Sonic Mach Cones Induced by Fast Partons in a Perturbative Quark-Gluon Plasma [1]Presented by Bryon Neufeld (of Duke University) on March 20th 2008 in collaboration with:Berndt Mueller, J. Ruppert, M. Asakawa, C. Nonaka[1] arXiv:0802.2254

Jets as a Probe of the QGPThanks to J. Casalderrey-SolanaFormed 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?Possible Explanations:Deflected JetsLarge Angle Gluon RadiationCherenkovMach cone shock wavesPHENIXAu-Au at 200 GeV c.m. energy di-hadron correlationsThanks to Terry Awes

Consistent with conical flowAu-Au three-hadron correlationsThanks to Jason Ulery

Angular Dependence on PTMach-cone: angle independent of pTCherenkov gluon radiation: decreasing angle with associated pTThanks to Jason Ulery

A Theoretical Approach to the Question: What is the energy and momentum perturbation of a QGP due to a fast parton?Start with a system of partons in the presence of an external color field, A, and described by the distribution f(x,p,Q). The Vlasov equation for this system is:

Wongs Chromomagnetic Equations of Motion:

Take moments in Q space:Yields the basic equations needed: f1 vanishes in equilibrium (color neutral), I have dropped f2 and higher, a series in gA

Solve for f1(f0) (see Asakawa et al. Prog.Theor.Phys.116:725-755,2007 ):To finally get:

Recap Up to This PointStart with a system of partons (QGP) in the presence of an external field, A, described by a Vlasov equationIntegrate out explicit color dependenceTruncate resulting series at order gASolve for f0

Application: Consider the external field, A, to be generated by the fast parton propagating through the medium-a pQGPField in HTL Approximation (constant u):

Dielectric Functions:

Taking the microscopic to the macroscopic: With assumption of local therm. Eq., yeilds:

Back to the Question: What is the energy and momentum perturbation of a QGP due to a fast parton?The answer: J gives the energy/momentum deposited per unit time, it is a source termAssumptions: the medium is perturbative in coupling g, hydrodynamics

Explicit Evaluation of the Source Term:Choose a medium of (locally thermal) gluons:mD = gT; At this point must plug in fields, will specifiy u = (0,0,u);

For an unscreened color charge have analytical result:

Discussion:Applying infrared (screening) and ultraviolet (quantum) cuts on the -integral gives the standard expression for collisional energy loss:

Enough Equations! Lets look at some plots. Set u = 0.99 cResult with screening done numerically5- 5

x-Momentum density

Linearized hydroThese equations are valid in the limit of a weak sourceSolve for deposited energy denisty, sound momentum, and diffusion momentumWe use: u = 0.99955 (gamma about 33), cs = Sqrt[1/3], s = 4/(3 T)*(eta/s) and T = 350 MeVSee: Casalderrey-Solana et al. Nucl.Phys.A774:577-580,2006.

What to use for Perturbative Assumption, must be consistentStandard AMY calculation, leading order [JHEP 0305:051,2003 ] Include (2,3) body processes, Xu et al. arXiv:0711.0961 [nucl-th]

The Mach cone! Unscreened source with min/max cutoffEnergy densityMomentum densitygLgT

Still a Mach cone! Unscreened source with min/max cutoffEnergy densityMomentum density

Velocity Flows (background energy density of 10 GeV/fm3)

There is strong experimental evidence that sonic Mach cones are induced by fast partons at RHIC 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?We calculate this distribution in a pQGP and find a mach cone in the linearized hydrodynamics. An attempt to explore the effects of the (screened) source term in a 3D relativistic, ideal hydro code in progress.Summary

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