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Conical Flow induced by Quenched QCD Jets

Conical Flow induced by Quenched QCD Jets. Jorge Casalderrey-Solana, Edward Shuryak and Derek Teaney, hep-ph/0411315. SUNY Stony Brook. Outline. Basic Ingredients: Hydrodynamics Thermalization of energy loss Assumption: small perturbations due to energy loss

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Conical Flow induced by Quenched QCD Jets

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  1. Conical Flow induced by Quenched QCD Jets Jorge Casalderrey-Solana, Edward ShuryakandDerek 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 nB) • Ideal case (h=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 pt 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 . Gs 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: The different terms lead to different excitations of the medium Adding all displacements we obtain the Mach cone

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

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

  9. Considerations about Expansion • c2s is not constant though system evolution: csQGP= , cs= in the resonance gas and cs~0 in the mixed phase. (Hung,E. Shuryak hep-ph/9709264) • Distance traveled by sound is reduced Mach direction changes <= RHIC • q = 1.23 rad =71o p/e(e) = EoS along fixed nB/s lines • Flow of the background medium modifies the shape and angle of the cone (Satarov et al.)

  10. Spectrum • Cooper-Fry with equal time freeze out • At low pt~Tf • Pt >>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. Normalized correlation function: f • The cone is also observed in the spectrum Gs=1/4pT Two Particle Correlations

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

  13. Conclusions • We have used hydrodynamics to follow the energy deposited in the medium. • Finite cs 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 Problems that need to be addressed (on progress): • 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.

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

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

  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 pt a punch through is expected, filling the cone

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