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Mach Cones in a Perturbative Quark-Gluon Plasma

Mach Cones in a Perturbative Quark-Gluon Plasma . Berndt M ue ller – Duke University Quark Matter 2008 Jaipur, India, 2 - 10 February 2008. Credits to: M. Asakawa R.B. Neufeld C. Nonaka J. Ruppert. What happens here ?!. An interesting question.

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Mach Cones in a Perturbative Quark-Gluon Plasma

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  1. Mach Conesin a PerturbativeQuark-Gluon Plasma Berndt Mueller – Duke University Quark Matter 2008 Jaipur, India, 2 - 10 February 2008 Credits to: M. Asakawa R.B. Neufeld C. Nonaka J. Ruppert

  2. What happens here ?! An interesting question • Is a Mach cone created when a supersonic parton propagates through the quark gluon plasma? • A Mach cone is formed when an object moves faster than the speed of sound in the medium. • What is the energy and momentum perturbation of the medium due to a fast parton?

  3. What happens here ?! In real life…. Relevant dynamical quantities:

  4. medium Formalism Calculate the interaction of the color field of the supersonic parton with the medium by means of semi-classical transport theory: If the medium is color neutral, to lowest order:

  5. Hydrodynamics In the macrocopic limit this yields hydrodynamic equations with source terms: Momentum space integrals yield term ~ mD2:

  6. Unscreened source For an unscreened color charge, analytical result in u1 limit: Applying infrared (screening) and ultraviolet (quantum) cuts on the -integral gives the standard expression for collisional energy loss:

  7. With screening Use HTL di-electric functions for  = ukz : Expressions for J(x) can be reduced to sums of products of two-dimensional Fourier integrals, which can be performed numerically after contour rotation in the complex plane.

  8. Energy density J0(,z)screened J0(,z)unscreened (GeV)4 (GeV)4   (z - ut)  (z - ut)  u = 0.99

  9. z-Momentum density Jz(,z)screened Jz(,z)unscreened (GeV)4 (GeV)4   (z - ut)  (z - ut)  u = 0.99

  10. x-Momentum density Jx(,z)screened Jx(,z)unscreened (GeV)4 (GeV)4   (z - ut)  (z - ut)  u = 0.99

  11. Unscreened Screened More comparisons u = 0.99 (GeV)4 (GeV)4 Jz(z-ut) at  = 2 GeV-1 Jx(z-ut) at  = 1 GeV-1

  12. Linearized hydro Linearize hydro eqs. for a weak source: T00  + , T0i  gi . Solvein Fourier space for longitudinal sound: … and dissipative transverse perturbation: See: J. Casalderrey-Solana, E.V. Shuryak and D. Teaney, arXiv:hep-ph/0602183

  13. gT gL   (z - ut) The Mach cone (at last!) Unscreened source with min/max cutoff Energy density Momentum density

  14.   z Contour plots

  15.   (z - ut) pQCD vs. N=4 SYM u = 0.99955 c R.B. Neufeld (preliminary) Chesler & Yaffe arXiv:0712.0050 u = 0.75 c

  16. Conclusion Summary: We have calculated the energy and momentum density deposited into a perturbative, thermal QCD plasma by the color field of a fast moving parton. When treated as a source in linearized dissipative hydrodynamics, the perturbation induces a sonar Mach cone and a diffusive wake. Apart from logarithmic effects, the effect has a well defined relativistic limit. The emerging picture closely resembles that found in the N = 4 super-symmetric gauge theory at strong coupling. An attempt to explore the effects of the (screened) source term in a 3D relativistic, ideal hydro code in progress.

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