# Presentation: 717063

## 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
- Solution to the linearized  problem:
-                Conical shock waves
- Possible experimental confirmation
- Conclusions.

## Hydrodynamics

- (local) Energy-momentum  and baryon  number conservation.
- In central collisions (neglecting nB)
- Ideal case (=0) provides a remarkable description of RHIC data.
- The viscosity at RHIC is very small.

## Jet Quenching and Energy Loss

- High pt particles lose energy in the medium
-         Radiative losses (main effect)
-         Collision losses
-         Ionization losses
-         (bound states)
- The second type of losses are deposited in the medium and modify its properties.
- We study this modification through hydrodynamics.

- 

- Shuryak+Zahed, hep-ph/0406100

## Where does the energy go?

- Previous studies
-         Constraints imposed by momentum conservation (Borghini Eur.Phys.J.C30:381-385,2003 )
-          Evolution through Boltzmann equation of the radiated gluons (Pal and Pratt Phys.Lett. B574 (2003) 21-26)

- They both lead to redistribution of the deposited energy in low momentum particles.
- We use hydrodynamics to track the deposited energy.

- The energy lost by the jet should be absorbed by the medium

- Pal and Pratt
- Phys.Lett. B574 (2003) 21-26

## Basic Assumptions

- The deposited energy thermalizes at a scale:
- Minimal value                   <<              point-like
- The modification of the properties of the medium is small
- The linearized hydrodynamic description is valid:

- <<

## Linearized Equations

- Medium at rest
-     Infinitesimal displacement

- R

- Summing all contributions
-    Mach Cone 

## Justification of approximations

- Linearization of the equation:
-      Eloss concentrated on

- Thermal fluctuations.
-       Estimating

## Distribution of radial velocity v (left) and modulus v (right).(note the positive and negative parts of the wave)

## Considerations about Expansion

**<= RHIC**

- Density  and dE/dx decrease with   The amplitude of the effect reduces.

- EOS of QCD is such that c2s is not constant

- p/e() = EoS along fixed nB/s lines
- (Hung,ES,hep-ph/9709264)

- The direction of the Mach cone changes with the expansion

## Evaluating the Mach cone angle

- Distance traveled by sound  is reduced since the velocity of sound is         in QGP, about 0 in the mixed phase and          in  a resonance gas
**                                             ****(not C****2****s****!)**
**Then ******** =arccos(c****av****s****)=71 degrees or 1.23 rad **

## Correlations in particle distributions

-  Cooper-Fry with equal time freeze out

- The cone is also observed in the spectra

## 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**

## 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/Ntrig)dN/d()

**STAR Preliminary**

## 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)
- The liquid flows preferentially on the direction of the cone which should be reflected in the final particle production.