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Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at $\sqrt{s_{NN}}$ = 200 GeV
Abstract
422 authors, 58 institutions, 6 pages text, 3 figures, REVTeX4. Submitted to Physical Review Letters. Version v2 has a replacement for Fig. 3 to fix an error in picking up a wrong theory curve. No change to text or data. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html - EI
... 7 See Refs. [12,13] for recent estimates. ...
... The proposals have been quickly extended to the other gauge theories [65]- [73]. 13 To discuss jet quenching, one now moves the fundamental string with a velocity v along a brane direction. Then, the momentum carried by the string flows towards the horizon and one interprets the flow as the energy loss rate. ...
... The large-λ limit of the AdS/CFT is g YM → 0 and N → ∞. But of course QGP has a large-λ since 13 See Refs. [74]- [80] for the other issues. ...
We review the AdS/CFT description of gauge theory plasmas for non-experts. We discuss the low shear viscosity, jet quenching, and J/psi-suppression, which are three major signatures for the quark-gluon plasma observed at RHIC experiments.
... The values of the parameters required for spacetime evolution are displayed in Table 3. With all these ingredients we evaluate the correlation function 2 for 0-5% Au+Au collisions centrality for RHIC at √ = 200 GeV [132] and Pb+Pb collisions at for LHC at √ = 2.76 TeV [133] for different invariant mass windows as a function of side and out which are related to transverse momenta of individual pair [134,135]. By choosing appropriate phase space for the QGP and hadron gas and performing the space time integration using the initial condition tabulated in Table 3, the 2 for different phase has been evaluated. ...
... Now we study the sensitivity of the HBT radii on the different collision energy. The side and out extracted from the 2 's evaluated for 0-5% centrality in Au+Au collisions for RHIC at √ = 200 GeV [132] and Pb+Pb collisions for LHC at √ = 2.76 TeV [133] for different invariant mass windows as a function of side and out are shown in Figure 32. The change of side with ⟨ ⟩ for RHIC and LHC is qualitatively similar but quantitatively different. ...
In this review, we have discussed the different sources of photons and dileptons produced in heavy ion collision (HIC). The transverse momentum () spectra of photons for different collision energies are analyzed with a view of extracting the thermal properties of the system formed in HIC. We showed the effect of viscosity on spectra of produced thermal photons. The dilepton productions from hot hadrons are considered including the spectral change of light vector mesons in the thermal bath. We have analyzed the and invariant mass () spectra of dileptons for different collision energies too. As the individual spectra are constrained by certain unambiguous hydrodynamical inputs, so we evaluated the ratio of photon to dilepton spectra, , to overcome those quantities. We argue that the variation of the radial velocity extracted from with is indicative of a phase transition from the initially produced partons to hadrons. In the calculations of interferometry involving dilepton pairs, it is argued that the nonmonotonic variation of HBT radii with invariant mass of the lepton pairs signals the formation of quark gluon plasma in HIC. Elliptic flow () of dilepton is also studied at TeV for 30–40% centrality using the hydrodynamical model.
... At both RHIC and the LHC, a suppression of the yield of D mesons and high-p T electrons and muons from heavy-flavour hadron decays was observed in AA collisions. The suppression is nearly as large as that of light-flavour hadrons at high p T [33][34][35][36][37]. The D meson and pion R PbPb were found to be consistent within uncertainties and described by model calculations that include a colour-charge dependent energy loss [35,38,39]. ...
The production of beauty hadrons was measured via semi-leptonic decays at mid-rapidity with the ALICE detector at the LHC in the transverse momentum interval $1<p_{\rm T}<8$ GeV/$c$ in minimum-bias p-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and in $1.3<p_{\rm T}<8$ GeV/$c$ in the 20% most central Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. The pp reference spectra at $\sqrt{s}=5.02$ TeV and $\sqrt{s}=2.76$ TeV, needed for the calculation of the nuclear modification factors $R_{\rm pPb}$ and $R_{\rm PbPb}$, were obtained by a pQCD-driven scaling of the cross section of electrons from beauty-hadron decays measured at $\sqrt{s}=7$ TeV. The $R_{\rm PbPb}$ is about 0.7 with an uncertainty of about 30% in the interval $3<p_{\rm T}<6$ GeV/$c$ and 0.47 with an uncertainty of 25% in $6<p_{\rm T}<8$ GeV/$c$ in Pb-Pb collisions. Below $p_{\rm T}=3$ GeV/$c$, the $R_{\rm PbPb}$ values increase with decreasing transverse momentum with systematic uncertainties of 30-45%. The $R_{\rm pPb}$ is consistent with unity within systematic uncertainties of about 20% at high $p_{\rm T}$, increasing at low $p_{\rm T}$, and is well described by theoretical calculations that include cold nuclear matter effects in p-Pb collisions. The measured $R_{\rm pPb}$ and these calculations indicate that cold nuclear matter effects are small at high transverse momentum also in Pb-Pb collisions. Therefore, the observed reduction of $R_{\rm PbPb}$ below unity for high $p_{\rm T}$ can be ascribed to an effect of the hot and dense medium formed in Pb-Pb collisions.
... (It is now possible to detect directly mesons at LHC detectors like ALICE, see [16]). Hence, no wonder that in the recent past a large number of attempts have been made to study both heavy flavour suppression [13,14] and elliptic flow [17] within the framework of perturbative QCD (pQCD) [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. ...
We focus on evaluating transport coefficients like drag and diffusion of
heavy quarks (HQ) passing through Quark Gluon Plasma using perturbative QCD
(pQCD). Experimental observable like nuclear suppression factor (RAA) of HQ is
evaluated for both zero and non-zero baryonic chemical potential ({\mu}_B)
scenarios using Fokker- Planck equation. Theoretical estimates of RAA are
contrasted with experiments.
We revisit the graphic table of QCD signatures in our 1996 Annual Reviews article “The Search for the Quark–Gluon Plasma” and assess the progress that has been made since its publication towards providing quantitative evidence for the formation of a quark–gluon plasma in relativistic heavy-ion collisions and its characteristic properties.
We employ the POWLANG transport setup, developed over the last few years, to provide new predictions for several heavy-flavour observables in relativistic heavy-ion collisions from RHIC to LHC center-of-mass energies. In particular, we focus on the development of the flow-harmonics v2 and v3 arising from the initial geometric asymmetry in the initial conditions and its associated event-by-event fluctuations. Within the same transport framework, for the sake of consistency, we also compare the nuclear modification factor of the p
T
spectra of charm and beauty quarks, heavy hadrons and their decay electrons. We compare our findings to the most recent data from the experimental collaborations. We also study in detail the contribution to the flow harmonics from the quarks decoupling from the fireball during the various stages of its evolution: although not directly accessible to the experiments, this information can shed light on the major sources of the final measured effect.
We propose a novel definition of a holographic light hadron jet and consider the phenomenological consequences, including the very first fully self-consistent, completely strong-coupling calculation of the jet nuclear modification factor RAA, which we find compares surprisingly well with recent preliminary data from LHC. We show that the thermalization distance for light parton jets is an extremely sensitive function of the a priori unspecified string initial conditions and that worldsheets corresponding to non-asymptotic energy jets are not well approximated by a collection of null geodesics. Our new string jet prescription, which is defined by a separation of scales from plasma to jet, leads to the re-emergence of the late-time Bragg peak in the instantaneous jet energy loss rate; unlike heavy quarks, the energy loss rate is unusually sensitive to the very definition of the string theory object itself. A straightforward application of the new jet definition leads to significant jet quenching, even in the absence of plasma. By renormalizing the in-medium suppression by that in the vacuum we find qualitative agreement with preliminary CMS RAAjet(pT) data in our simple plasma brick model. We close with comments on our results and an outlook on future work.
A bstract
Yields of prompt and non-prompt J/ ψ , as well as $ \Upsilon $ (1S) mesons, are measured by the CMS experiment via their μ ⁺ μ ⁻ decays in PbPb and pp collisions at $ \sqrt {{{s_{\text{NN}}}}} = 2.76 $ TeV for quarkonium rapidity | y | < 2.4. Differential cross sections and nuclear modification factors are reported as functions of y and transverse momentum p T , as well as collision centrality. For prompt J/ ψ with relatively high p T (6.5 < p T < 30 GeV/ c ), a strong, centrality-dependent suppression is observed in PbPb collisions, compared to the yield in pp collisions scaled by the number of inelastic nucleon-nucleon collisions. In the same kinematic range, a suppression of non-prompt J/ ψ , which is sensitive to the in-medium b-quark energy loss, is measured for the first time. Also the low- p T $ \Upsilon $ (1S) mesons are suppressed in PbPb collisions.
This report reviews the study of open heavy-flavour and quarkonium production
in high-energy hadronic collisions, as tools to investigate fundamental aspects
of Quantum Chromodynamics, from the proton and nucleus structure at high energy
to deconfinement and the properties of the Quark-Gluon Plasma. Emphasis is
given to the lessons learnt from LHC Run 1 results, which are reviewed in a
global picture with the results from SPS and RHIC at lower energies, as well as
to the questions to be addressed in the future. The report covers heavy flavour
and quarkonium production in proton-proton, proton-nucleus and nucleus-nucleus
collisions. This includes discussion of the effects of hot and cold strongly
interacting matter, quarkonium photo-production in nucleus-nucleus collisions
and perspectives on the study of heavy flavour and quarkonium with upgrades of
existing experiments and new experiments. The report results from the activity
of the SaporeGravis network of the I3 Hadron Physics programme of the European
Union 7th Framework Programme.
The properties of the vector meson current-current correlation function and
its spectral representation are investigated in details with and without
isoscalar-vector interaction within the framework of effective QCD approach,
namely Nambu-Jona-Lasinio (NJL) model and its Polyakov Loop extended version
(PNJL), at finite temperature and finite density. The influence of the
isoscalar-vector interaction on the vector meson correlator is obtained using
the ring resummation known as the Random Phase Approximation (RPA). The
spectral as well as the correlation function in PNJL model show that the vector
meson retains its bound property up to a moderate value of temperature above
the phase transition. Using the vector meson spectral function we, for the
first time, obtained the dilepton production rate from a hot and dense medium
within the framework of PNJL model that takes into account the nonperturbative
effect through the Polyakov Loop fields. The dilepton production rate in PNJL
model is enhanced compared to NJL and Born rate in the deconfined phase due to
the suppression of color degrees of freedom at moderate temperature. The
presence of isoscalar-vector interaction further enhances the dileption rate
over the Born rate in the low mass region. Further, we also have computed the
Euclidean correlation function in vector channel and the conserved density
fluctuation associated with temporal correlation function appropriate for a hot
but very dense medium. The dilepton rate and the Euclidean correlator are also
compared with available lattice data and those quantities in PNJL model are
found to agree well in certain domain.
In the present paper, based on the principles of gauge/gravity duality we
analytically compute the shear viscosity to entropy ratio corresponding to the
superfluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note
that the ratio indeed receives a finite temperature correction below certain
critical temperature. This proves the non universality of shear viscosity to
entropy ratio in higher derivative theories of gravity. We also compute the
upper bound for the Gauss-Bonnet coupling corresponding to the symmetry broken
phase and note that the upper bound on the coupling does not seem to change as
long as we are close to the critical point of the phase diagram. However the
corresponding lower bound of the shear viscosity to entropy ratio seems to get
modified due to the finite temperature effects.
We propose a novel definition of a holographic light hadron jet and consider the phenomenological consequences, including the very first fully self-consistent, completely strong-coupling calculation of the jet nuclear modification factor R
AA
, which we find compares surprisingly well with recent preliminary data from LHC. We show that the thermalization distance for light parton jets is an extremely sensitive function of the a priori unspecified string initial conditions and that worldsheets corresponding to non-asymptotic energy jets are not well approximated by a collection of null geodesics. Our new string jet prescription, which is defined by a separation of scales from plasma to jet, leads to the re-emergence of the late-time Bragg peak in the instantaneous jet energy loss rate; unlike heavy quarks, the energy loss rate is unusually sensitive to the very definition of the string theory object itself. A straightforward application of the new jet definition leads to significant jet quenching, even in the absence of plasma. By renormalizing the in-medium suppression by that in the vacuum we find qualitative agreement with preliminary CMS R
AA
jet(p
T
) data in our simple plasma brick model. We close with comments on our results and an outlook on future work.
The status of the physics of heavy ion collisions is reviewed based on measurements over the past 6 years from the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. The dense nuclear matter produced in Au+Au collisions with nucleon-nucleon c.m. energy at RHIC corresponds roughly to the density and temperature of the universe a few microseconds after the ‘big-bang’ and has been described as “a perfect liquid” of quarks and gluons, rather than the gas of free quarks and gluons, “the quark-gluon plasma” as originally envisaged. The measurements and arguments leading to this description will be presented.
We use holographic duality to analyze the drag force on, and consequent
energy loss of, a heavy quark moving through a strongly coupled conformal fluid
with non-vanishing gradients in its velocity and temperature. We derive the
general expression for the drag force to first order in the fluid gradients.
Using this general expression, we show that a quark that is instantaneously at
rest, relative to the fluid, in a fluid whose velocity is changing with time
feels a nonzero force. And, we show that for a quark that is moving
ultra-relativistically, the first order gradient "corrections" become larger
than the zeroth order drag force, suggesting that the gradient expansion may be
unreliable in this regime. We illustrate the importance of the fluid gradients
for heavy quark energy loss by considering a fluid with one-dimensional boost
invariant Bjorken expansion as well as the strongly coupled plasma created by
colliding sheets of energy.
Relativistic heavy ion collisions create a strongly coupled quark-gluon plasma. Some of the plasma’s properties can be approximately
understood in terms of a dual black hole. These properties include shear viscosity, thermalization time, and drag force on
heavy quarks. They are hard to calculate from first principles in QCD. Extracting predictions about quark-gluon plasmas from
dual black holes mostly involves solving Einstein’s equations and classical string equations of motion. AdS/CFT provides a
translation from gravitational calculations to gauge theory predictions. The gauge theory to which the predictions apply is
N\mathcal {N} = 4 super-Yang-Mills theory. QCD is different in many respects from super-Yang-Mills, but it seems that its high temperature
properties are similar enough to make some meaningful comparisons.
The Langevin diffusion process of a relativistic heavy quark in a non-conformal holographic setup is analyzed. The bulk geometry
is a general, five-dimensional asymptotically AdS black hole. The heavy quark is described by a trailing string attached to
a flavor brane, moving at constant velocity. From the equations describing linearized fluctuations of the string world-sheet,
the correlation functions defining a generalized Langevin process are constructed via the AdS/CFT prescription. In the local
limit, analytic expressions for the Langevin diffusion and friction coefficients are obtained in terms of the bulk string
metric. Modified Einstein relations between these quantities are also derived. The spectral densities associated to the Langevin
correlators are analyzed, and simple analytic expressions are obtained in the small and large frequency limits. Finally, a
numerical analysis of the jet-quenching parameter, and a comparison to RHIC phenomenology are performed in the case of Improved
Holographic QCD. It is shown that the jet-quenching parameter is not enough to describe energy loss of very energetic charm
quarks and the full Langevin correlators are needed.
KeywordsGauge-gravity correspondence–Black Holes–QCD
We carry out an analytic study of the early-time motion of a quark in a strongly-coupled maximally-supersymmetric Yang-Mills plasma, using the AdS/CFT correspondence. Our approach extracts the first thermal effects as a small perturbation of the known quark dynamics in vacuum, using a double expansion that is valid for early times and for (moderately) ultrarelativistic quark velocities. The quark is found to lose energy at a rate that differs significantly from the previously derived stationary/late-time result: it scales like T
4 instead of T
2, and is associated with a friction coefficient that is not independent of the quark momentum. Under conditions representative of the quark-gluon plasma as obtained at RHIC, the early energy loss rate is a few times smaller than its late-time counterpart. Our analysis additionally leads to thermally-corrected expressions for the intrinsic energy and momentum of the quark, in which the previously discovered limiting velocity of the quark is found to appear naturally.
We study the properties of the holographic CFT dual to Gauss-Bonnet gravity in general D(≥ 5) dimensions. We establish the AdS/CFT dictionary and in particular relate the couplings of the gravitational theory to
the universal couplings arising in correlators of the stress tensor of the dual CFT. This allows us to examine constraints
on the gravitational couplings by demanding consistency of the CFT. In particular, one can demand positive energy fluxes in
scattering processes or the causal propagation of fluctuations. We also examine the holographic hydrodynamics, commenting
on the shear viscosity as well as the relaxation time. The latter allows us to consider causality constraints arising from
the second-order truncated theory of hydrodynamics.
KeywordsGauge-gravity correspondence-AdS-CFT Correspondence
Studies of medium-induced QCD radiation usually rely on the calculation of
single-gluon radiation spectrum off an energetic parton traversing an extended
colored medium. Recently, the importance of interference effects between
emitters in the medium has been explored. In this work we extend previous
studies by calculating the single-gluon coherent spectrum off an antenna
consisting of a massive quark-antiquark pair. Interferences dominate the
spectrum of soft gluons, which are mainly emitted outside of the cone made by
the antenna opening angle, while the antenna results in a superposition of
independent emitters above a critical gluon energy scale. We study the
interplay between the dead-cone effect and medium-induced jet broadening in
both cases of soft and hard gluons and present results on energy loss
distributions.
By making use of a non-perturbative definition of a momentum diffusion
coefficient as well as Heavy Meson Chiral Perturbation Theory, we investigate
the Brownian motion and kinetic equilibration of heavy quark flavours deep in
the confined phase. It appears that the momentum diffusion coefficient can be
expressed in terms of known low-energy constants; it increases rapidly at
temperatures above 50 MeV, behaving as ~ T^7/F_pi^4 for m_pi / pi << T << F_pi,
where m_pi and F_pi are the pion mass and decay constant, respectively. The
early increase may suggest a broad peak in kappa/T^3 around the QCD crossover.
For a more detailed understanding the computation could be generalized in a
number of ways.
The spectral function related to the correlator of two colour-electric fields along a Polyakov loop determines the momentum diffusion coefficient of a heavy quark near rest with respect to a heat bath. We compute this spectral function at next-to-leading order, O(alpha_s^2), in the weak-coupling expansion. The high-frequency part of our result (omega >> T), which is shown to be temperature-independent, is accurately determined thanks to asymptotic freedom; the low-frequency part of our result (omega << T), in which Hard Thermal Loop resummation is needed in order to cure infrared divergences, agrees with a previously determined expression. Our result may help to calibrate the overall normalization of a lattice-extracted spectral function in a perturbative frequency domain T << omega << 1/a, paving the way for a non-perturbative estimate of the momentum diffusion coefficient at omega -> 0. We also evaluate the colour-electric Euclidean correlator, which could be directly compared with lattice simulations. As an aside we determine the Euclidean correlator in the lattice strong-coupling expansion, showing that through a limiting procedure it can in principle be defined also in the confined phase of pure Yang-Mills theory, even if a practical measurement could be very noisy there. Comment: 38 pages
We use the gauge/gravity duality to investigate various properties of strongly coupled
gauge theories, which we interpret as models for the quark-gluon plasma (QGP). In particular,
we use variants of the D3/D7 setup as an implementation of the top-down approach of connecting
string theory with phenomenologically relevant gauge theories.
We focus on the effects of finite temperature and finite density on fundamental matter in the
holographic quark-gluon plasma, which we model as the
N=2
hypermultiplet in addition to the
N=4
gauge multiplet of supersymmetric Yang-Mills theory.
We use a setup in which we can describe the holographic plasma at finite temperature and either
baryon or isospin density and investigate the properties of the system from three different viewpoints.
(i) We study meson spectra. Our observations at finite temperature and particle density are in
qualitative agreement with phenomenological models and experimental observations. They agree
with previous publications in the according limits.
(ii) We study the temperature and density dependence of transport properties of fundamental
matter in the QGP. In particular, we obtain diffusion coefficients. Furthermore, in a kinetic model we
estimate the effects of the coupling strength on meson diffusion and therewith equilibration processes
in the QGP.
(iii) We observe the effects of finite temperature and density on the phase structure of fundamental
matter in the holographic QGP. We trace out the phase transition lines of different phases in the
phase diagram.
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