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Induced Sonic Mach Cones in QGP by Fast Partons: Investigating Energy and Momentum Perturbation

Explore the formation of Mach cones in Quark-Gluon Plasma (QGP) induced by fast partons. Investigate energy and momentum perturbation due to partons, consider perturbative assumptions, and utilize theoretical models. Study source terms, density, and momentum fluctuations using hydrodynamics. Investigate experimental evidence supporting Mach cone formation by energetic partons at RHIC.

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Induced Sonic Mach Cones in QGP by Fast Partons: Investigating Energy and Momentum Perturbation

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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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