Drag force to all orders in gradients
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Springer
Received: December Revised: May Accepted: June Published: July
23, 27, 22, 22,
2019 2020 2020 2020
Jared Reitena,b,c and Andrey V. Sadofyevc a
Department of Physics and Astronomy, University of California, 475 Portola Plaza, Los Angeles, CA 90095, U.S.A. b Mani L. Bhaumik Institute for Theoretical Physics, University of California, 475 Portola Plaza, Los Angeles, CA 90095, U.S.A. c Theoretical Division, MS B283, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.
E-mail: [email protected], [email protected] Abstract: We study the energy loss of a heavy quark slowly moving through an evolving strongly coupled plasma. We use the linearized fluid/gravity correspondence to describe small perturbations of the medium flow with general spacetime dependence. This all order linearized hydrodynamics results in a drag force exerted on a heavy quark even when it is at rest with the fluid element. We show how the general contribution to the drag force can be derived order by order in the medium velocity gradients and provide explicit results valid up to the third order. We then obtain an approximate semi-analytic result for the drag force to all orders in the gradient expansion but linearized in the medium velocity. Thus, the effects of a class of hydrodynamic gradients on the drag force are re-summed, giving further insight into the dissipative properties of strongly coupled plasmas. The all order result allows us to study the drag force in the non-hydrodynamic regime of linear medium perturbations that vary rapidly in space and time. Keywords: Holography and quark-gluon plasmas, Gauge-gravity correspondence ArXiv ePrint: 1912.08816
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)146
JHEP07(2020)146
Drag force to all orders in gradients
Contents 1
2 Fluid/gravity correspondence 2.1 First order hydrodynamics 2.2 All order linearized hydrodynamics
3 4 5
3 Drag force: static medium
6
4 Drag force: fluid motion 4.1 Gradient expansion 4.2 Matching procedure for the linearized string equations 4.3 Drag force in all order linearized hydrodynamics
7 7 10 12
5 Summary and outlook
15
A Fully numerical solutions
16
1
Introduction
The strong energy loss of partons propagating through the quark-gluon plasma (QGP) produced in heavy-ion collisions (HIC) is a distinctive feature of heavy-ion experiments. This phenomenon, known as jet quenching, has attracted significant attention in the literature — for a review see [1]. If one treats the QGP as weakly coupled, then parton energy loss can be successfully described with perturbative techniques based on fundamental QCD [2– 13]. However, the plasma produced in HIC exhibits strong collective phenomena [14–20] and, at later stages, is described by relativistic hydrodynamics — for a review see [21] — with parameters indicating its strongly coupled nature. While there is no reliable tool to describe QCD plasma at all length scales, insights into how strongly coupled dynamics affect parton energy loss can be
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