1. 1 Mach Cones in Quark Gluon Plasma Jorge Casalderrey-Solana Lawrence Berkeley Laboratory

2. 2 Jet-Medium Coupling What happens to the energy lost by jets? Leaves the interaction region being transferred to propagating modes: Remains in the medium Hydrodynamical behaviour  the medium reacts collectively Described as a parton cascade ( Ma et al.) Themalize (Stoecker, JCS, Teaney & Shuryak, Renk & Ruppert, Chaudhuri & Heinz) Plasma modes { Plasmon (Ruppert & Mueller) Cherenkov ( Koch, Majumder & Wang, Dremin) Large angle induced radiation (Vitev, Polosa & Salgado)

3. 3 Hydrodynamic Modes Diffuson (R μ ) Propagating mode, c s Sound (φ) Wave interference  Mach cone at Not propagating mode Remembers source direction The strength of the two modes is set by the shape of the bullet What sets relative mode amplitude in Jet-Medium interaction? NR fluid dynamics 

4. 4 Isentropic excitations: No significant entropy production. Medium excitation by sound wave emission. The Eloss is quadratic in the amplitude. Non isentropic excitations: the main excitation mechanism is entropy production and the flow field introduces vorticity. Excitation Mechanisms x (fm) ρ (fm) x (fm) Depostion/thermaliztion process One integral constraint Function with zero integral The source is not unique: Jet modification of hydro:

5. 5 Spectrum Excitation independent low p assoc T (  T) angular dependence, the distribution from different fluid cells overlaps High p assoc T particles reflect the flow picture Spectrum: Cooper-Fry No large angle correlation at small p assoc T    The fluid picture is not directly observed p assoc T fluid cell velocity Peaks at p assoc T ║ v but broad angle distribution at low p T Peaks at back jet direction

6. 6 Non Isentropic Excitations Diffuson  flow along jet direction No large angle correlation Chaudhuri & Heinz: Non linear hydro + source  dN/dyd  

7. 7 Isentropic Excitations Static Medium  Large dE/dx  12 Gev/fm The correlations develops as p assoc T increases The magnitude of the correlation decreases exponentially. Expanding medium the  necessary dE/dx  1.5 Gev/fm (dilution of the medium)  dN/dyd  4.0<P T Trig<6.0 GeV/c 0.15<P T Assoc<4.0 GeV/c D

8. 8 Expanding Medium The underlying flow v affects the directionality of the Mach cone (Satarov 05) Renk + Ruppert : studies in a realistic background + BDMPS radiative losses Fraction f=0.75 of energy into θ M θ M updated with local c s Rapidity distribution of Back Jet P(y) Elongation due to longitudinal flow Observed 3-p signal (strong radial expansion destroys the cone) Dominated by Radial flow ║ Mach flow (Cooper-Fry) Longitudinal flow  Elongation in y Radial flow broadens the peaks (misalignment of flow and jet)

9. 9 Mach Angle from Transport AMPT Transport model: Large angle correlation is observed Hadronic re-scattering increases the magnitude of the correlation Y. G. Ma, G. L. Ma et al. (06) 2  2 parton cascade + recombination The signal has a partonic origin 3-particle analysis: the medium excitation is conical. It requires “long” partonic phase  p > 1.5 fm Large partonic σ  Hydro limit? collective effects? 2  2 interaction  Isentropic ? (no particle production)

10. 10 Cherenkov radiation: At high T, plasma modes are time like  cannot be excited by ω=vq If there are bound states in the plama: (space like gluon) Large angle radiation happens mostly at low p assoc t as opposed to Mach cone. Koch, Majumder, Wang (05) Processes likelead to A similar mechanism in the plasmon (longitudinal gluon) can happen if it also becomes spacelike, ε L >1 (Ruppert and Mueller) Dremin (05)  p n(ω) >1 for ω  inter-level spacing Heavy bound states are required for Cherenkov gluons at ω  1 GeV

11. 11 Radiation at Large Angle Induced gluon radiation is suppressed at small angle (interference) Vitev (05) Smearing: Polosa + Salgado: since p trig T  p asso T only one gluon can be radiated Exclusive process  Sudakov  Stronger angular dependence than inclusive distribution. After smearing: Centrality dependence of the splitting parameter is reproduced. For low p assoc T becomes inclusive  no large angle correlations Inclusive distribution do not show large angle correlations

12. 12 Deflected Jets Scattering of an energetic parton in the medium leads to a change in jet direction The collinear fragmentation along the back jet is the source of off π. At each event there are particle in only one side Clearly distinguishable through 3 particle correlation Chiu and Hwa (06) Follow path of the partons Random deflection (gaussian) α At initial times σ/2=0.88 (large deflections) (Armesto et al., Fries)

13. 13 Au+Au 0-12%  12  13 θ* = 120 PHENIX Acceptance Indications of abnormal jets Star: signal along the off-diagonal consistent with conical structure Three Particle Correlations

14. 14 Conical Flow in AdS/CFT (Friess, Gubser, Michalogiorgakis, Pufu hep-th/0607022) String theory study of Heavy Quark motion in strongly coupled N =4 SYM Looking at T 00 they found the shock waves in N =4 SYM This is a dynamical model. No assumption about hydro- dynamical behavior is made! = Energy Density 024 KLKL 1 K┴K┴ 2 024 KLKL 1 K┴K┴ 2 024 KLKL 1 K┴K┴ 2 024 KLKL 1 K┴K┴ 2 Mach cone v=0.75v=0.9 v=0.95v=0.99 Drag { Herzog et al. JCS & Teaney Gubser

15. 15 CONCLUSIONS  Hydrodynamic description of deposited jet energy: Mach cone formation.  Particle spectrum reflects the cone (initial conditions!).  Transport calculations: compatible with the Mach cone  Mach like signals for plasma modes if n>1.  Large angle correlations from one gluon radiation.  p T asso dependence of D:  Deflected Jets  Different three particle correlation.  Cherenkov: decreases (unless heavy bound states)  Mach cone and gluon radiation: increases

16. 16 Buck up

17. 17 Expansion effects: Amplitude Static fluid  the amplitude of sound waves decrease like v α 1/r For RHIC, the evolution changes the fireball radius (from ~ 6fm to ~ 15 fm) and the c 2 s from 1/3 to 0.2  the amplitude v/T grows by a factor 3. Energy loss quadratic in the amplitude  necessary dE/dx  1.5 GeV/fm. Expanding medium: also the fluids temperature lowers with . The spectrum is controlled by v/T velocity field v 1 > v 2 T 1 < T 2 T1 T1 T2 T2 v1 v1 v2 v2 < t1 t1 t2 t2

18. 18 From STAR highlights :