cu - TP - 626 / EERNIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII I.12RI=IR1I;s. QI.; 621426
VACUUM AS A PHYSICAL MEDIUM
(RELATIVISTIC HEAVY ION COLLISIONS
AND THE BOLTZMANN EQUAT ION)
T. D. LEE
COLUMBIA UNIvERsI1Y, New Y0RI<, N.Y. 10027
A LECTURE GIVEN AT THE INTERNATIONAL SYMPOSIUM IN HONOUR OF BOLTZMANN'S 1 50TH BIRTHDAY, FEBRUARY 1994.
THIS RESEARCH WAS SUPPORTED IN PART BY THE U.S. DEPARTMENT OF ENERGY. OCR Output
OCR OutputVACUUM AS A PHYSICAL MEDIUM
(Relativistic Heavy Ion Collisions
and the Boltzmann Equation)
T. D. Lee
Columbia University, New York, N.Y. 10027
It is indeed a privilege for me to attend this international symposium in honor of Boltzmann's 150th birthday. ln this lecture, I would like to cover the following topics:
1) Symmetries and Asymmetries: Parity P (right—left symmetry) Charge conjugation C (particle-antiparticle symmetry) Time reversal T Their violations and CPT symmetry.
2) Two Puzzles of Modern Physics: Missing symmetry Vacuum as a physical medium Unseen quarks.
3) Relativistic Heavy Ion Collisions (RHIC): How to excite the vacuum? Phase transition of the vacuum Hanbury-Brown-Twiss experiments.
4) Application of the Relativistic Boltzmann Equations: ARC model and its Lorentz invariance AGS experiments and physics in ultra-heavy nuclear density. OCR Output One of the underlying reasons for viewing the vacuum as a physical medium is the discovery of missing symmetries. I will begin with the nonconservation of parity, or the asymmetry between right and left. ln everyday life, right and left are obviously distinct from each other. Our hearts, for example, are usually not on the right side. The word right also means "correct,' right? The word sinister in its Latin root means "left"; in Italian, "left" is sinistra. Such asymmetry in daily life, however, is attributed either to the accidental asymmetry of our environment or to initial conditions. Before the discovery of right-left symmetry violation (parity nonconservation) at the end of 1956, it was taken for granted that the laws of nature are symmetrical under a right—left transformation; that is, the world in the looking glass could be a real world.
Let me give you an example. Suppose there are two cars which are made exactly alike, except that one is the mirror image of the other, as shown in Figure 1. Car a has a driver on the left front seat and the gas pedal near his right foot, while s has the driver on the right front seat with the gas pedal near his left foot. Both cars are filled with the same amount of gasoline, which is asumed to have no impurities and is right-left symmetrical. Now, suppose the driver of Car a starts the car by turning the ignition key clockwise and stepping on the gas pedal with his right foot, causing the car to move forward at a certain speed, say 30 mph. The other does exactly the same thing, except that he interchanges right with left; that is, he turns the ignition key counterclockwise and steps on the gas pedal with his left foot, but keeps the pedal at the same degree of inclination. What will the motion of Car s be? You are encouraged to make a guess.
Probably your common sense will say that obviously both cars should move forward at exactly the same speed. lf so, you are just like the pre-1956 physicists. lt would seem reasonable that two arrangements, identical except that one is the mirror image of the other, should subsequently behave in exactly the same way in all respects, except of course for the original right-left difference. In other words, while right and left are different from each other it seems self-evident that, except for that difference, there should be no other difference. Therefore, which one we call "right" and which "Ieft" would be entirely relative. This is precisely the right-left symmetry principle in physics.
Surprisingly, this is found to be not true. ln 1956, C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes and R.P. Hudson investigated the decay of polarized cobalt nuclei, Cow, into electrons. Because these nuclei are polarized they rotate parallel to each other. The experiment consisted of two setups, identical except that the directions of rotation of the initial nuclei were opposite; that is, each was a mirror image of the other. The experimenters found, however, that the patterns of the final electron OCR Output distributions in these two setups are not mirror images of each other. ln short, the initial states are mirror images, but the final configurations are not (see Figure 2). Now come back to our example of two cars. ln principle it is possible to install a B decay source as part of the car's ignition mechanism. lt would then be feasible, though perhaps not economical, to construct two cars that are mirror images of each other, but may nevertheless move in a completely different way: Car a moves forward at a certain speed, while car s may move at a totally different speed, or may even move backward. That is the essence of the discovery of right·left asymmetry, or nonconservation of parity
Sign of the electric charge A related symmetry is that between the positive and negative signs of electric charge. ln our usual terminology the sign of electric charge is merely a convention. The electron is considered to be negatively charged because we happened to assign the proton a positive charge, and the converse is also true. But now, with the discovery of asymmetry, is it possible to give an absolute definition to the sign of electric charge? Can we find some absolute difference between the positive and negative signs of electricity, like that between left and right? This baffling problem can be resolved by studying the decay of the long—Iived neutral kaon Ki; this particle carries no electric charge, no electromagnetic moment of any kind, has no spin, is spherically symmetric and is about 1,000 times more massive than the electron. The KZ is unstable and can decay into either an electron e` , a neutrino u, and a positive pion 1r+ , or their antiparticles: a positron e+ , an antineutrino TJ, and a negative pion 1r“ . These two different decay modes can easily be distinguished by a magnetic separation of e+ from e". Although the parent particle KZ is electrically neutral, nevertheless these two decay rates are different:
= 1.00648:l; 0.00025. rate (KZ —> e" + 1r+ + u)
This is indeed remarkable since it means that by rate counting one can differentiate 6+ from e" . Thus, there is an absolute difference between the opposite signs of electric charge. lf we pause to think about this, we are struck by how truly extraordinary it is: the original particle, KZ , is completely neutral electrically. Therefore we would assume it should have no preference for positive or negative signs of electricity; yet it decays faster into e+ than e
We use P to denote the interchange between right and left, and C that between particle and antiparticle. Since the sign of charge of any particle is the opposite of OCR Output its antiparticle, C also means the interchange between the signs of charges. ln the K}; decay, the asymmetry between the decay rates into e' and e+ would remain the same if the experiment were observed through a mirror. Therefore the same result also proved the asymmetry between the compound action of right ·—» left and particle +—> antiparicle; i.e., CP violation.
CPT Symmetry lt turns out that there is a close tie among three seemingly unrelated symmetries:
C sign change in electric charge, P mirror reflection, T time reversal.
As we have discussed, nature is not symmetrical under C or P. By more careful examination of kaon decay, it was found that nature is also not symmetrical under time reversal. However, as far as we know, the combination of these three operations seems to be an exact symmetry. ln other words, if we interchange
particle <—> antiparticle, right <—» left, past +—» future,
all physical laws appear to be symmetrical and this is called CPT symmetry. The origin of symmetry·breaking is one of the major challenges in physics. As we shall discuss, these discoveries and other strange properties observed in the particle world led us to question whether the vacuum might be a physical medium. OCR Output 2. TWO PUZZLES OF MODERN PHYSICS
Historical Remark
At the end of the last century, there were two physics puzzles: 1. No absolute inertial frame (Michelson-Morley Experiment 1887). 2. Wave-particle duality (P|anck’s formula 1900).
These two seemingly esoteric problems struck classical physics at its very foundation. The first became the basis for Einstein's theory of relativity and the second laid the foun dation for us to construct quantum mechanics. ln this century, all the modern scientific and technological deve|opments—nucleur energy, atomic physics, molecular struc ture, lasers, ac-ray technology, semiconductors, superconductors, supercomputers only exist because we have relativity and quantum mechanics. To humanity and to our understanding of nature, these are all—encompassing.
Now, near the end of the twentieth century, we must ask what will be the legacy we give to the next generation in the next century? At present, like the physicists at the end of the 1890's, we are also faced with two profound puzzles.
Two Puzzles
The status of our present theoretical structure can be summarized as follows: QCD (strong interaction) SU (2) x U (1) Theory (electro-weak) General Relativity (gravitation). However, in order to apply these theories to the real world, we need a set of about 17 parameters, all of unknown origins. Thus, this theoretical edifice cannot be considered . complete.
The two outstanding puzzles that confront us today are: i) Missing symmetries - All present theories are based on symmetry, but most symmetry quantum numbers are not conserved. ii) Unseen quarks - All hadrons are made of quarks; yet, no individual quark can be seen.
As we shall see, the resolutions of these two puzzles probably are tied to the structure of our physical vacuum. The puzzle of missing symmetries implies the existence of an entirely new class of fundamental forces, the one that is responsible for symmetry breaking. Of this new OCR Output force, we know only of its existence, and very little else. Since the masses of all known particles break these symmetries, an understanding of the symmetry-breaking forces will lead to a comprehension of the origin of the masses of all known particles. One of the promising directions is the spontaneous symmetry-breaking mechanism in which one assumes that the physical laws remain symmetric, but the physical vacuum is not. lf so, then the solution of this puzzle is closely connected to the structure of the physical vacuum; the excitations of the physical vacuum may lead to the discovery of Higgs-type mesons. The vacuum, though Lorentz invariant (therefore not aether), can be full of complexity. In some textbooks, the second puzzle is often "exp|ained" by using the analogy of the magnet. A magnet has two poles, north and south. Yet, if one breaks a bar magnet in two, each half becomes a complete magnet with two poles. By splitting a magnet open one will never find a single pole (magnetic monopole). However, in our usual description, a magnetic monopole can be considered as either a fictitious object (and therefore unseeable) or a real object but with exceedingly heavy mass beyond our present energy range (and therefore not yet seen). ln the case of quarks, we believe them to be real physical objects and of relatively low masses (except the top quark); furthermore, their interaction becomes extremely weak at high energy. If so, why don't we ever see free quarks? This is, then, the real puzzle. The current explanation of the quark confinement puzzle is again to invoke the vacuum. We assume the QCD vacuum to be a condensate of gluon pairs and quark antiquark pairs so that it is a perfect color dia-electric (i.e., color dielectric constant rc = O). This is in analogy to the description of a superconductor as a condensate of electron pairs in BCS theory, which results in making the superconductor a perfect dia—magnet (with magnetic susceptibility u = O). When we switch from QED to QCD we replace the magnetic field H by the color electric field Ecoim, the superconductor by the QCD vacuum, and the QED vacuum by the interior of the hadron. As shown in Figures 3 and 4, the roles of the inside and the outside are interchanged. Just as the magnetic field is expelled outward from the superconductor, the color electric field is pushed into the hadron by the QCD vacuum, and that leads to color confinement, or the formation of hadrons (mesons, nucleons and other baryons). This situation is summarized in Table 1. OCR Output QED superconductivity QCD vacuum as a perfect dia—magnet as a perfect color dia-electric
Ecolor
Hinside = O Kvacuum = 0
Prvacuum : 1 Kinside : 1
inside outside
outside inside
Table 1. Analogies between superconductivity and the QCD vacuum.
Vacuum as a Physical Medium
ln the resolution of both puzzles, missing symmetry and quark confinement, the system of elementary particles no longer forms a self·contained unit. The microscopic particle physics depends on the coherent properties of the macroscopic world, repre sented by the appropriate operator averages in the physical vacuum state. This is a rather startling conclusion, contrary to the traditional view of particle physics which holds that the microscopic world can be regarded as an isolated system. To a very good approximation it is separate and uninfluenced by the macroscopic world at large. Now, however, we need these vacuum averages; they are due to some long-range ordering in the state vectors. At present our theoretical technique for handling such coherent effects is far from being developed. Each of these vacuum averages appears as an independent parameter, and that accounts for the large number of constants needed in the present theoretical formulation. On the experimental side, there has hardly been any direct investigation of these coherent phenomena. This is because hitherto in most high-energy experiments, the higher the energy the smaller has been the spatial region we are able to examine. OCR Output 3. RELATIVISTIC HEAVY ION COLLISIONS (RHIC)
How To Excite the Vacuum?
ln order to explore physics in this fundamental area, relativistic heavy ion collisions offer an important new direction.1 The basic idea is to collide heavy ions, say gold on gold, at an ultra-relativistic region. Before the collision, the vacuum between the ions is the usual physical vacuum; at a sufficiently high energy, after the collision almost all of the baryon numbers are in the forward and backward regions (in the center-of-mass system). The central region is essentially free of baryons and, for a short duration, it is of a much higher energy density than the physical vacuum. Therefore, the central region could become the excited vacuum (Figure 5). As we shall see, we need RHIC, the 100 GeV >< 100 GeV (per nucleon) relativistic heavy ion collider at the Brookhaven National Laboratory, to explore the QCD vacuum.
Phase Transition of the Vacuum
A normal nucleus of baryon number A has an average radius rA z 1.2A? fm and an average energy density
e ~ JE A - e 130M V 6 ff"; 1 ( l (4W/sy;
Each of the A nucleons inside the nucleus can be viewed as a smaller bag which contains three relativistic quarks inside; the nucleon radius is r·N z 0.8fm and its average energy density is
s e —@ N - e 44oM v C Hm 2 ( l (4W/s)i·5§,
Consequently, even without any sophisticated theoretical analysis we expect the QCD phase diagram to be of the form given by Figure 6. ln Figure 6, the ordinate is kT (k = Boltzmann constant, T = temperature), the abscissa is p/pA (p = nucleon density, pA = average nucleon density in a normal nucleus A) and the dot denotes the configuration of a typical nucleus A. The scale can be estimated by noting that the critical kT ~ 150 — 300 MeV is about é— 1 times fm3 times the difference EN —· EA, and the critical p/pA ~ 4 — 8 is in the range of 1 -— 2 times (rA/rN)3 ~ (1.2/0.8);* Accurate theoretical calculation exists only for pure lattice QCD (i.e., without dynamical quarks). The result is shown in Figure 7. OCR Output If one assumes scaling, then the phase transition in pure QCD (zero baryon number, p = 0) occurs at kT ~ 150 MeV with the energy density of the gluon plasma
Ep ~ 3GeV/fm‘, (3) because of the large latent heat. To explore this phase transition in a relativistic heavy ion collision, we must examine the central region. Since only a small fraction of the total energy is retained in the central region, it is necessary to have a beam energy (per nucleon) at least an order of magnitude larger than EN x (1.2fm)‘ ~ 5 GeV; this makes it necessary to have an ion collider of about 100 GeV >< 100 GeV (per nucleon) for the study of the QCD vacuum. Another reason is that at 100 GeV >< 100 GeV the heavy nuclei are almost trans parent, leaving the central region (in Figure 5) to be one almost without any baryon number. As remarked before, this makes it an ideal situation for the study of the excited vacuum. Suppose that the central region does become a quark-gluon plasma. How can we detect it? This will be discussed in the following.
Hanbury-Brown-Twiss Type Experiments
As shown in Figure 8, the emission amplitude of two pions of the same charge with momenta kl and kg from points F1 and F2 is proportional to
A E c'I;E1·F1+‘iE;·1-5 + eiE2·1-:1+iE1·‘F3 because of Bose statistics. Let
rj;-l;1—l?2 and FEF1-F2. (5)
Since |A|z 2 1+cos¢j'·f·’ (6) changes from |A|2 = 2 as rj’—» 0, to |A|2 = 1 as gi': oo, a measurement of the vrrr correlation gives a determination of the geometrical size R of the region that emits these pions, like the Hanbury—Brown-Twiss determination of the stellar radius. Now, if the central region is a plasma of entropy density Sp occupying a volume Vp, which later hadronizes to ordinary hadronic matter (of entropy density SH and volume VH ), the total final entropy SHVH must be larger than the total initial entropy SpVp, because of the second law of thermodynamics. Since Sp > SH , we have
VH > Vp. (7) OCR Output The experimental configurations and resu|ts3 are given in Figure 9 and Table 2. One sees that the hadronization radius in the central region is indeed much larger than that in the fragmentation region. Of course, we are far from being able to make any conclusion about the quark-gluon plasma. Much work and higher energy are needed. Nevertheless, it does show that relativistic heavy ions can be an effective means of exploring the structure of the vacuum.
Rcpldity Gaussian Interval R1-(fm}
`l “* R?,_= 4A :1.0 rm 2.6 t 0.6 ¤·¤4t3;32 2 R (Oxygen) ?=' 3 fm Table 2. mr-interference resultg from the collision of an O beam (200 GeV/nucleon) on a stationary Au target. 10 OCR Output 4. APPLICATION OF THE RELATIVISTIC BOLTZMANN EQUATION An alternative possibility to generate the quark—gluon plasma is to increase the nuclear density. This approach is being explored at the AGS (Alternating Gradient Syn chrotron) at Brookhaven, as indicated in Figure 6. ln this case, there are a large number of hadrons present throughout the entire collision process. Before any conclusion can be drawn about the exotic state of quark-gluon plasma, one must first address the problem of normal hadronic collisions. An ideal method for examining this complex situation is to apply the relativisitc Boltzmann equation: r#6,.W.. * An-ml E2, mZ c1,c2,···,c,,, /1;1 j:1 %( W) cj -(2rr)‘6‘ Emi — Epo, ·i=1 j=1 — Z i=1 M. 63(1$'— 15%.)+ L 6uc, 6’(5— 152,) j=1 where W,,(:i:’,t,p‘) is the probability distribution for hadron species ¤=p,¤,vnK,p,A,/\,Z, (9) and the elements of the S—matrix are given by < c11c21 ' ' ' 1 cm I Slb11 b21` ` '1 bn >= An-vm4 4 (2706ph;TI TTI EZj `_i=1 pcj=1 Because of the great variety of hadron species, it is not easy to solve the Boltzmann equation. An effective numerical method is the relativistic cascade (ARC) model. 11 OCR Output ARC Model The ARC m0deI° is described in Table 3. Because ofthe use of a nonzero impact parameter d = x/v / rr, (11) it raises questions of Lorentz invariance which we shall now address. Cascade (AHC) 1. Initial condition _ §$i 5%} Wq(f,t,f) l°4.§I% 8°¢& a =Z6” 2. Straight line trajectories rl = ii (I) = Eg (0) + Gil 3. Collision at closest approach d < `/Z'! 4. Outgoing channel selection partial cross-sections: elastic, inelastic (productions of pion, kaon, ...) 5. Momentum distribution d (phase — space) | A |2 Repeat steps 2-5 Table 3. Computational steps of the ARC modeI‘. 12 OCR Output Relativistic Invariance of the ARC Model Decompose each hadron into a very large number A of partons, say A = 10 Thus, we regard the initial state of Au + Au as that of 197 x 10g nucleon-partons colliding with 197 x 109 nucleon-partons. Apply the cascade code of Table 3 to these partons and replace the usual hadron—hadron collisions by reactions nuc|eon-parton + nucleon-parton —» nucleon-parton + nucleon-parton (12) + vr-partons + K- partons, rr-parton + nucleon-parton (13) —» A—parton + rr-partons, etc., the final state may consist of several thousand x 109 hadron-partons, whose distribution functions can be converted back to those of the usual hadrons by a division of A = 109. As we shall see, the ARC model is Lorentz invariants in the limit A —> oo. Let W¤p(5I°,t,]$•) be the Boltzmann distribution function of partons of species a, whose integral over the phase space is equal to the total number of a-partons, and let W,,(5:’,t,g$') be that of the "parent" hadron of the same species. As we increase the number of partons per hadron from 1 to A, the Boltzmann distribution function changes from Wa —> Wap = AWG. (14) Correspondingly, the binary cross—section varies from 0 (the original hadron cross section) to ap (the parton cross·section): a—>0p=0/A. (15) As a result, the mean free path of the a-parton Z = Wap Up = Wav remains the same as its "parent" hadron. On the other hand the impact parameter for a parton-parton collision dp = (/ap/rr, as A —» oo, approaches zero: d——>dp=d/N/X—>O. (16) OCR Output Thus, 13 ARC model ——» relativistic Boltzmann equation, which is invariant under the scale transformation (14)-(15). The theoretical results and predictions of the ARC model are in very good agreement with AGS experiments°"1° as shown in Figures 10-12. This also means that the quark—gluon plasma is not yet discovered, and we have to continue in our search for vacuum excitations. When Boltzmann wrote his equation more than a century ago, very little was known about molecules or atoms. Yet he postulated the existence of basic tiny units of matter whose collisions could be completely "|oca|ized" in a space-time point. An effective way to realize Boltzmann's formulation is to invoke Feynman's idea of partons. In turn, this space—time localization ensures relativistic invariance, a concept developed just one year before Boltzmann`s death. lt is indeed a tribute to Boltzmann`s genius that 150 years after his birth, his equation remains one of the most powerful tools of modern physics. Concluding Remarks As we look into the future, the completion of RHIC in 1998 offers an exciting op portunity for physicists to explore the possibility of altering the vacuum and to examine whether it is indeed a physical medium. If the vacuum is the underlying cause for the strange phenomena in the microscopic world of particle physics, it must also have been actively responsive to the macroscopic distribution of matter and energy in the universe. Because the vacuum is everywhere and forever, these two, the micro- and the macro-, have to be linked together; neither can be considered a separate entity. Future history books might record that ours was a time when humankind was able to forge this bond on a scientific basis. 14 OCR Output REFERENCES [1]. T.D. Lee and G.C. Wick, Phys.Rev. D9, 2291 (1974); T.D. Lee, in Report of the Workshop on BcV/Nuclcon Collisions of Heavy Ions—How and Why, Bear Mountain, 1974 (BNL N0. 50445), 1,"Rc|ativistic Heavy Ion Collisions and Future Physics," in Symmctries in Particle Physics, ed. I. Bars, A. Chodos and C.H. Tze (New York, Plenum Press, 1984), p. 93. [21. F.R. Brown, N.H. Christ, Y.F. Deng, M.S. Gao and T.J. Woch, Phys.Rev.Lett. 61, 2058 (1988). [3] ‘ W. Willis, "Experimental Studies on States of the Vacuum," in Relativistic Heavy Ion Collisions (Proceedings ofthe CCAST Symposium/Workshop, 1989) , ed. R.C. Hwa, C.S. Gao and M.H. Ye (New York, Gordon and Breach Science Publishers, 1990), p. 39. [4] ‘ Y. Pang, T.J. Schlagel and S.H. Kahana, Nuc|.Phys. A544, 435c (1992); Phys. Rev.Lett. 68, 2743 (1992). [5]_ Y. Pang, in Particle Physics at the Fermi Scale (Proceedings of the CCAST Symposium/Workshop, 1993), to be published by Gordon and Breach Science Publishers. [61. J. Barrett et al. (E814 Collaboration), Phys.Rev.Lett. 64, 1219 (1990). [7] ‘ P. Braun-Munzinger et al. (E814 Collaboration), Nuc|.Phys. A544, 137c (1992). [8] _ T. Abbott et al. (E802 Collaboration), Phys.Lett. B271, 447 (1991). [9] _ T. Abbott et al. (E802 Collaboration), Phys.Rev. C47, R1352 (1993). [10]. M. Gonin, in Proceedings of Heavy Ion Physics at the AGS-HIPAGS ’.98, eds. G.S.F. Stephens, S.G. Steadman and W.L. Kehoe (13-15 January 1993), p.184. 15 OCR Output FIGURE CAPTIONS Figure 1. Two cars manufactured exactly alike except that one is the mirror image of the other. Figure 2. The initial setups of these two experiments on Co°° decay are exact mirror images, but the final electron distributions are not. as indicated by the different readings on the counters. Figure 3. In QED, magnetic fields are expelled out of a superconductor; in QCD the color electric field is impelled to stay within the hadrons, away from the vacuum. Figure 4. The formation of mesons (q§) and baryons (qqq compounds) due to the QCD vacuum being a perfect color dia-electric. Figure 5. Vacuum excitation through relativistic heavy ion collision. Figure 6. Phase diagram in the (kT, p/pA) plane. Figure 7. Phase transitionz (pure QCD). Figure 8. Hanbury-Brown-Twiss-type experiment. Fig1u·e 9. Experimental configuration for 7T — 1r interferometry. Figure 10. The proton rapidity spectra from ARC4, for two centrality cuts, 2% (solid line) and 7% (dashed line), compared with E8O28‘° for Si + Au, and E814° for Si + Pb. Figure 11. E802and8‘° ARC proton-mt spectra for Si -l— Au in many rapidity bins, at 14.6 GeV/c. Successive rapidity bins are scaled by 10`1 for clarity. The lines join ARC points. Figure 12. Theoretical calculations from ARC4 compared with experimental resu|ts1°OCR Output for the rapidity spectra of 7T+, K+ and K‘ in Au + Au collisions. 16 Driver 1evi1CI Gas pedal Isbeq esi) * 7* 1 1 R | I I ·I I Car a s 183 OCR Output Figure 1 OCD vacuum = perfect cclcr dia-electric E= O Kvac = O cclcr OCR OutputOCR Output/ clcn / OO q q OCR Output Vic Figure4 physical VGCUUITI Au Au before after central region excited vacuum Figure 5 OCR Output kT k = Boltzmann constant 100 GaV >< 100 GeV /nuclson Au + Au RHIC Quark Gluon Plasma 11.6 GaV/nuclaon 150 Au A + U NI V 9 Ass Hadronlc l\/latter normal nuclsar P *°3'V°“ "° d""S"V mattsr _ _ p A normal nuclsar danslty Flgurc 6 OCR Output QL =®§ 5.6 5.8 OCR Output B cc T Figure 7 Hanbury - Brown / Twiss - type Experiment mg) ¤<*<}> _,--9 MQ) Mk;) ’ ’ IAmpI OC |J€3·T1 +1*%-% + €¤F2·?2 + WE; 1 + cos E-?. (varies from 1 t0 2) R1 " R2 & F=) F?] " Q lf the central rapidity region is a plasma of entropy density Smasma , which later hadronizes (of entropy density 5,.,8d), Figure 8 OCR Output BEAM AXIS Hgh LONGITUDINAL : ol \ rx \ ` g \ Figure 9 OCR Output 10 10 E 100 ———· ARC - 2% E. out ARC - 7% Et cut E814 (Si+Pb) 10 E802 (Si+Au) Preliminary 10 Figure 10 OCR Output Au + Au OCR Output‘l O gQgO$966g6Q6 <>9Y 10 °° 6% 2>°<> 6 {ls Q <> 10 E866 Preliminary E866 Reflected <> ARC 10 (S0 far, no quark-gluon plasma signal.) Figure 12