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Sonic Mach Cones Induced by Fast Partons in a Perturbative Quark-Gluon Plasma [1]

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:0802.2254. Jets as a Probe of the QGP. leading

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Sonic Mach Cones Induced by Fast Partons in a Perturbative Quark-Gluon Plasma [1]

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  1. 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

  2. Jets as a Probe of the QGP leading particle suppressed hadrons q q hadrons leading particle suppressed Formed when two energetic partons scatter at a large angle and acquire a large transverse momentum relative to the beam direction • Thanks to J. Casalderrey-Solana

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

  4. Why so much interest? Possible Explanations: Deflected Jets Large Angle Gluon Radiation Cherenkov‏ Mach cone shock waves Au-Au at 200 GeV c.m. energy di-hadron correlations PHENIX Thanks to Terry Awes

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

  6. Angular Dependence on PT Au+Au 0-12% 3<pTTrig<4 GeV/c 0.5<pTAssoc<0.75 GeV/c 0.75<pTAssoc<1.0 GeV/c 1.0<pTAssoc<1.5 GeV/c 1.5<pTAssoc<2.0 GeV/c • Mach-cone: angle independent of pT • Cherenkov gluon radiation: decreasing angle with associated pT Thanks to Jason Ulery

  7. 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:

  8. Wong’s Chromomagnetic Equations of Motion:

  9. 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

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

  11. 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 f0

  12. 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):

  13. Dielectric Functions:

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

  15. 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

  16. 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);

  17. For an unscreened color charge have analytical result:

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

  19. Enough Equations! Let’s look at some plots. Set u = 0.99 c Result with screening done numerically 5 - 5

  20. x-Momentum density

  21. 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 = 0.99955 (gamma about 33), cs = Sqrt[1/3], Γs = 4/(3 T)*(eta/s) and T = 350 MeV See: Casalderrey-Solana et al. Nucl.Phys.A774:577-580,2006.

  22. 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:0711.0961 [nucl-th]

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

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

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

  26. 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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