelasticity effect in the LHM. So far inelasticity K was considered inthe LHM by assuming that only the function K of the available energy contributed tothe mass of the fireball which underwent hydrodynamical expansion [3,4].
In this waythe leading particles “had done their job” and did not interfere anymore with the cen-tral fireball. This treatment may be an oversimplification.
A more realistic approach inthis direction is represented by the two component model proposed in [5]. It is basedon the analysis of multiplicity distributions P(n) at energies between 20 and 540 GeV[6].
They were interpreted as indicating the presence of two different types of sourcesemitting secondaries: (i) - chaotic, provided by gluonic interaction (i.e., equilibrated) andconcentrated in the central rapidity (i.e., hydrodynamical) region with P(n) of negativebinomial type and (ii) - coherent, provided by the leading valence quarks (therefore farfrom equilibrium) and extending over the entire rapidity region (but contributing mainlyto fragmentation region) with P(n) consistent with a Poisson distribution. In this contextthe anisotropy and the elongation of τ3d can be viewed as a manifestation of the coherent
3component due to the leading valence quarks5.Formally these possibilities could be formulated in terms of anisotropic hydrodynamicsas proposed in [7].In the present study we shall limit ourselves just to consider theextended 1d stage as a phenomenological observation which may have consequences forthe interpretation of data from future experiments for hadronic and heavy ion collisions(RHIC, LHC or SSC). Here the hadronic reactions provide a lower limit for stopping,lifetime and equilibration and an upper limit for the width of the rapidity distribution σ.For this last quantity we get as an upper limitσ ≤qln R/δi + σtherm;(σtherm < 1.65forTf < 0.2 GeV).
(2)where δi is the initial longitudinal extension of the fireball and σtherm the contribution ofthe thermal motion to the rapidity width. It grows with energy slower than the phasespace.
This is shown in Fig. 3.
A hydrodynamic stage in high energy collisions leadstherefore to a limited value of σ (e.g. σ < 5 at LHC energies).
It can be also shown that allrelevant information concerning the transition from a strongly interacting non-equilibriumsystem to a thermalized fireball is contained in the fragmentation region (i.e., the phasespace region where the transition from a local equilibrium in a pre-equilibrium stage takesplace. This is also illustrated in Fig.4 where one can see how the initial longitudinal sizeof the fireball (determined in the pre-equilibrium stage) is strongly reflected in the shapeof rapidity distribution.
The main effects appear in the fragmentation region.We conclude than that a hydrodynamical analysis of ¯pp data indicates a large extensionof the 1d stage of the expansion and is described approximately by the Khalatnikovsolution [2]. The observation of the fragmentation region (3 < ycm < 5) is essential forthe investigation of the transition from the pre-equlibrium to the local equilibrium stageof the reaction.This work was supported in part by the Deutsche Forschungsgemeinschaft, the Gesellschaftf¨ur Schwerionenforschung and the Polish State Committee for Scientific Research, GrantNo.
2 0957 91 01.REFERENCES1.Cf. e.g.
E. Shuryak, The QCD Vacuum, Hadrons and the Superdense Matter, WorldScientific 1988; L.Van Hove, Z. Phys. C21 (1983) 93 and C27 (1985) 135.2.L.D.
Landau and S.Z. Bilenkij, Nouvo Cim.
Suppl. 3 (1956) 15; I.M.
Khalatnikov, Zh.Eksper. Teor.
Fiz. 27 (1954) 185.3.U.Ornik, F.W.Pottag and R.M.
Weiner, Phys. Rev.
Lett. 63 (1989) 2641.4.P.
Carruthers and Minh Duong-Van, Phys.Rev. D28 (1983), 130.5.G.N.
Fowler et al.,Phys. Rev.
Lett. 57 (1986), 2119; M. Biyajima et al., Phys.Rev.D43 (1991), 1541; cf.
also: G.Wilk et al., in Proc. of The First German-Polish Symp.5 Another, more radical possibility would be to assume that the configuration space in high energyhadronic reactions has fractal nature meaning effectively that the number of dimensions d is less than 3.
4on Particles and Fields, April 1992, Rydzyna Castle, Poland, eds. M.Paw lowski et al.,World Scientific 1993, in print.6.G.
Alner et al., Phys.Lett. B160 (1985) 193.7.I.
Lovas et al., Phys. Rev C45 (1987) 141; B. Kaempfer et al., Phys.
Lett. B240 (1990)297.
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