# Presentation: 519865

## Sonic Mach Cones in a Perturbative Quark-Gluon Plasma

**Presented by ****Bryon Neufeld**** (of Duke University) on August 23****rd**** 2008:**
**In collaboration with Berndt Mueller and Joerg Ruppert**

***[1] arXiv:0802.2254, [2]  arXiv:0805.0385, [3]  arXiv:0807.2996***

## Jets as a Probe of the QGP

- Thanks to J. Casalderrey-Solana

**Jets as a Probe of the QGP**

**Formed when two energetic partons scatter at a large angle and acquire a large transverse momentum relative to the beam direction**

## A Mach cone is formed when an object moves faster than the speed of sound relative to it's medium. 

**Interesting Questions:**
**What is the energy and momentum perturbation of a QGP due to a fast parton?**
**Similarly, Is a Mach cone created by a supersonic parton propagating through the quark gluon plasma?**** **

## Why so much interest?

**PHENIX**

- Au-Au at 200 GeV c.m. energy di-hadron correlations:
- Per-trigger yield  distribution

- Possibilities: Deflected Jets,
-  Large Angle Gluon Radiation,
- Cherenkov,
- Mach cone shock waves

## Start with the Question: What is the energy and momentum perturbation of a QGP due to a fast parton?

- Treat the fast parton as the source of an external color field interacting with a QGP and described by the distribution f(x,p,Q).  The Vlasov equation for this system is:

## Using Wong’s Chromomagnetic Equations of Motion:

**Take moments in  Q space:**

## Yields the basic equations needed:

** ****f****1 ****vanishes in equilibrium (color neutral), truncate the series at order gA**

**To finally get:**

## Taking the microscopic to the macroscopic: 

**With assumption of local therm. Eq., yields: **

## Back to the Question: What is the energy and momentum perturbation of a QGP due to a fast parton?In this approach the answer is: 

- J gives the energy/momentum deposited per unit time, it is a source term
- Assumptions: the medium is perturbative in coupling g, hydrodynamics

## Linearized hydro

- These equations are valid in the limit of a weak source
- Solve for deposited energy denisty, sound momentum, and diffusion momentum
- Parameters:

**Linearized hydro**

- The source term has been explicitly evaluated both with and without medium screening included.

## Results: deposited energy density

**-4 fm**

## Results: deposited momentum density

**-4 fm**

## Use a Cooper Frye Freeze-Out Prescription (choose the minimal viscosity solution)‏

**Use a Cooper Frye Freeze-Out Prescription ****(choose the minimal viscosity solution)****‏**

**Compare the spectrum for two different freeze-out scenarios.  Examine sensitivity of result to freeze-out assumption.  Remove the diffusive contribution for clarity.**

## Two different Freeze-Out Scenarios:

**Phi = 0**

**5 fm rad.**

- Freeze-Out Surface

**Two different Freeze-Out Scenarios:**

**Radial Scenario:**

**Isochronous Brick:**

- Infinite Freeze-Out Volume at fixed time

## Results:

**Results:**

**Radial Scenario:**

**Isochronous Brick:**

## Summary

- A theoretical investigation into the formation of Mach cones in the QGP should first start with the more general question: What is the distribution of energy and momentum deposited into a QGP due to a fast parton?
- This distribution is calculated in a pQGP and we find a mach cone in the linearized hydrodynamics.
- With _***CERTAIN ASSUMPTIONS***_, one can obtain a particle spectrum that has a similar structure as that seen at RHIC—_However, take this with a big grain of salt! __ _
- Any meaningful comparison with data requires incorporating a realistic source term in an expanding medium

**Summary**

## Backup Slides

**Backup Slides**