Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss
W. A. Horowitz, M. Gyulassy
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4 pages, 4 figures. Presented at the 20th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions: Quark Matter 2008 (QM2008), Jaipur, India, 4-10 Feb 2008
We present charm and bottom nuclear modification factors for RHIC and LHC using Standard Model perturbative QCD and recent AdS/CFT string drag energy loss models. We find that extreme extrapolations to LHC mask potential experimentally determinable differences in the individual $R_{AA}$s but that their ratio, $R_{AA}^c/R_{AA}^b$ as a function of transverse momentum is a remarkably robust observable for finding deviations from either theoretical framework.
We compare calculations of jet quenching observables at sqrt s = 2.76 ATeV to preliminary LHC data from weak-coupling pQCD and strong-coupling AdS/CFT drag energy loss models. Rigorously constrained to sqrt s = 200 AGeV RHIC pi^0 suppression data and introducing no free parameters, the pQCD-based WHDG model simultaneously describes qualitatively the suppression of light hadrons and quantitatively the azimuthal anisotropy (over many centrality classes) of light hadrons and the suppression of D mesons at LHC. The drag predictions shown here--qualitatively constrained to RHIC data--compare poorly…
LHC predictions for the charm and bottom nuclear modification factors using pQCD and AdS/CFT drag energy loss models are given. We show that a new observable, the double ratio of charm to bottom nuclear modification factors, allows for easy experimental distinction between the two classes of energy loss models.
We compare away-side hadron correlations with respect to tagged heavy quark jets computed within a weakly coupled pQCD and a strongly coupled AdS/CFT model. While both models feature similar far zone Mach and diffusion wakes, the far zone stress features are shown to be too weak to survive thermal broadening at hadron freeze-out. Observable away-side conical correlations are dominated by the jet-induced transverse flow in near zone "Neck" region, which differs significantly for both models. Unlike in AdS/CFT, the induced transverse flow in the Neck zone is too weak in pQCD to produce conical c…
We propose an identified heavy quark jet observable to discriminate between weakly coupled pQCD and strongly coupled AdS/CFT models of quark gluon plasma dynamics in ultra-relativistic nuclear collisions at RHIC and LHC energies. These models are shown to predict qualitatively different associated hadron correlations with respect to tagged heavy quark jets. While both models feature similar far zone Mach and diffusion wakes, the far zone stress features are shown to be too weak to survive thermal broadening at hadron freeze-out. However, these models differ significantly in a near zone "Neck" …
After an introduction to jet phenomenology and tests of AdS/CFT at LHC we derive the heavy quark drag of a string dangling in a shock metric of AdS space, thus generalizing the AdS/CFT drag calculations in strongly coupled thermal media to momentum loss in both hot and cold nuclear matter.
The AdS/CFT correspondence and a classical test string approximation are used to calculate the drag force on an external quark moving in a thermal plasma of N=4 super-Yang-Mills theory. This computation is motivated by the phenomenon of jet-quenching in relativistic heavy ion collisions.
We investigate drag force in a thermal plasma of N=4 super Yang-Mills theory via both fundamental and Dirichlet strings under the influence of non-zero NSNS $B$-field background. In the description of AdS/CFT correspondence the endpoint of these strings correspondes to an external monopole or quark moving with a constant electromagnetic field. We demonstrate how the configuration of string tail as well as the drag force obtains corrections in this background.
The drag and diffusion coefficients of heavy quarks propagating through quark gluon plasma (QGP) have been evaluated using Hard Thermal Loop (HTL) approximations. The HTL corrections to the relevant propagators and vertices have been considered. It is observed that the magnitudes of both the transport coefficients are changed significantly from values obtained by earlier approaches where either (i) the $t$ channel divergence in T=0 pQCD matrix element is shielded simply by Debye mass. or (ii) only HTL resummed propagator is used ignoring the HTL corrections at the interaction vertices. The imp…
We compute for the first time the suppression of bottomonia in a strongly coupled QGP and compare the results to those from a weakly coupled QGP. Using imaginary time techniques we numerically determine the real and imaginary parts of the ground state binding energy of the bottomonia in one potential computed from AdS/CFT and another computed from pQCD. We then use these binding energies in a suppression model to determine the $Υ$(1S) nuclear modification factor in $\sqrt{s}_{NN}=2.76$ TeV Pb+Pb collisions. AdS/CFT significantly overpredicts the suppression compared to data, although the predi…
The drag and diffusion coefficients of heavy quarks propagating through quark gluon plasma (QGP) have been estimated by shielding both the electric and magnetic type infra-red divergences. The electric type screening in perturbative quantum chromodynamics (pQCD) has been widely studied and used in evaluating the diffusion coefficient of heavy quarks (HQs). To our knowledge the impact of magnetic screening in diffusion coefficients of HQs is not studied before. It is found that the effect of magnetic screening mass on the drag and diffusion coefficients of HQs is quite significant and its contr…
Despite the 300% systematic theoretical uncertainty associated with extracting qhat using current energy loss models due to the collinear approximation, and despite the uncertainties in the initial geometry and corrections due to the fluctuations in the initial overlap of a heavy ion collision, a simultaneous description of high-pT pi^0 RAA and v2 is not possible with current pQCD-based energy loss models. However a good description of out-of-plane RAA as a function of centrality is possible. Alternatively, energy loss models based on AdS/CFT give a better qualitative description of pi^0 and n…
Two AdS/CFT based energy loss models are used to compute the suppression and azimuthal correlations of heavy quarks in heavy ion collisions. The model with a velocity independent diffusion coefficient is in good agreement with B and D meson data up to high $p_T$. The partonic azimuthal correlations we calculate exhibit an order of magnitude difference in low momentum correlations to pQCD calculations [arXiv:1305.3823]. We thus propose heavy flavour momentum correlations as a distinguishing observable of weakly- and strongly-coupled energy loss mechanisms.
The drag and diffusion coefficients of charm and bottom quarks propagating through quark gluon plasma (QGP) have been evaluated within the framework of perturbative Quantum Chromodynamics (pQCD). Both radiative and collisional processes of dissipation are included in evaluating these transport coefficients. The dead cone as well as the LPM effects on radiative energy loss of heavy quarks have also been considered. The Fokker Planck equation has been solved to study the dissipation of heavy quarks momentum in QGP. The nuclear suppression factor, $R_{\mathrm AA}$ and the elliptic flow $v_2^{HF}$…
Recent LHC data suggest that perturbative QCD provides a qualitatively consistent picture of jet quenching. Constrained to RHIC pi0 suppression, zero parameter WHDG energy loss predictions agree quantitatively with the charged hadron v2 and D meson RAA measured at LHC and qualitatively with the charged hadron RAA. On the other hand, RHIC-constrained LHC predictions from fully strongly-coupled AdS/CFT qualitatively oversuppress D mesons compared to data; light meson predictions are on less firm theoretical ground but also suggest oversuppression. More detailed data from heavy, especially B, mes…
The effects of gluon radiation by charm quarks on the transport coefficients {\it e.g.} drag, longitudinal and transverse diffusion and shear viscosity have been studied within the ambit of perturbative quantum chromodynamics (pQCD) and kinetic theory. We found that while the soft gluon radiation has substantial effects on the transport coefficients of the charm quarks in the quark gluon plasma its effects on the equilibrium distribution function is insignificant.
We show that Mach-like azimuthal correlations of associated hadrons in the wake of heavy quark jets modeled in the AdS/CFT string drag picture originate only from the near-quark ``Head'' region. The contributions from the far zones lead only to a yield peaked in the opposite direction with respect to the trigger jet.
A generic jet-energy loss model that is coupled to state-of-the-art hydrodynamic fields and interpolates between a wide class of running coupling pQCD-based and AdS/CFT-inspired models is compared to recent data on the azimuthal and transverse momentum dependence of high-pT pion nuclear modification factors and high-pT elliptic flow measured at RHIC and LHC. We find that RHIC data are surprisingly consistent with various scenarios considered. However, extrapolations to LHC energies favor running coupling pQCD-based models of jet-energy loss. While conformal holographic models are shown to be i…
We develop a relativistic Langevin dynamics under the background of strongly interacting quark-gluon fluid described by the (3+1)-dimensional hydrodynamics. The drag force acting on charm and bottom quarks is parametrized according to the formula obtained from the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. In this setup, we calculate the nuclear modification factor $R_{\rm{AA}}$ for the single-electrons from the charm and bottom quarks to extract the magnitude of the drag force from the PHENIX and STAR data. The $R_{\rm{AA}}$ for single-electrons with $p_{T}\geq 3$ G…
Heavy flavor research is a vigorous and active topic in high-energy QCD physics. Comparing theoretical predictions to data as a function of flavor provides a unique opportunity to tease out properties of quark-gluon plasma. We explicitly demonstrate this utility with energy loss predictions based on the assumption of 1) a weakly-coupled plasma weakly coupled to a high-pT probe using pQCD and 2) a strongly-coupled plasma strongly coupled to a high-pT probe using AdS/CFT; we find that while the former enjoys broad qualitative agreement with data, it is difficult to reconcile the latter with expe…
We calculate the drag force on a heavy quark hit by a shock wave, thus generalizing the strongly coupled AdS/CFT heavy quark drag calculations to both hot and cold nuclear matter. The derivation employs the trailing string configuration, similar to that used in the literature for a quark moving through a thermal medium, though in the shock metric the string profile is described by a much simpler analytic function. Our expression for the drag depends on the typical transverse momentum scale of the matter in the shock. For a thermal medium this scale becomes proportional to the temperature, maki…
Using the gauge/string duality, we derive a set of Langevin equations describing the dynamics of a relativistic heavy quark moving with constant average speed through the strongly-coupled N=4 SYM plasma at finite temperature. We show that the stochasticity arises at the string world-sheet horizon, and thus is causally disconnected from the black hole horizon in the space-time metric. This hints at the non-thermal nature of the fluctuations, as further supported by the fact that the noise term and the drag force in the Langevin equations do not obey the Einstein relation. We propose a physical …
Using AdS/CFT we investigate the effect of angular-momentum-induced anisotropy on the instantaneous drag force of a heavy quark. The dual description is that of a string moving in the background of a Kerr-AdS black holes. The system exhibits the expected focussing of jets towards the impact parameter plane. We put forward that we can use the connection between this focussing behavior and the angular momentum induced pressure gradient to extrapolate the pressure gradient correction to the drag force that can be used for transverse elliptic flow in realistic RHIC. The result is recognizable as a…
The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in Itô discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the AdS/CFT correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor R_{AA} and the elliptic flow v_{2} for the single …
Results based on a generic jet-energy loss model that interpolates between running coupling pQCD-based and AdS/CFT-inspired holographic prescriptions are compared to recent data on the high-p_T pion nuclear modification factor and the high-p_T elliptic flow in nuclear collisions at RHIC and LHC. The jet-energy loss model is coupled to various (2+1)d (viscous hydrodynamic) fields. The impact of energy-loss fluctuations is discussed. While a previously proposed AdS/CFT jet-energy loss model with a temperature-independent jet-medium coupling is shown to be inconsistent with the LHC data, we find …
We show that Mach-like correlations from heavy quark jets in the Gubser et al AdS/CFT string drag model arise not from the expected (weak) hydrodynamical Mach sound wakes zone but from a near ``Neck'' zone where strong chromo-viscous field effects dominated and lead to a distinctive stress in the plasma of the form $T^{μν}_{Neck} \propto \surd λT_0^2 Y^{μν}(x)/x^2$. We propose that measurement of the jet velocity dependence of moderate $p_T$ hadrons associated with future {\em identified heavy quark jets} at RHIC and LHC could be used to look for this novel source of conical correlations which…
We compute the jet path-length dependence of energy-loss for higher azimuthal harmonics of jet-fragments in a generalized model of energy-loss that can interpolate between pQCD and AdS/CFT limits and compare results with Glauber and CGC/KLN initial conditions. We find, however, that even the high-pT second moment is most sensitive to the poorly known early-time evolution during the first fm/c. Moreover, we demonstrate that quite generally the energy and density-dependence leads to an overquenching jet fragments relative to the first LHC $R_{AA}$-data, once the parameters of the energy-loss mod…
I discuss several novel and unexpected aspects of quantum chromodynamics. These include: (a) the nonperturbative origin of intrinsic strange, charm and bottom quarks in the nucleon at large light-cone momenta x; the breakdown of pQCD factorization theorems due to the lensing effects of initial- and final-state interactions; (b) important corrections to pQCD scaling for inclusive reactions due to processes in which hadrons are created at high transverse momentum directly in the hard processes and their relation to the baryon anomaly in high-centrality heavy-ion collisions; and (c) the nonuniver…
We consider the diffusion of a non-relativistic heavy quark of fixed mass M, in a one-dimensionally expanding and strongly coupled plasma using the AdS/CFT duality. The Green's function constructed around a static string embedded in a background with a moving horizon, is identified with the noise correlation function in a Langevin approach. The (electric) noise decorrelation is of order 1/T(τ) while the velocity de-correlation is of order MD(τ)/T(τ). For MD>1, the diffusion regime is segregated and the energy loss is Langevin-like. The time dependent diffusion constant D(τ) asymptotes its adia…
We investigate the robustness with respect to nonconformality of five properties of strongly coupled plasmas that have been calculated in N=4 supersymmetric Yang-Mills (SYM) theory at nonzero temperature, motivated by the goal of understanding phenomena in heavy ion collisions. (The properties are the jet quenching parameter, the velocity dependence of screening, and the drag and transverse and longitudinal momentum diffusion coefficients for a heavy quark pulled through the plasma.) We use a toy model in which nonconformality is introduced via a one-parameter deformation of the AdS black hole…
Using the recently published model for the collisional energy loss of heavy quarks (Q) in a Quark Gluon Plasma (QGP), based on perturbative QCD (pQCD) with a running coupling constant, we study the interaction between heavy quarks and plasma particles in detail. We discuss correlations between the simultaneously produced $c$ and $\bar{c}$ quarks, study how central collisions can be experimentally selected, predict observable correlations and extend our model to the energy domain of the large hadron collider (LHC). We finally compare the predictions of our model with that of other approaches li…
Heavy quarks (charm and bottoms) are one of the few probes which are sensitive to the degrees of freedom of a Quark Gluon Plasma (QGP), which cannot be revealed by lattice gauge calculations in equilibrium. Due to the rapid expansion of the QGP energetic heavy quarks do not come to an equilibrium with the QGP. Their energy loss during the propagation through the QGP medium depends strongly on the modelling of the interaction of the heavy quarks with the QGP quarks and gluons, i.e. on the assuption of the degrees of freedom of the plasma. Here we compare the results of different models, the pQC…
We compare fully perturbative and fully nonperturbative pictures of high-pT energy loss calculations to the first results from LHC. While over-suppressed compared to published ALICE data, parameter-free pQCD predictions based on the WHDG energy loss model constrained to RHIC data simultaneously describe well the preliminary CMS hadron suppression, ATLAS charged hadron v2, and ALICE D meson suppression; we also provide for future reference WHDG predictions for B meson RAA. However, energy loss calculations based on AdS/CFT also qualitatively describe well the RHIC pion and non-photonic electron…
We argue that classical bulk gravitational radiation effects in AdS/CFT, previously ignored because of their subleading nature in the 1/Nc-expansion, are magnified by powers of large Lorentz factors gamma for ultrarelativistic jets, thereby dominating other forms of jet energy loss in holography at finite temperature. We make use of the induced gravitational self-force in thermal AdS5 to estimate its effects. In a thermal medium, relativistic jets may loose most of their energy through longitudinal drag caused by the energy accumulated in their nearby field as they zip through the strongly cou…
Perturbative QCD (pQCD) running coupling a(Q^2) (=alpha_s(Q^2)/pi) is expected to get modified at low spacelike momenta 0 < Q^2 < 1 GeV^2 so that, instead of having unphysical (Landau) singularities it remains smooth and finite there, due to infared (IR) fixed point. This behavior is suggested by: Gribov-Zwanziger approach, Dyson-Schwinger equations (DSE) and other functional methods, lattice calculations, light-front holographic mapping AdS/CFT modified by a dilaton background, and by most of the analytic (holomorphic) QCD models. All such couplings, A(Q^2), differ from the pQCD couplings a(Q…
The radiative energy loss of fast partons traveling through the quark-gluon plasma (QGP) is commonly studied within perturbative QCD (pQCD). Nonperturbative (NP) effects, which are expected to become important near the critical temperature, have been much less investigated. Here, we utilize a recently developed $T$-matrix approach to incorporate NP effects for gluon emission off heavy quarks propagating through the QGP. We set up four cases that contain, starting from a Born diagram calculation with color-Coulomb interaction, an increasing level of NP components, by subsequently including (rem…
Results from an energy loss model that includes thermal fluctuations in the energy loss for heavy quarks in a strongly-coupled plasma are shown to be qualitatively consistent with single particle data from both RHIC and LHC. The model used is the first to properly include the fluctuations in heavy quark energy loss as derived in string theory and that do not obey the usual fluctuation-dissipation relations. These fluctuations are crucial for simultaneously describing both RHIC and LHC data; leading order drag results without fluctuations are falsified by current data. Including the fluctuation…
Within the framework of the AdS/CFT correspondence, we study the time evolution of an energetic R-current propagating through a finite temperature, strongly coupled, N=4 SYM plasma and propose a physical picture for our results. In this picture, the current splits into a pair of massless partons, which then evolve via successive branchings, in such a way that energy is quasi-democratically divided among the products of a branching. We point out a duality between the transverse size of the partonic system produced through branching and the radial distance traveled by the dual Maxwell wave in th…
We make use of the AdS/CFT correspondence to determine the energy of an external quark-antiquark pair that moves through strongly-coupled thermal N=4 super-Yang-Mills plasma, both in the rest frame of the plasma and in the rest frame of the pair. It is found that the pair feels no drag force, has an energy that reproduces the expected 1/L (or gamma/L) behavior at small quark-antiquark separations, and becomes unbound beyond a certain screening length whose velocity-dependence we determine. We discuss the relation between the high-velocity limit of our results and the lightlike Wilson loop prop…
Recent data on the high-pT pion nuclear modification factor, $R_{AA}(p_T)$, and its elliptic azimuthal asymmetry, $v_2(p_T)$, from RHIC/BNL and LHC/CERN are analyzed in terms of a wide class of jet-energy loss models coupled to different (2+1)d transverse plus Bjorken expanding hydrodynamic fields. We test the consistency of each model by demanding a simultaneous account of the azimuthal, the transverse momentum, and the centrality dependence of the data at both 0.2 and 2.76 ATeV energies. We find a rather broad class of jet-energy independent energy-loss models $dE/dx= κ(T) x^z T^{2+z} ζ_q$ t…
I discuss a number of novel phenomenological features of QCD in high transverse momentum reactions. The presence of direct higher-twist processes, where a proton is produced directly in the hard subprocess, can explain the "baryon anomaly" -- the large proton-to-pion ratio seen at RHIC in high centrality heavy ion collisions. Direct hadronic processes can also account for the deviation from leading-twist PQCD scaling at fixed x_T = 2p_T/\sqrt s. I suggest that the "ridge" -- the same-side long-range rapidity correlation observed at RHIC in high centrality heavy ion collisions is due to the imp…
We systematically study holographic effects on the magnetic field dependence of the drag force, diffusion coefficient, jet quenching parameter of heavy quarks and the shooting string energy loss of light quarks in the RHIC and LHC energy regions by using the AdS/CFT correspondence in this paper. This study is motivated by the phenomena of strong magnetic field and jet quenching, which have been found in relativistic heavy ion collisions. The probe's direction of motion is perpendicular and parallel to the direction of magnetic field $B$. The effects of magnetic field on energy loss when moving…
