Back reaction effects on the dynamics of heavy probes in heavy quark cloud

Published for SISSA by Springer Received: March 2, 2016 Accepted: April 20, 2016 Published: May 16, 2016 Shankhadeep Chakraborttya and Tanay K. Deyb a Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands b Department of Physics, Sikkim Manipal Institute of Technology, Majitar, Rongpo, East Sikkim, Sikkim-737136, India E-mail: , Abstract: We holographically study the effect of back reaction on the hydrodynamical properties of N = 4 strongly coupled super Yang-Mills (SYM) thermal plasma. The back reaction we consider arises from the presence of static heavy quarks uniformly distributed over N = 4 SYM plasma. In order to study the hydrodynamical properties, we use heavy quark as well as heavy quark-antiquark bound state as probes and compute the jet quenching parameter, screening length and binding energy. We also consider the rotational dynamics of heavy probe quark in the back-reacted plasma and analyse associated energy loss. We observe that the presence of back reaction enhances the energy-loss in the thermal plasma. Finally, we show that there is no effect of angular drag on the rotational motion of quark-antiquark bound state probing the back reacted thermal plasma. Keywords: Gauge-gravity correspondence, AdS-CFT Correspondence ArXiv ePrint: 1602.04761 Open Access, c The Authors. Article funded by SCOAP3 . doi:10.1007/JHEP05(2016)094 JHEP05(2016)094 Back reaction effects on the dynamics of heavy probes in heavy quark cloud Contents 1 2 Jet quenching parameter 4 3 Screening length 7 4 Energy loss of a rotating heavy quark 11 5 Effect of angular drag on rotating heavy q q̄ probe 18 6 Conclusion 20 1 Introduction The recent experimental results obtained at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) indicate that a deconfined plasma phase consisted of free quarks and gluons (QGP) has been created at high temperature and high number density [1–5]. Further, the interaction between the high energetic parton probes and the QGP medium signifies that the associated free quarks and gluons are strongly coupled [6, 7]. From the theoretical point of view, among the pre-existing successful theories of quantum chromodynamics, the perturbative QCD and the lattice methods turn out to be inadequate to address the strong coupling issues. On the other hand, the gauge/gravity correspondence seems to be a promising theoretical candidate since it has been widely utilized to study a large class of previously inaccessible strongly coupled gauge theories [8–11]. However, to make use of this correspondence we need to know the exact gravity dual of real QCD at strong coupling and that is not well-understood till date. Nevertheless, the gauge/gravity correspondence can extract some universal properties of a large class of strongly coupled theories having well-defined gravity duals. Interestingly, those universal properties qualitatively agree with the experimental data associated with strong coupling phase of QGP [12–16]. Moreover, the correspondence holds true for some strongly coupled gauge theories exhibiting some QCD like features such as chiral symmetry breaking, confinement to deconfinement crossover etc [17–19]. Along this line of development, within the regime of gauge/gravity correspondence, there has been a number of seminal works to obtain a better theoretical understanding of strongly coupled QGP phase. For example, the dissipative dynamics of an external heavy quark probing through the N = 4 SYM plasma is holographically computed in [20, 21]. The rate of radiative energy loss of an external quark rotating in the N = 4 SYM plasma is successfully addressed in [22]. Furthermore, the holographic technique to compute the jet quenching parameter carrying a measure of suppression of the heavy quark spectrum with –1– JHEP05(2016)094 1 Introduction where l2 2mu4 2 bu3 and h(u) = 1 − − . u2 l6 3 l4 Here, b is the string cloud density, u is the radial coordinate of AdS space with boundary at u = 0 and l is the radius of AdS space. The radius of horizon can be constructed by solving the equation, 2mu4+ 2 bu3+ h(u+ ) = 1 − − = 0. (1.2) l6 3 l4 f (u) = The black hole geometry (1.1) turns out to be stable under vector and tensor perturbation. The back reacted geometry is holographically dual to a system of large number of heavy, static flavour quarks uniformly distributed over the N = 4 SU(Nc ) SYM thermal plasma. It is important to note that in the boundary theory, the SYM plasma together with the quark distribution is effectively considered as back reacted plasma. Using the holographic method applicable to the dual black hole background, dissipative force imparted by the back reacted thermal plasma on an external heavy probe quark has been studied [35] Phenomenologically, in case of quark gluon plasma, the dynamical quantities –2– JHEP05(2016)094 high transverse momentum due to the medium induced scattering has been first prescribed in [24]. The non-perturbative dynamics of heavy probe mesons moving through the N = 4 SYM plasma has been studied and the corresponding quark-antiquark binding energy as well as screening length are qualitatively estimated in [25]. The holographic understanding of the Brownian motion of an external probe quark is achieved in [26, 27]. There has been a lot of further generalisations along this direction of research [28–52]. In spite of several such developments, except in the very few examples [53, 54, 56], it remains very difficult to study the strongly coupled boundary gauge theory with large number of flavour quarks. The introduction of the flavour quarks in the boundary theory corresponds to adding an extra stack of Nf flavour branes probing the pre-existed Nc number of colour branes in the dual gravity [55]. The addition of these flavour branes exerts N a back reaction of the order of Nfc on the bulk geometry. Therefore, the back reaction can not be neglected in the presence of large number of flavour branes (Nf ∼ Nc2 or more) even in the large Nc limit. The difficulty of going beyond the probe approximation motivated one of us to construct a backreacted gravity background without any approximation [35]. The gravity background is realised as an AdS black hole back reacted in the presence of a uniform distribution of large number of fundamental strings. These strings are assumed to be non-interacting, static and infinitely long. One of the end points of each string is attached to the boundary and the body of the string is aligned along the radial direction. The bulk space time gets deformed due to the back reaction of the string distribution. The back reacted geometry is explicitly computable by solving Einstein equation of motion with negative cosmological constant sourced by the uniform string distribution. It turns out to be a deformed black hole in AdS space time parameterized by the mass and density of the stri (...truncated)