Sonic Mach Cones Induced Sonic Mach Cones Induced by Fast Partons in a by Fast Partons in a

Perturbative Quark-Gluon Perturbative Quark-Gluon Plasma Plasma [1][1]

Presented by Presented by Bryon NeufeldBryon Neufeld (of (of Duke University) on March 20Duke University) on March 20thth 2008 in collaboration with:2008 in collaboration with:

Berndt Mueller, J. Ruppert, M. Berndt Mueller, J. Ruppert, M. Asakawa, C. NonakaAsakawa, C. Nonaka

[1] arXiv:0802.2254

hadrons

q

q

hadrons

leadingparticle suppressed

leading particle suppressed

Thanks to J. Casalderrey-Solana

Jets as a Probe of the QGPJets as a Probe of the QGPFormed when two energetic partons scatter Formed when two energetic partons scatter at a large angle and acquire a large at a large angle and acquire a large transverse momentum relative to the beam transverse momentum relative to the beam directiondirection

A Mach cone is A Mach cone is formed when an formed when an object moves faster object moves faster than the speed of than the speed of sound relative to it's sound relative to it's medium.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?Why so much interest?

Possible Possible Explanations:Explanations: Deflected JetsDeflected Jets Large Angle Large Angle

Gluon RadiationGluon Radiation CherenkovCherenkov Mach cone shock Mach cone shock

waveswaves

PHENIX

Au-Au at 200 GeV c.m. energy di-hadron correlationsAu-Au at 200 GeV c.m. energy di-hadron correlations

Thanks to Terry AwesThanks to Terry Awes

Au+Au Central 0-12% Triggered

Medium

away

near

di-jets

away

near

Medium

Conical

Consistent with conical flowConsistent with conical flowAu-Au three-hadron correlationsAu-Au three-hadron correlations

Thanks to Jason UleryThanks to Jason Ulery

Angular Dependence on PAngular Dependence on PTT

Mach-cone: angle independent of pMach-cone: angle independent of pTT

Cherenkov gluon radiation: decreasing angle with Cherenkov gluon radiation: decreasing angle with associated passociated pTT

0.5<pTAssoc<0.75 GeV/c 0.75<pT

Assoc<1.0 GeV/c 1.0<pTAssoc<1.5 GeV/c 1.5<pT

Assoc<2.0 GeV/c

3<pTTrig<4 GeV/cAu+Au 0-12%

Thanks to Jason UleryThanks to Jason Ulery

A Theoretical Approach to the A Theoretical Approach to the Question: Question: What is the energy and What is the energy and momentum perturbation of a QGP due momentum perturbation of a QGP due to a fast parton?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 Wong’s Chromomagnetic Equations of Motion:Motion:

Take moments in Q space:Take moments in Q space:

Yields the basic equations needed:Yields the basic equations needed:

ff1 1 vanishes in equilibrium (color neutral), I vanishes in equilibrium (color neutral), I

have dropped fhave dropped f2 2 and higher, a series in gAand higher, a series in gA

Solve for fSolve for f11(f(f00) ) (see Asakawa et al. (see Asakawa et al.

Prog.Theor.Phys.116:725-755,2007Prog.Theor.Phys.116:725-755,2007 ):):

To finally get:To finally get:

Recap Up to This PointRecap Up to This Point

Start with a system of partons (QGP) in Start with a system of partons (QGP) in the presence of an external field, A, the presence of an external field, A, described by a Vlasov equationdescribed by a Vlasov equation

Integrate out explicit color dependenceIntegrate out explicit color dependence Truncate resulting series at order gATruncate resulting series at order gA Solve for fSolve for f00

Application: Application:

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

Dielectric Functions:Dielectric Functions:

Taking the microscopic to Taking the microscopic to the macroscopic: the macroscopic:

With assumption of local therm. Eq., With assumption of local therm. Eq., yeilds: yeilds:

Back to the Question: Back to the Question: What is the What is the energy and momentum perturbation of energy and momentum perturbation of a QGP due to a fast parton?a QGP due to a fast parton?The answer: The answer:

J gives the energy/momentum deposited per unit J gives the energy/momentum deposited per unit time, time, it is a source termit is a source term

Assumptions: the medium is perturbative in Assumptions: the medium is perturbative in coupling g, hydrodynamicscoupling g, hydrodynamics

Explicit Evaluation of the Explicit Evaluation of the Source Term:Source Term:

Choose a medium of (locally thermal) Choose a medium of (locally thermal) gluons:gluons:

mD = gT; At this point must plug in mD = gT; At this point must plug in fields, will specifiy u = (0,0,u);fields, will specifiy u = (0,0,u);

For an unscreened color charge have For an unscreened color charge have analytical result:analytical result:

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

Enough Equations! Let’s look Enough Equations! Let’s look at some plots. Set u = 0.99 cat some plots. Set u = 0.99 c Result with screening done numericallyResult with screening done numerically

5

- 5

x-Momentum densityx-Momentum density

Linearized hydroLinearized hydro

These equations are valid in the limit of a weak sourceThese equations are valid in the limit of a weak source Solve for deposited energy denisty, sound momentum, Solve for deposited energy denisty, sound momentum,

and diffusion momentumand diffusion momentum We use: u = 0.99955 (gamma about 33), cWe use: u = 0.99955 (gamma about 33), css = Sqrt[1/3], = Sqrt[1/3],

ΓΓs s = 4/(3 T)*(eta/s) and T = 350 MeV= 4/(3 T)*(eta/s) and T = 350 MeV

See: Casalderrey-Solana et al. Nucl.Phys.A774:577-580,2006.

What to use for What to use for Perturbative Assumption, must be Perturbative Assumption, must be

consistentconsistent Standard AMY calculation, leading order [Standard AMY calculation, leading order [JHEP JHEP

0305:051,20030305:051,2003 ]]

Include (2,3) body processes, Xu et al.Include (2,3) body processes, Xu et al.arXiv:0711.0961 [nucl-th]arXiv:0711.0961 [nucl-th]

The Mach cone! The Mach cone! Unscreened source with min/max cutoff

Energy density Momentum density

gL

gT

Still a Mach cone! Still a Mach cone! Unscreened source with min/max cutoff

Energy density Momentum density

Velocity Flows (background Velocity Flows (background energy density of 10 GeV/energy density of 10 GeV/fmfm33))

There is strong experimental evidence that sonic Mach There is strong experimental evidence that sonic Mach cones are induced by fast partons at RHIC cones are induced by fast partons at RHIC

A theoretical investigation into the formation of Mach A theoretical investigation into the formation of Mach cones in the QGP should first start with the more cones in the QGP should first start with the more general question: What is the distribution of energy general question: What is the distribution of energy and momentum deposited into a QGP due to a fast and momentum deposited into a QGP due to a fast parton?parton?

We calculate this distribution in a pQGP and find a We calculate this distribution in a pQGP and find a mach cone in the linearized hydrodynamics. mach cone in the linearized hydrodynamics.

An attempt to explore the effects of the (screened) An attempt to explore the effects of the (screened) source term in a 3D relativistic, ideal hydro code in source term in a 3D relativistic, ideal hydro code in progress.progress.

SummarySummary