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

hadrons q q leading particle suppressed leading particle suppressed  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?  Possible Explanations:  Deflected Jets  Large Angle Gluon Radiation  Cherenkov‏  Mach cone shock waves PHENIX Au-Au at 200 GeV c.m. energy di-hadron correlations Thanks to Terry Awes

Au+Au Central 0-12% Triggered Medium away near di-jets away near Medium Conical Consistent with conical flow Au-Au three-hadron correlations Thanks to Jason Ulery

Angular Dependence on P T  Mach-cone: angle independent of p T  Cherenkov gluon radiation: decreasing angle with associated p T 0.5<p T Assoc <0.75 GeV/c0.75<p T Assoc <1.0 GeV/c1.0<p T Assoc <1.5 GeV/c1.5<p T Assoc <2.0 GeV/c 3<p T Trig <4 GeV/cAu+Au 0-12% Thanks 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:

 Wong’s Chromomagnetic Equations of Motion:

Take moments in Q space: Yields the basic equations needed: f 1 vanishes in equilibrium (color neutral), I have dropped f 2 and higher, a series in gA f 1 vanishes in equilibrium (color neutral), I have dropped f 2 and higher, a series in gA

Solve for f 1 (f 0 ) (see Asakawa et al. Prog.Theor.Phys.116: ,2007): Solve for f 1 (f 0 ) (see Asakawa et al. Prog.Theor.Phys.116: ,2007 ): To finally get:

Recap Up to This Point  Start with a system of partons (QGP) in the presence of an external field, A, described by a Vlasov equation  Integrate out explicit color dependence  Truncate resulting series at order gA  Solve for f 0

Application:  Consider the external field, A, to be generated by the fast parton propagating through the medium-a pQGP  Field 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 term  Assumptions: 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! Let’s look at some plots. Set u = 0.99 c  Result with screening done numerically 5 - 5

x-Momentum density

Linearized hydro  These equations are valid in the limit of a weak source  Solve for deposited energy denisty, sound momentum, and diffusion momentum  We use: u = (gamma about 33), c s = Sqrt[1/3], Γ s = 4/(3 T)*(eta/s) and T = 350 MeV See: Casalderrey-Solana et al. Nucl.Phys.A774: ,2006.

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

The Mach cone! Unscreened source with  min/max cutoff Energy density Momentum density gL gT

Still a Mach cone! Unscreened source with  min/max cutoff Energy density Momentum density

Velocity Flows (background energy density of 10 GeV/fm 3 ) ‏

 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