1. Conical Flow induced by Quenched QCD Jets Jorge Casalderrey-Solana, Edward Shuryak and Derek Teaney, hep- ph/0411315 SUNY Stony Brook

2. Outline Basic Ingredients: Hydrodynamics Thermalization of energy loss Assumption: small perturbations due to energy loss Solution to the linearized problem: Conical shock waves Possible experimental confirmation Conclusions.

3. Hydrodynamics (local) Energy-momentum and baryon number conservation. At mid rapidity (neglecting n B ) Ideal case (  =0) provides a remarkable description of radial and elliptic flows at RHIC The viscosity at RHIC seems to be close to its minimal conjectured bound.

4. Jet Quenching and Energy Loss High p t particles lose energy in the medium Radiative losses (main effect) Collision losses Ionization losses (bound states) From the hydrodynamical point of view, the different mechanisms may be only distinguished by the deposition process (what mode they excite) We study this modification through hydrodynamics. Similar ideas have been discussed by H. Stoeker (nucl-th/0406018)  Shuryak+Zahed, hep-ph/0406100

5. Basic Assumptions The deposited energy thermalizes at a scale: Minimal value >> point-like.  s will be the only scale of the “source” Outside of the “source”, the modification of the properties of the medium is small Thus, linearized hydrodynamic description is valid: <<

6. Summing the Spherical Waves Particle moving in the static medium with velocity v After the disturbance is thermalized Given the symmetries of the problem, we need to specify: Adding all displacements we obtain the Mach cone The different terms lead to different excitations of the medium

7. Two (linear) Hydro Modes  Sound waves (propagating)Diffuson (not propagating) By defining the system decouples: After Fourier transformed (space coordinates) Excitations:SoundDiffuson Yes No Yes No

8. Flow Picture Diffuson: Matter moving mainly along the jet direction Sound motion along Mach direction.

9. <= RHIC Flow of the background medium modifies the shape and angle of the cone (Satarov et al.) c 2 s is not constant though system evolution: c sQGP =, c s = in the resonance gas and c s ~0 in the mixed phase. p/e(  ) = EoS along fixed n B /s lines Considerations about Expansion Distance traveled by sound is reduced  Mach direction changes (Hung,E. Shuryak hep-ph/9709264)  = 1.23 rad =71 o

10. Spectrum Cooper-Fry with equal time freeze out At low p t ~T f P t >>the spectrum is more sensitive to the “hottest points” (shock and regions close to the jet) If the jet energy is enough to punch through,  fragmentation part on top of “thermal” spectrum

11. Two Particle Correlations Normalized correlation function:  The cone is also observed in the spectrum  s=1/4  T

12. Is such a sonic boom already observed? M.Miller, QM04 Flow of matter normal to the Mach cone seems to be observed!  +/- 1.23=1.91,4.37 (1/N trig )dN/d(  ) STAR Preliminary

13. Conclusions We have used hydrodynamics to follow the energy deposited in the medium. Finite c s leads to the appearance of a Mach cone (conical flow correlated to the jet) Depending on the initial conditions,the direction of the cone is reflected in the final particle production.

14. Outlook Systematic study of initial conditions Role of non-linearities (mixing the modes) Precise effect of changing speed of sound as well as the expanding media Realistic simulation of collision geometry Three particle correlations. Problems that need to be addressed (on progress):

15. Swinging the back jet Assume a boost invariant medium and a y j -distribution for the backjet P(y j ) (flat). Boosting by y j we assume a particle distribution: After boosting back to the lab frame Now we integrate over yj: p **

16. Swinging the back jet (II) If we simply rotate the jet axis (Vitev): And use Integrating over  **   z y x I. Vitev hep-ph/0501255 However long tails may fill up the cone.

17. How to observe it? the direction of the flow is normal to the Mach cone, defined entirely by the ratio of the speed of sound to the speed of light Unlike the (QCD) radiation, the angle is not shrinking (1/  with the increase of the momentum of the jet but is the same for all jet momenta At high enough p t a punch through is expected, filling the cone