Mach Cones at central LHC Collisions via MACE
aa r X i v : . [ nu c l - t h ] O c t Last Call for Predictions
Mach Cones at central LHC Collisions via MACE
Bj¨orn B¨auchle , ‡ , Horst St¨ocker , , L´aszl´o P Csernai , Institut f¨ur theoretische Physik, Universit¨at Frankfurt, Max-von-Laue-Straße1, D-60438 Frankfurt am Main, Germany Section for Theoretical Physics, Departement of Physics, University of Bergen,All´egaten 55, 5007 Bergen, Norway Frankfurt Institute for Advanced Studies, Universit¨at Frankfurt,Max-von-Laue-Straße 1, D-60438 Frankfurt am Main, Germany KFKI Research Institute for Particle and Nuclear Physics, P.O. Box 49, 1525Budapest, HungaryE-mail: [email protected]
Abstract.
The shape of Mach Cones in central lead on lead collisions at √ s NN = 5 . Submitted to:
J. Phys. G: Nucl. Part. Phys.
1. Introduction
After the discovery of “non-trivial parts” in three-particle correlations at RHIC [1],which are compatible with the existence of Mach cones [2], it is interesting to see howthe signal for Mach cones will look like under the influence of a medium created atthe LHC in PbPb-Collisions.Mach cones caused by ultrarelativistic jets going in midrapidity will create adouble-peaked two-particle correlation function d N/ d(∆ ϕ ). Those peaks are locatedat ∆ ϕ = π ± cos − c S , where c S is the speed of sound as obtained by the equation ofstate. The model MACE (“Mach Cones Evolution”) has been introduced to simulatethe propagation of sound waves through a medium and recognize and evaluate machcones [3].The medium is calculated without influence of a jet using the hydrodynamicalParticle-in-Cell-method (PIC) [4]. For the equation of state, a massless ideal gas isassumed, so that c S = 1 / √ − c S = 0 .
96. The sound waves are propagatedindependently of the propagation of the medium and without solving hydrodynamicalequations. Only the velocity field created by PIC is used. To recognize collectivephenomena, the shape of the region affected by sound waves is evaluated. ‡ Speaker
ACE (a) (b) ∆ ϕ ) , a . u . d N / d ( ∆ϕ ∆ ϕ ) , a . u . d N / d ( ∆ϕ Figure 1.
Two-particle-correlation function (away-side-part) for central PbPb-Collisions at √ s NN = 5 . ϕ ≈ π ± .
2. (b):Midrapidity jets starting from a position 70 % on the way outside left and rightof as well as in the middle.
2. Correlation functions
The correlation functions from the backward peak show a clear double-peakedstructure. The data for arbitrary jet origin and jet direction (minimum jet bias)is shown in figure 1 (a). Here, the peaks are visible at ∆ ϕ ≈ π ± .
2. This correspondsto a speed of sound of c S ≈ .
36. Note that the contributions from the forward jetare not shown. Deeper insight into different jet directions do not show a qualitativelydifferent picture.Triggers on the origin of the jet, though, show the dependence of the correlationfunction on the position where the jet was created (see figure 1 (b)). It shows thatonly the jet coming from the middle of the reaction results in a symmetric correlationfunction with peaks at the mach angle ∆ ϕ = π ± .
96. All other jets result incorrelations that have peaks at different angles, with the deviation getting biggerwhen going away from the middle. Therefore, the speed of sound will always appearto be smaller than it actually is.
3. Conclusions
If sound waves are produced from jet quenching in LHC-Collisions, the two-particlecorrelation function will show the expected double-humped structure in the backwardregion. The peaks will, though, be further apart than δ (∆ ϕ ) = 2 cos − c S , thusalluding to a speed of sound smaller than is actually present in the medium.The only case in which the true speed of sound can be measured is a midrapidityjet that creates a symmetric correlation function. ∆ϕ ∆ ϕ dN / d( ∆ϕ ) d( ∆ϕ ), a.u. 0 1 2 3 4 5 0 1 2 3 4 5 Figure 2.
Three-particle-correlation function for the same data as in figure 1.
ACE References [1] J. G. Ulery [STAR Collaboration], arXiv:0704.0224 [nucl-ex].[2] L. M. Satarov, H. Stoecker and I. N. Mishustin, Phys. Lett. B (2005) 64[arXiv:hep-ph/0505245].[3] B. Baeuchle, L. Csernai and H. Stoecker, arXiv:0710.1476 [nucl-th].[4] R. B. Clare and D. Strottman, Phys. Rept.141