Abstract
We compute and study the drag force acting on a heavy quark propagating through the matter produced in the collision of two sheets of energy in a strongly coupled gauge theory that can be analyzed holographically. Although this matter is initially far from equilibrium, we find that the equilibrium expression for heavy quark energy loss in a homogeneous strongly coupled plasma with the same instantaneous energy density or pressure as that at the location of the quark describes many qualitative features of our results. One interesting exception is that there is a time delay after the initial collision before the heavy quark energy loss becomes significant. At later times, once a liquid plasma described by viscous hydrodynamics has formed, expressions based upon assuming instantaneous homogeneity and equilibrium provide a semi-quantitative description of our results — as long as the rapidity of the heavy quark is not too large. For a heavy quark with large rapidity, the gradients in the velocity of the hydrodynamic fluid result in qualitative consequences for the ‘drag’ force acting on the quark. In certain circumstances, the force required to drag the quark through the plasma can point opposite to the velocity of the quark, meaning that the force that the plasma exerts on a quark moving through it acts in the same direction as its velocity. And, generically, the force includes a component perpendicular to the direction of motion of the quark. Our results support a straightforward approach to modeling the drag on, and energy loss of, heavy quarks with modest rapidity in heavy ion collisions, both before and after the quark-gluon plasma hydrodynamizes, and provide cautionary lessons at higher rapidity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP 07 (2006) 013 [hep-th/0605158] [INSPIRE].
S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [INSPIRE].
J. Casalderrey-Solana and D. Teaney, Heavy quark diffusion in strongly coupled N = 4 Yang-Mills, Phys. Rev. D 74 (2006) 085012 [hep-ph/0605199] [INSPIRE].
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618 [INSPIRE].
P.M. Chesler and L.G. Yaffe, Holography and colliding gravitational shock waves in asymptotically AdS 5 spacetime, Phys. Rev. Lett. 106 (2011) 021601 [arXiv:1011.3562] [INSPIRE].
J. Casalderrey-Solana, M.P. Heller, D. Mateos and W. van der Schee, From full stopping to transparency in a holographic model of heavy ion collisions, arXiv:1305.4919 [INSPIRE].
P.M. Chesler and L.G. Yaffe, Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes, arXiv:1309.1439 [INSPIRE].
R.A. Janik and R.B. Peschanski, Asymptotic perfect fluid dynamics as a consequence of AdS/CFT, Phys. Rev. D 73 (2006) 045013 [hep-th/0512162] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Boost invariant flow, black hole formation and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 82 (2010) 026006 [arXiv:0906.4426] [INSPIRE].
I. Booth, M.P. Heller and M. Spalinski, Black brane entropy and hydrodynamics: The Boost-invariant case, Phys. Rev. D 80 (2009) 126013 [arXiv:0910.0748] [INSPIRE].
M.P. Heller, R.A. Janik and P. Witaszczyk, The characteristics of thermalization of boost-invariant plasma from holography, Phys. Rev. Lett. 108 (2012) 201602 [arXiv:1103.3452] [INSPIRE].
M.P. Heller, D. Mateos, W. van der Schee and D. Trancanelli, Strong Coupling Isotropization of Non-Abelian Plasmas Simplified, Phys. Rev. Lett. 108 (2012) 191601 [arXiv:1202.0981] [INSPIRE].
W. van der Schee, Holographic thermalization with radial flow, Phys. Rev. D 87 (2013) 061901 [arXiv:1211.2218] [INSPIRE].
M.P. Heller, D. Mateos, W. van der Schee and M. Triana, Holographic isotropization linearized, JHEP 09 (2013) 026 [arXiv:1304.5172] [INSPIRE].
C. Shen, U. Heinz, P. Huovinen and H. Song, Systematic parameter study of hadron spectra and elliptic flow from viscous hydrodynamic simulations of Au+Au collisions at \( \sqrt{{{s_{NN }}}}=200 \) GeV, Phys. Rev. C 82 (2010) 054904 [arXiv:1010.1856] [INSPIRE].
P.F. Kolb and U.W. Heinz, Hydrodynamic description of ultrarelativistic heavy ion collisions, in Quark gluon plasma, R.C. Hwa et al. eds. (2003), pg. 634 [nucl-th/0305084] [INSPIRE].
U.W. Heinz, Thermalization at RHIC, AIP Conf. Proc. 739 (2005) 163 [nucl-th/0407067] [INSPIRE].
M.E. Carrington, K. Deja and S. Mrowczynski, Parton Energy Loss in the Extremly Prolate quark-gluon Plasma, PoS(Confinement X)175 [arXiv:1301.4563] [INSPIRE].
D. Grumiller and P. Romatschke, On the collision of two shock waves in AdS 5, JHEP 08 (2008) 027 [arXiv:0803.3226] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
K. Skenderis, Asymptotically Anti-de Sitter space-times and their stress energy tensor, Int. J. Mod. Phys. A 16 (2001) 740 [hep-th/0010138] [INSPIRE].
C.P. Herzog, Energy Loss of Heavy Quarks from Asymptotically AdS Geometries, JHEP 09 (2006) 032 [hep-th/0605191] [INSPIRE].
P. Chesler, M. Lekaveckas and K. Rajagopal, Far-from-equilibrium heavy quark energy loss at strong coupling, Nucl. Phys. A904 (2013) 861c [arXiv:1211.2186] [INSPIRE].
G. Giecold, Heavy quark in an expanding plasma in AdS/CFT, JHEP 06 (2009) 002 [arXiv:0904.1874] [INSPIRE].
A. Stoffers and I. Zahed, Holographic Jets in an Expanding Plasma, Phys. Rev. C 86 (2012) 054905 [arXiv:1110.2943] [INSPIRE].
N. Abbasi and A. Davody, Moving Quark in a Viscous Fluid, JHEP 06 (2012) 065 [arXiv:1202.2737] [INSPIRE].
J. Bjorken, Highly Relativistic Nucleus-Nucleus Collisions: The Central Rapidity Region, Phys. Rev. D 27 (1983) 140 [INSPIRE].
S. Peigne, P.-B. Gossiaux and T. Gousset, Retardation effect for collisional energy loss of hard partons produced in a QGP, JHEP 04 (2006) 011 [hep-ph/0509185] [INSPIRE].
A. Guijosa and J.F. Pedraza, Early-Time Energy Loss in a Strongly-Coupled SYM Plasma, JHEP 05 (2011) 108 [arXiv:1102.4893] [INSPIRE].
M. Chernicoff, D. Fernandez, D. Mateos and D. Trancanelli, Drag force in a strongly coupled anisotropic plasma, JHEP 08 (2012) 100 [arXiv:1202.3696] [INSPIRE].
A. Nata Atmaja and K. Schalm, Anisotropic Drag Force from 4D Kerr-AdS Black Holes, JHEP 04 (2011) 070 [arXiv:1012.3800] [INSPIRE].
K.B. Fadafan and H. Soltanpanahi, Energy loss in a strongly coupled anisotropic plasma, JHEP 10 (2012) 085 [arXiv:1206.2271] [INSPIRE].
G.D. Moore and D. Teaney, How much do heavy quarks thermalize in a heavy ion collision?, Phys. Rev. C 71 (2005) 064904 [hep-ph/0412346] [INSPIRE].
H. van Hees, V. Greco and R. Rapp, Heavy-quark probes of the quark-gluon plasma at RHIC, Phys. Rev. C 73 (2006) 034913 [nucl-th/0508055] [INSPIRE].
H. van Hees, M. Mannarelli, V. Greco and R. Rapp, Nonperturbative heavy-quark diffusion in the quark-gluon plasma, Phys. Rev. Lett. 100 (2008) 192301 [arXiv:0709.2884] [INSPIRE].
Y. Akamatsu, T. Hatsuda and T. Hirano, Heavy Quark Diffusion with Relativistic Langevin Dynamics in the quark-gluon Fluid, Phys. Rev. C 79 (2009) 054907 [arXiv:0809.1499] [INSPIRE].
R. Rapp and H. van Hees, Heavy Quarks in the quark-gluon Plasma, in Quark Gluon Plasma 4, R.C. Hwa, X.-N. Wang eds., World Scientific (2010), pg. 111 [arXiv:0903.1096] [INSPIRE].
W. Alberico, A. Beraudo, A. De Pace, A. Molinari, M. Monteno et al., Heavy-flavour spectra in high energy nucleus-nucleus collisions, Eur. Phys. J. C 71 (2011) 1666 [arXiv:1101.6008] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1306.0564
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Chesler, P.M., Lekaveckas, M. & Rajagopal, K. Heavy quark energy loss far from equilibrium in a strongly coupled collision. J. High Energ. Phys. 2013, 13 (2013). https://doi.org/10.1007/JHEP10(2013)013
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2013)013