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Collectivity in ultra-relativistic heavy ion collisions
Nuclear Physics A54 ("1992) 463c-466c North-Holland, Amsterdam
YSICS
Collectivity in Ultra ,elativistic Heavy Ton Co11isi0ns N.S. Amelinat, L.P. Csernaia,c, E.F. Staube ,' and D. Strottmand aPhysics Department, University of Bergen, Allegt. 55, 5007 Bergen, Norway, 6NORDITA, Blegdamsvej 17, 2100 Copenhagen 0, Denmark, Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA, dTheoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Abstract Important basic features of the relativistic Fluid Dynamical Model (FDM) and MonteCarlo Quark Gluon String Model (AGSM) are compared and discussed . ER.
ALIZATION, STOPPING and PLASMA FORMATION
The AGSM does not assume QGP formation, but secondary hadrons can rescatter, moving the system towards thermal equilibrium . Other than the rescatterings, the interaction of strings via scattering of valence di-quarks in a string is the most important feature of the AGSM. _ 1.
0.30 0.45 0.60 1 .05 1 .35 2.25 4 .05
n/no etoe elae 2.7 3.25 1 .79 4 .8 8.18 4.53 8.0 13.80 7.06 16.0 20 .10 8A1 13.9 16.80 6.31 6.1 5.29 3.57 2.6 2.03 1 .87
Ncou
9.8 42 132
1090
2340 7770
18900
pare 44 203
567 2590 3370
3838
4030
Table l'
The average of the baryon density [re/no], total energy density, eto ,jGeV/ fm3], latent energy density, elat, the number of all collisions, N,ou, and of all participants, Npart, in a 160 A-GeV Pb+Pb collision at C=6.2 ;.,., cat- alated in the QGSM as a function of time, t [fm/c] . From /1,.
The importance of rescattering is clearly indicated by the peak of the proton rapidity distribution at y ~ 0 in central 160 A-GeV Pb+Pb collisions which cannot be reproduced without rescatterings .[1] The peak is obtained in both FDM and AGSM . In AGSM the total multiplicity of particles is about 3-4000 in central collisions (Table 1) . The FDM, unlike AGSM, inherently assumes local thermodynamic equilibrium and one of its inputs is the Equation of State (EOS). Thus, consequences of a possible phase 0375-9474/92;$05.00 © 1992 - Elsevier science Publishers B.V. All rights reserved .
MS. Amehn et al. 1 Céllecùvity in ultra-reltitivistic heavy ion collâffins transition can be directly tested in this model. Two different theoretical scenarios were used: i) with a hadroni- gas EOS, and ii) with a QGP EOS.[4] The QGP EOS used in F M was a complete EOS with hadronic, pure QGP and mixed phases [4]. The grid size in the FDM is of importance. Not only because the numerical viscosity arising from the finite cell she has a stabilizing effect, but also because the cell size should not be smaller than the underlying microscopic correlation length or mean free path. (Else the thermodynatuical parameters will have no tneaning.) In case of a first order phase transition, if d's niininium cell-size is used, a given cell could contain one phase of matter only, and the extra surface energy of the phase interface should be taken into account explicitly. In the present calculation, however, we used larger cell sizes, and consequently we used an EOS with phase mixture . The results of a numerical calculation with a resolution of Ax = Ay = 0.87 fin and Az = 0.14 fm (AZ(LR) = 1.31 fm in the projectile and target region before the collision) are shown in Figs. 1, 2.
tae Fluid Hydrodynamics Sierk-Nix + QG? K=550
Fig- ure
1 : Contour lines of *he temperature distribution . T [Ale
L'7,
in the reaction plane of a Pb+Pb
recetion of inapact parainetcr, b = 4 fin, eat .1 60 A GeV beam energy and at c.m . times 0.3-,', 0.68, 1.03, 1 .3s, L 72 PnM Th -? figures are distoried for sake of better recognizability, the size of the frame in t.-'-e
beam direction is 5 fm, while in the transuerse direction 20
fin.
According to the FDM about .50 fM3 Of Q(;p is formed for a period of 2 fin/c. The pare plasma decays completely after 4 .5 fm/c. 10 evaluated the average baryon density, n, during the reaction, Table 1 . A density increase nearly 17 times over normal nuclear density was reached in the QGSM, and 17
N .S . Amelin et al . A Collectivity in ultra-relativistic heavy ion collisions
465c
or 21 in the FDM depending on the EOS. The total energy density, e, was also calculate in the QGS . However, the "unformed" hadrons are not allowed to interact or fescatter prior to their formation time. In the string picture they form a string. dVe evaluated the energy carried by particles not yet formed . This we call the "latent" energy, elat, which plays a role similar to the latent heat in our QGP EOS in M. It is striking that at the maximum, etat .:: 8 GeV/ fms .
Figure 2: ('a
left) Contour line of the pure QGP in the reaction plane of the reaction shown in Peg . 1, at c .m . time 1 .37 fm/c . (b right) Contour lines of the temperature distribution . T [Ale tij, ?n the reaction plane at the same time. The longitudinal size of QGP 13 about lfin at this time .
Thus based on AGSM results we expect strong stopping and thermalization in heavy :Jn collisions at AGS and CERN energies . Recently difficulties in reproducing AGS E802 measurements for central Si+Au reactions at 14 .0 A GeV, were interpreted as a sign of transparency . In AGSM these data were compared to calculations with impact parameters, b=2, 4.5 and 7 fm.[3] Although AGSM did not fit the pion data for b=2fm, the admixture of peripheral events in the experimental sample might be able tv :;;plain the deviation between the experiment and QGSIXI . Thus, in our opinion, this experiment does not contradict the existence of strong stopping . 2.
ANSVE SE FLOW ANALYSIS
Azimuthally symmetric transverse flow is frequently discussed and considered as a signal of collectivity and as a sensitive indicator of a phase transition . Recently Lévai and Müller, estimated the equilibration of flow in high energy hadronic matter, and concluded that this is not sufficient to explain the observed equality of transverse flow velocities of anti-protons, pions, and I{ mesons in pp reactions at T EVATRON energy. The formation of QGP would obviously solve this problem, which indicates probable QGP formation in the TEVATRON experiment .
466c
S. Amehn et A 1 Collectivity in ultra-relativistic heavy ion collisions
A more sensitive measure of the transverse flow is the directed, azimuthally asymmetric, flow in the reaction plane. At BEVALAC energies this flow is identified, and used to determine the compressibility of nuclear matter, w well as the onset of nuclear liquid-gas phase transition at low energies, where this transverse flow vanishes and changes sign . the CERN SPS, however, with Sulphur projectiles, the directed flow and the reaction plane could not be identified. GSNI calculations confirm this finding, [21 showing that azimuthal anticorrelation in S+S collisions is too iniall to detect . On the other hand, it might be possible to detect flow for Pb + Pb at 160 A-GeV . In the QGSM the sidewards flow is a consequence of rescatterings . At b = 4 fm the maximum flow is of the order 50 MeV/c, ( Fig. 3) . In the FDTN1 the 3ow is larger than in QCSM and it depends on the EOS. For the purely hadronic EOS the maximuni directed transverse flow was around 400 MeV/c . The flow is very sensitive on the EOS, so that it is smaller by a factor of two for QGP EOS, we used than for the hadronic EOS. 200
T
-200
-4 -2 0 2 4 Figure 3: Proton transverse flow, < p, >, versus the rapidity, y, in the QGS,11for a 160 A-GeV Pb-4-Pb collision at b = 4 fm. Labels P and T denote projectile and target rapidaties . The dashed line indicates QGSJ! results without rescattering . From [2]_ This difference in the directed transverse flow provides a possibility to detect the formation of QGP, partictilarly to detect the thresi)old energy for the QGP formation . S t I 2 3 4
On extended leave fiom VS . Awhn et al ., Phys . AS. Amenn et al ., Phys. VS. Amelin et al ., Phys. A.K . Holme et al., Phys.
JINR, Dubna, USSU.. Lett. B261 (1991) 352 . Rev . Lett . 67 (1991) 1523. Rev . C44 (1991) 1 .541 . Rev . D40 (1989) 3735.
YSICS
Collectivity in Ultra ,elativistic Heavy Ton Co11isi0ns N.S. Amelinat, L.P. Csernaia,c, E.F. Staube ,' and D. Strottmand aPhysics Department, University of Bergen, Allegt. 55, 5007 Bergen, Norway, 6NORDITA, Blegdamsvej 17, 2100 Copenhagen 0, Denmark, Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455, USA, dTheoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Abstract Important basic features of the relativistic Fluid Dynamical Model (FDM) and MonteCarlo Quark Gluon String Model (AGSM) are compared and discussed . ER.
ALIZATION, STOPPING and PLASMA FORMATION
The AGSM does not assume QGP formation, but secondary hadrons can rescatter, moving the system towards thermal equilibrium . Other than the rescatterings, the interaction of strings via scattering of valence di-quarks in a string is the most important feature of the AGSM. _ 1.
0.30 0.45 0.60 1 .05 1 .35 2.25 4 .05
n/no etoe elae 2.7 3.25 1 .79 4 .8 8.18 4.53 8.0 13.80 7.06 16.0 20 .10 8A1 13.9 16.80 6.31 6.1 5.29 3.57 2.6 2.03 1 .87
Ncou
9.8 42 132
1090
2340 7770
18900
pare 44 203
567 2590 3370
3838
4030
Table l'
The average of the baryon density [re/no], total energy density, eto ,jGeV/ fm3], latent energy density, elat, the number of all collisions, N,ou, and of all participants, Npart, in a 160 A-GeV Pb+Pb collision at C=6.2 ;.,., cat- alated in the QGSM as a function of time, t [fm/c] . From /1,.
The importance of rescattering is clearly indicated by the peak of the proton rapidity distribution at y ~ 0 in central 160 A-GeV Pb+Pb collisions which cannot be reproduced without rescatterings .[1] The peak is obtained in both FDM and AGSM . In AGSM the total multiplicity of particles is about 3-4000 in central collisions (Table 1) . The FDM, unlike AGSM, inherently assumes local thermodynamic equilibrium and one of its inputs is the Equation of State (EOS). Thus, consequences of a possible phase 0375-9474/92;$05.00 © 1992 - Elsevier science Publishers B.V. All rights reserved .
MS. Amehn et al. 1 Céllecùvity in ultra-reltitivistic heavy ion collâffins transition can be directly tested in this model. Two different theoretical scenarios were used: i) with a hadroni- gas EOS, and ii) with a QGP EOS.[4] The QGP EOS used in F M was a complete EOS with hadronic, pure QGP and mixed phases [4]. The grid size in the FDM is of importance. Not only because the numerical viscosity arising from the finite cell she has a stabilizing effect, but also because the cell size should not be smaller than the underlying microscopic correlation length or mean free path. (Else the thermodynatuical parameters will have no tneaning.) In case of a first order phase transition, if d's niininium cell-size is used, a given cell could contain one phase of matter only, and the extra surface energy of the phase interface should be taken into account explicitly. In the present calculation, however, we used larger cell sizes, and consequently we used an EOS with phase mixture . The results of a numerical calculation with a resolution of Ax = Ay = 0.87 fin and Az = 0.14 fm (AZ(LR) = 1.31 fm in the projectile and target region before the collision) are shown in Figs. 1, 2.
tae Fluid Hydrodynamics Sierk-Nix + QG? K=550
Fig- ure
1 : Contour lines of *he temperature distribution . T [Ale
L'7,
in the reaction plane of a Pb+Pb
recetion of inapact parainetcr, b = 4 fin, eat .1 60 A GeV beam energy and at c.m . times 0.3-,', 0.68, 1.03, 1 .3s, L 72 PnM Th -? figures are distoried for sake of better recognizability, the size of the frame in t.-'-e
beam direction is 5 fm, while in the transuerse direction 20
fin.
According to the FDM about .50 fM3 Of Q(;p is formed for a period of 2 fin/c. The pare plasma decays completely after 4 .5 fm/c. 10 evaluated the average baryon density, n, during the reaction, Table 1 . A density increase nearly 17 times over normal nuclear density was reached in the QGSM, and 17
N .S . Amelin et al . A Collectivity in ultra-relativistic heavy ion collisions
465c
or 21 in the FDM depending on the EOS. The total energy density, e, was also calculate in the QGS . However, the "unformed" hadrons are not allowed to interact or fescatter prior to their formation time. In the string picture they form a string. dVe evaluated the energy carried by particles not yet formed . This we call the "latent" energy, elat, which plays a role similar to the latent heat in our QGP EOS in M. It is striking that at the maximum, etat .:: 8 GeV/ fms .
Figure 2: ('a
left) Contour line of the pure QGP in the reaction plane of the reaction shown in Peg . 1, at c .m . time 1 .37 fm/c . (b right) Contour lines of the temperature distribution . T [Ale tij, ?n the reaction plane at the same time. The longitudinal size of QGP 13 about lfin at this time .
Thus based on AGSM results we expect strong stopping and thermalization in heavy :Jn collisions at AGS and CERN energies . Recently difficulties in reproducing AGS E802 measurements for central Si+Au reactions at 14 .0 A GeV, were interpreted as a sign of transparency . In AGSM these data were compared to calculations with impact parameters, b=2, 4.5 and 7 fm.[3] Although AGSM did not fit the pion data for b=2fm, the admixture of peripheral events in the experimental sample might be able tv :;;plain the deviation between the experiment and QGSIXI . Thus, in our opinion, this experiment does not contradict the existence of strong stopping . 2.
ANSVE SE FLOW ANALYSIS
Azimuthally symmetric transverse flow is frequently discussed and considered as a signal of collectivity and as a sensitive indicator of a phase transition . Recently Lévai and Müller, estimated the equilibration of flow in high energy hadronic matter, and concluded that this is not sufficient to explain the observed equality of transverse flow velocities of anti-protons, pions, and I{ mesons in pp reactions at T EVATRON energy. The formation of QGP would obviously solve this problem, which indicates probable QGP formation in the TEVATRON experiment .
466c
S. Amehn et A 1 Collectivity in ultra-relativistic heavy ion collisions
A more sensitive measure of the transverse flow is the directed, azimuthally asymmetric, flow in the reaction plane. At BEVALAC energies this flow is identified, and used to determine the compressibility of nuclear matter, w well as the onset of nuclear liquid-gas phase transition at low energies, where this transverse flow vanishes and changes sign . the CERN SPS, however, with Sulphur projectiles, the directed flow and the reaction plane could not be identified. GSNI calculations confirm this finding, [21 showing that azimuthal anticorrelation in S+S collisions is too iniall to detect . On the other hand, it might be possible to detect flow for Pb + Pb at 160 A-GeV . In the QGSM the sidewards flow is a consequence of rescatterings . At b = 4 fm the maximum flow is of the order 50 MeV/c, ( Fig. 3) . In the FDTN1 the 3ow is larger than in QCSM and it depends on the EOS. For the purely hadronic EOS the maximuni directed transverse flow was around 400 MeV/c . The flow is very sensitive on the EOS, so that it is smaller by a factor of two for QGP EOS, we used than for the hadronic EOS. 200
T
-200
-4 -2 0 2 4 Figure 3: Proton transverse flow, < p, >, versus the rapidity, y, in the QGS,11for a 160 A-GeV Pb-4-Pb collision at b = 4 fm. Labels P and T denote projectile and target rapidaties . The dashed line indicates QGSJ! results without rescattering . From [2]_ This difference in the directed transverse flow provides a possibility to detect the formation of QGP, partictilarly to detect the thresi)old energy for the QGP formation . S t I 2 3 4
On extended leave fiom VS . Awhn et al ., Phys . AS. Amenn et al ., Phys. VS. Amelin et al ., Phys. A.K . Holme et al., Phys.
JINR, Dubna, USSU.. Lett. B261 (1991) 352 . Rev . Lett . 67 (1991) 1523. Rev . C44 (1991) 1 .541 . Rev . D40 (1989) 3735.