MACE. Mach-Cones-Evolution

Transcription

1 Bjørn Bäuchle Mach-Cones-Evolution Palaver, ITP Frankfurt am Main,

2 Collaborators/Supporters This work is supported by the German National Academic Foundation and the International Uni Frankfurt. It is the major part of my diploma thesis which I write under supervision of Horst Stöcker (Frankfurt) Laszlo P. Csernai (Bergen) I use the Hydro Code by Csernai, Strottman and Magas (Particle in Cell PIC). 2/28

3 Outline Introduction Heavy Ions, Hydrodynamics, Speed of Sound Mach Cones in everyday- and Heavy-Ion-Physics Calculations for static medium -model: How we model jet and sound waves How we see the cone in the model How we get correlation signals Results: Static medium (test case) RHIC Collisions Central LHC-Collisions Summary 3/28

4 Heavy Ion Reactions 4/28

5 Hard scattering and jets In a high-energetic ( hard ) parton scattering, two bunches of hadron ( jets ) are produced Should arrive in the detector at Δφ π: Di-Jets. Do so in pp and pa at RHIC. In AA, only one of them is seen! Adams (STAR), PRL 91 (2003) /28

6 Relativistic Hydrodynamics Conservation of baryon number N =0 N =ϱ u Conservation of energy and momentum T =0 T = P u u P g Some equation of state P=P,ϱ 6/28

7 Relativistic Hydrodynamics The equation of state is intimately connected to the speed of sound: c2s = P EoS used for all calculations: 1 P= 3 (massless ideal gas) 7/28

8 Mach cones Named after Austrian physicist Ernst Mach ( ) Describes the wave front occuring behind a supersonic projectile Commonly known from supersonic airplanes cs cos = v Pic: Österreichische Nationalbibliothek (via en.wikipedia.org) John Gwynn and sons, ``The Water-Rocket Explorer'', April 15, 2003, 8/28

9 Mach cones (II) First predicted by Stöcker in 1975 (shock waves) Developed further by Shuryak (sound waves) More works by Stöcker and Satarov, Stöcker & Mishustin in 2005 and many more Claimed to be seen at RHIC! Wang (STAR), Nucl. Phys. A 774, 129 (2006) 9/28

10 Mach cones signatures Double-hump structure in two-particle correlations could be randomly deflected jets More insight from three-particle correlations: Show if secondary particles have been on both sides simultaneously. 10/28

11 Mach cones signatures (II) Off-diagonal peaks show clear signal for conical emission only random deflection conical emission Δφ2 Δφ2 Δφ1 Δφ1 11/28

12 Mach cones Evidence!? Signal seen in AuAu at RHIC! Ulery (STAR), arxiv:nucl-ex/ /28

13 Expectations in static medium Particle distribution homogeneous along β: dn =1 d Experiments measure along Δφ: d dn dn d = = d d d d β(δφ) is required! α:mach angle cos-1(cs) ( 0.96 ) 13/28

14 Expectations in static medium For midrapidity-jet: = arcsin tan tan Keep this in mind! 1 tan2 dn = d tan2 tan2 For arbitrary jet: = arccos arctan dn d = cos tan 1 tan 1 sin 2 tan2 1 sin tan 1 tan2 1 tan2 sin2 { cos tan2 tan2 [tan2 sin2 cos2 ] sin } α:mach angle cos-1(cs) ( 0.96 ) τ:jet deviation from midrapidity 14/28

15 in short Run a Hydro Code Particle in Cell (PIC) Los Alamos/Bergen Create new velocity field Usual Way Conventional Analysis Analyse momentumor velocity field Use velocity field to propagate sound waves Perfect Background Subtraction Analyse sound waves directly 15/28

16 Jet is created: random position within the extent of matter random direction (as long as it ends up in the detector) Jet is considered to cause sound like perturbations to be massless (i.e., moves with speed of light) to have infinitely high energy to move straight and with constant velocity 16/28

17 Sound waves are modelled as perturbation on top of hydro Elementary sound-waves are represented by a (big) set of wave markers with random directions Only carry information about position and direction Move with speed of sound in the local rest frame of the matter. 17/28

18 1 1 u u ln 2 1 u Sound has always the same speed w.r.t. the medium a) non-relativistic Wave markers must v u therefore have speed of sound flow velocity u v Relativistic addition by c) adding rapidity vectors Of course, outside the medium there is no sound propagation. 1 1 u u ln 2 1 u 1 1 c v ln S 2 1 cs b) v relativistic u v 1 c S 1 ln 2 1 c S d) v u 18/28

19 Propagation Static medium, jet started in origo real medium (RHIC AGeV), jet started at arbitrary point t=6 dt y t=6 dt y x z z x y t=10 dt Jet Wave markers started at odd timesteps Wave markers started at even timesteps z x 19/28

20 Mach-Cones!? Soundwave-propagation works fine BUT Soundwaves are spherical no direction is emphasized (or only through hydro flow) But we can see there is a cone! 20/28

21 Finding the Surface Surface is created by taking a number of lines, wave lines that go along the outside. Wave lines all start at the position of the jet and go in different plains around the jet (cmp. longitudes on a sphere wrt to the axis) The wave lines finally represent the surface. Particle emission is perpendicular to them. 21/28

22 Particle flow Perpendicular to wave lines Signal created at regular intervals along the lines Correlation calculated only from this signal, without Hydro-background ( perfect background subtraction) 22/28

23 Results Static medium, midrapidity Jet in midrapidity dn/d(δφ) Expectations well matched! 23/28

24 Results b=0 b = 10% ( 1.4 fm) dn/d(δφ) RHIC 130 AGeV, centrality Results from RHIC all look alike! (independent of impact parameter) b = 25% ( 3.5 fm) 24/28

25 Results LHC 5.5 ATeV central Δφ2 Minimum jet bias Δφ1 Δφ Forward jets dn/d(δφ) Δφ d2n/d(δφ1)d(δφ2) Midrapidity jets Δφ 25/28

26 Results Signal very robust Cones always too far apart (cs2, apparent 0.17) Reason: no constraints on origin of jet: Satarov (2005) and Chaudhuri (2006) predicted a broadening of mach angle for jets from peripheral regions Satarov: Phys. Lett. B 627 (2005) 64 Chaudhuri: nucl-th/ /28

27 Results LHC 5.5 ATeV central Starting position fixed; central collisions, midrapidity jets My startpoints Δφ Chaudhuris startpoints With centrally started jets, the real speed of sound can be seen. 27/28

28 Summary Conical structures are present in Heavy-IonCollisions, proved by 3-particle correlations. No δ-functions expected due to geometry creates and propagates sound waves shows robust mach signal for all considered cases. Speed of sound cannot be easily read off from correlation plots True speed of sound is larger than apparent Single event trigger is the only chance to see true speed of sound, but this might be useless due to fluctuations 28/28

29 Thank you very much 29/28

30 Backup Slides 30/28

31 Angles Pseudorapidity: angles: = 2 =ln cot 2 =ln tan 2 Midrapidity Beam direction back 31/28

32 Mach-Cones!? Interference does not work: during (isocronic) FO only directions survive, not positions (no contradiction to experience with planes) taking the amplitude neglects directions Only source of information is the shape of the affected region 32/28

33 Experience with Planes Visually: See the shape of the machfront use spatial information NO information on direction! Audible: FO at constant place(s) Evaluation of pressure information time-dependent back 33/28

34 Wavelines in detail For each wave line, only a subset (an azimuthal slice) of all wave markers are relevant Consider only this slice: Draw line along this slice Do not draw along the last elementary wave! Easy in static medium not easy in less-uniform distributions of the markers! 34/28

35 Wavelines in more detail They should never go backwards They should not be too jagged Artefact of too few elementary waves Artefact of too few wave markers Should not conceal physical effects 35/28

36 Wavelines in more detail They should never go backwards They should not be too jagged Artefact of too few elementary waves Artefact of too few wave markers Should not conceal physical effects 36/28

37 Wavelines in more detail They should never go backwards They should not be too jagged Artefact of too few elementary waves Artefact of too few wave markers Should not conceal physical effects Maximize angle between jet-axis and waveline Allow for single elementary waves to be ignored 37/28

38 Wavelines in more detail They should never go backwards They should not be too jagged Artefact of too few elementary waves Artefact of too few wave markers Should not conceal physical effects Maximize angle between jet-axis and waveline Allow for single elementary waves to be ignored 38/28