Determining the jet transport coefficient $\hat{q}$ of the quark-gluon plasma using Bayesian parameter estimation
J. Mulligan, A. Angerami, R. Arora, S. A. Bass, S. Cao, Y. Chen, J. Coleman, L. Cunqueiro, T. Dai, L. Du, R. Ehlers, H. Elfner, D. Everett, W. Fan, R. Fries, C.… 展开作者
J. Mulligan, A. Angerami, R. Arora, S. A. Bass, S. Cao, Y. Chen, J. Coleman, L. Cunqueiro, T. Dai, L. Du, R. Ehlers, H. Elfner, D. Everett, W. Fan, R. Fries, C. Gale, F. Garza, Y. He, M. Heffernan, U. Heinz, B. V. Jacak, P. M. Jacobs, S. Jeon, W. Ke, B. Kim, M. Kordell, A. Kumar, D. Liyanage, M. Luzum, A. Majumder, S. Mak, M. McNelis, C. Nattrass, D. Oliinychenko, C. Park, J. -F. Paquet, J. H. Putschke, G. Roland, B. Schenke, L. Schwiebert, C. Shen, A. Silva, C. Sirimanna, R. A. Soltz, Y. Tachibana, G. Vujanovic, X. -N. Wang, R. L. Wolpert, Y. Xu
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contribution to the 2021 QCD session of the 55th Recontres de Moriond
We present a new determination of $\hat{q}$, the jet transport coefficient of the quark-gluon plasma. Using the JETSCAPE framework, we use Bayesian parameter estimation to constrain the dependence of $\hat{q}$ on the jet energy, virtuality, and medium temperature from experimental measurements of inclusive hadron suppression in Au-Au collisions at RHIC and Pb-Pb collisions at the LHC. These results are based on a multi-stage theoretical approach to in-medium jet evolution with the MATTER and LBT jet quenching models. The functional dependence of $\hat{q}$ on jet energy, virtuality, and medium temperature is based on a perturbative picture of in-medium scattering, with components reflecting the different regimes of applicability of MATTER and LBT. The correlation of experimental systematic uncertainties is accounted for in the parameter extraction. These results provide state-of-the-art constraints on $\hat{q}$ and lay the groundwork to extract additional properties of the quark-gluon plasma from jet measurements in heavy-ion collisions.
One of the key signatures of the Quark Gluon Plasma (QGP) is the energy loss of high momentum particles as they traverse the strongly interacting medium. The energy loss of these particles is governed by the jet transport coefficient $\hat{q}/T^3$, wherein it has been thought that there is a large jump as the system transitions between the hadron gas and Quark Gluon Plasma phases. Here we calculate $\hat{q}/T^3$ within the Hadron Resonance Gas (HRG) model with the particle list PDG16+ and find that, if one incorporates the experimental error in the hadronic calculation of $\hat{q}/T^3$ and ass…
The transport coefficient $\hat{q}$ plays a pivotal role in describing the phenomenon of jet quenching in the quark-gluon plasma (QGP) produced in ultra-relativistic nucleus-nucleus collisions. It is challenging to compute this coefficient from first principles due to its non-perturbative nature. In this article, we present an $ab$-$initio$ formulation of $\hat{q}$ based on the standard techniques of perturbative quantum chromodynamics (pQCD) and lattice gauge theory. We construct $\hat{q}$ by considering a leading order (LO) process where a hard parton produced from the hard scattering underg…
$\hat q$ is the average squared transverse momentum transfer per unit length to a high-energy particle traversing a QCD medium such as a quark-gluon plasma. We find the (UV-regulated) value of $\hat q$ to leading order in the weak coupling limit, $\alphas(T) \ll 1$. We then use this value to generalize previous analytic results on the gluon bremsstrahlung and pair production rates for massless high-energy particles in a weakly-coupled quark-gluon plasma, at next-to-leading logarithmic order.
The transport coefficient $\hat{q}$ is a leading coefficient that controls the modification of the hard parton traversing QGP, and hence, responsible for the suppression of the high transverse momentum (transverse to the beam direction) charged-hadrons in heavy-ion collisions. In this article, we present the first unquenched lattice QCD calculation of $\hat{q}$. The calculation is carried out using (2+1)-flavor of quarks, using the highly improved staggered quark action (HISQ) and tree-level Symanzik improved gauge action. The calculation is performed in a wide range of temperatures, ranging f…
Closed-form expressions for tree-level gluon-gluon scattering: a framework for obtaining theoretical systematic uncertainties for jet-medium Monte Carlo simulations
We use linear viscous hydrodynamics to describe the energy and momentum deposited by a fast moving parton in a quark gluon plasma. This energy-momentum is in turn used to compute the probability density for the production of soft partons by means of the Cooper-Frye formula. We use this probability density to render manifest a relation between the average transverse momentum given to the fast moving parton from the medium $\hat{q}$, the entropy density to shear viscosity ratio $η/s$ and the energy lost by the fast moving parton $ΔE$ in an expanding medium under similar conditions to those gener…
We compute the jet quenching parameter $\hat q$ of QCD plasma in the presence of strong magnetic field in both weakly and strongly coupled regimes. In weakly coupled regime, we compute $\hat q$ in perturbative QCD at complete leading order (that is, leading log as well as the constant under the log) in QCD coupling constant $α_s$, assuming the hierarchy of scales $α_s eB\ll T^2\ll eB$. We consider two cases of jet orientations with respect to the magnetic field: 1) the case of jet moving parallel to the magnetic field, 2) the case jet moving perpendicular to the magnetic field. In the former c…
A new model of jet quenching in nuclear collisions, CUJET3.0, is constructed by generalizing the perturbative QCD based CUJET2.0 model to include two complementary non-perturbative features of the QCD confinement cross-over phase transition near $T_c\approx 160$ MeV: (1) the suppression of quark and gluon degrees of freedom and (2) the emergence of chromo-magnetic monopole degrees of freedom. Such a semi-Quark-Gluon-Monopole Plasma (sQGMP) microscopic scenario is tested by comparing predictions of the leading hadron nuclear modification factors, $R^h_{AA}(p_T>10{\rm GeV/c},\sqrt{s})$, and thei…
We utilize a new framework, CUJET3.0, to deduce the energy and temperature dependence of jet transport parameter, $\hat{q}(E>10\; {\rm GeV},T)$, from a combined analysis of available data on nuclear modification factor and azimuthal asymmetries from RHIC/BNL and LHC/CERN on high energy nuclear collisions. Extending a previous perturbative-QCD based jet energy loss model (known as CUJET2.0) with (2+1)D viscous hydrodynamic bulk evolution, this new framework includes three novel features of nonperturbative physics origin: (1) the Polyakov loop suppression of color-electric scattering (aka "semi-…
We present here a possible resolution of the jet quenching parameter $\hat{q}$ puzzle by exploring the momentum fraction $x$ and scale $Q^2$ dependence of $\hat{q}$, in addition to temperature dependence. We explore the momentum broadening of the jet due to Glauber gluon exchange with the quark-gluon plasma (QGP). This has led us to define the momentum fraction $x$ for the partons in the QGP. We also show here, for the first time, possible forms of the parton distribution function (PDF) of the QGP. The QGP-PDF as input in $\hat{q}$ has been used to fit the PHENIX and CMS data simultaneously. W…
Within the framework of a high-twist approach, we show the first complete next-to-leading order calculation of transverse momentum broadening in semi-inclusive deeply inelastic $e+A$ scattering and Drell-Yan dilepton production in $p+A$ collisions. We demonstrate at one-loop level how QCD factorization holds for multiple scattering in nuclear medium, and the university of the associated quark-gluon correlation function. Our calculation also identifies QCD evolution equation for the quark-gluon correlation function, which determines the QCD factorization scale and energy dependence of jet trans…
Multi-particle potentials from light-like Wilson lines in quark-gluon plasmas: a generalized relation of in-medium splitting rates to jet-quenching parameters $\hat q$
The average transverse momentum transfer per unit path length to a fast parton scattering elastically in a perturbative quark-gluon plasma is related to the radiative energy loss of the parton. We first calculate the momentum transfer coefficient $\hat q$ in terms of a classical Langevin problem and then define it quantum-mechanically through scattering matrix element. After treating the well known case of a quark-gluon plasma in equilibrium we consider an off-equilibrium unstable plasma. As a specific example, we treat the two-stream plasma with unstable modes of longitudinal chromoelectric f…
We report a new determination of $\hat{q}$, the jet transport coefficient of the Quark-Gluon Plasma. We use the JETSCAPE framework, which incorporates a novel multi-stage theoretical approach to in-medium jet evolution and Bayesian inference for parameter extraction. The calculations, based on the MATTER and LBT jet quenching models, are compared to experimental measurements of inclusive hadron suppression in Au+Au collisions at RHIC and Pb+Pb collisions at the LHC. The correlation of experimental systematic uncertainties is accounted for in the parameter extraction. The functional dependence …
The jet transport coefficient $\hat{q}$ is the leading transport coefficient that controls the modification of hard jets produced in heavy-ion collisions. This coefficient is inherently non-perturbative, and hence, is challenging to compute from first principles. In this report, we present a perturbative quantum chromodynamics (pQCD) and lattice gauge theory based formulation to study $\hat{q}$. We formulate $\hat{q}$ within a 4-dimensional (4D) quenched SU(3) lattice. We consider a leading order diagram for a hard parton passing through the quark-gluon plasma. The non-perturbative part is exp…
Nuclear modification factors of single hadrons and dihadrons at large transverse momentum ($p_{\rm T}$) in high-energy heavy-ion collisions are studied in a next-to-leading-order (NLO) perturbative QCD parton model. Parton fragmentation functions (FFs) in $A+A$ collisions are modified due to jet energy loss which is proportional to the jet transport coefficient $\hat{q}$ characterizing the interaction between the parton jet and the produced medium. By confronting 6 current sets of NLO parton FFs for large $p_{\rm T}$ hadron productions, we extract $\hat{q}$ quantitatively via a global fit to d…
Quark-gluon plasma produced at the early stage of ultrarelativistic heavy ion collisions is unstable, if weakly coupled, due to the anisotropy of its momentum distribution. Chromomagnetic fields are spontaneously generated and can reach magnitudes much exceeding typical values of the fields in equilibrated plasma. We consider a high energy test parton traversing an unstable plasma that is populated with strong fields. We study the momentum broadening parameter $\hat q$ which determines the radiative energy loss of the test parton. We develop a formalism which gives $\hat q$ as the solution of …
Color charge correlations in the proton at moderately small $x\sim 0.1$ are extracted from its light-cone wave function. The charge fluctuations are far from Gaussian and they exhibit interesting dependence on impact parameter and on the relative transverse momentum (or distance) of the gluon probes. We provide initial conditions for small-$x$ Balitsky-Kovchegov evolution of the dipole scattering amplitude with impact parameter and $\hat r \cdot \hat b$ dependence, and with non-zero $C$-odd component due to three-gluon exchange. Lastly, we compute the (forward) Weizsaecker-Williams gluon distr…
In this article we investigate how the drag coefficient $A$ and $\hat{q}$, the transverse momentum transfer by unit length, of charm quarks are modified if the QGP is not in complete thermal equilibrium using the dynamical quasi-particle model (DQPM) which reproduces both, the equation-of-state of the QGP and the spatial diffusion coefficient of heavy quarks as predicted by lattice QCD calculations. We study three cases: a) the QGP has an anisotropic momentum distribution of the partons which leads to an anisotropic pressure b) the QGP partons have higher or lower kinetic energies as compared …
Minijet production in $\sqrt{s} = 5.5$ TeV Pb+Pb collisions at the LHC is expected to produce a gluon-dominated plasma with large initial temperatures and energy densities. We discuss the implications of the high initial temperatures on the screening mass and on the relative suppression of members of the $Υ$ family. We demonstrate that $p_T$-dependence of the $Υ'/Υ$ ratio is only expected if a quark-gluon plasma with significant energy density is present, and that the precise dependence of this ratio will strongly constrain the QGP models. We also propose that the $p_T$ spectra of the $Υ$ reso…
Within the generalized high-twist factorization formalism, we express the contribution from multiple parton scattering and induced gluon radiation to the DY dilepton spectra in terms of nuclear modified effective beam quark distribution function. We show that beam quark energy loss is characterized by jet transport parameter $\hat{q}$, which is related to the local gluon density of the medium. Using the value of $\hat{q}$ determined from the deeply inelastic scattering (DIS) data, we evaluate the nuclear modification factor in Drell-Yan process in p+A collisions. Effects of parton energy loss …
We study the evolution and saturation of the gluon distribution function in the quark-gluon plasma as probed by a propagating parton and its effect on the computation of jet quenching or transport parameter $\hat{q}$. For thermal partons, the saturation scale $Q^2_s$ is found to be proportional to the Debye screening mass $μ_D^2$. For hard probes, evolution at small $x=Q^2_s/6ET$ leads to jet energy dependence of $\hat{q}$. We study this dependence for both a conformal gauge theory in weak and strong coupling limit and for (pure gluon) QCD. The energy dependence can be used to extract the shea…
The case of gluon bremsstrahlung off a heavy quark in extended nuclear matter is revisited within the higher twist formalism. In particular, the in-medium modification of "semi-hard" heavy quarks is studied, where the momentum of the heavy quark is larger but comparable to the mass of the heavy quark ($p \gtrsim M$). In contrast to all prior calculations, where the gluon emission spectrum is entirely controlled by the transverse momentum diffusion parameter ($\hat q$), both for light and heavy quarks, in this work, we demonstrate that the gluon emission spectrum for a heavy quark (unlike that …
We revisited gluon bremsstrahlung off a heavy quark in nuclear matter within higher twist formalism. In this work, we demonstrate that, in addition to transverse momentum diffusion parameter ($\hat q$), the gluon emission spectrum for a heavy quark is quite sensitive to $\hat e$, which quantify the amount of light-cone drag experienced by a parton. This effect leads to an additional energy loss term for heavy-quarks. From heavy flavor suppression data in ultra-relativistic heavy-ion collisions one can now estimate the value of this sub-leading non-perturbative jet transport parameter ($\hat e$…
We present an attempt to probe the underlying structure of the quark-gluon plasma (QGP) at high resolution, based on the extracted jet transport coefficient $\hat{q}$. We argue that the exchanged momentum $k$ between the hard parton and the medium varies over a range of scales, and for $k\geq$ 1 GeV, $\hat{q}$ can be expressed in terms of a parton distribution function (PDF). Because the mass of a QGP constituent is unknown, we define a scaling variable $x_N$ to represent the ratio of the parton momentum to the momentum of a self-contained section of the plasma which has a mass of 1 GeV. This …
As a step towards understanding the in-medium evolution of a hard jet, we consider the interference pattern for the medium induced gluon radiation produced by a color singlet quark-antiquark antenna embedded in a QCD medium with size L. We focus on the typical kinematics for medium-induced gluon radiation in the BDMPS-Z regime, that is, short formation times τ_f << L and relatively large emission angles θ>>θ_c = 2/\sqrt{\hat q L^3}, with \hat q the `jet quenching' parameter. We demonstrate that, for a dipole opening angle θ_{q\bar q} larger than θ_c, the interference between the medium-induced…
We present a new definition of the jet quenching parameter $\hat{q}$ in a weakly-coupled quark-gluon plasma undergoing boost-invariant longitudinal expansion. We propose a boost-invariant definition of $\hat{q}$, which is proportional to the broadening of the angular variables $η$ (the pseudo-rapidity) and $ϕ$ (the azimuthal angle). We furthermore consider radiative corrections to $\hat{q}$ and find potentially large corrections enhanced by a double logarithm like the case of a static medium. But unlike for the static medium, these corrections are now local in (proper) time.
It is argued that heavy-quarks traversing a Quark Gluon Plasma, undergo a multi-stage modification process, similar to the case of light flavors. Such an approach is applied to heavy-quark energy loss, which includes a rare-scattering, multiple emission formalism at momenta large compared to the mass (sensitive only to the transverse diffusion coefficient $\hat{q}$), and a single scattering induced emission formalism (Gunion-Bertsch) at momenta comparable to the mass of the quark [sensitive to $\hat{q}$, and the longitudinal drag ($\hat{e}$) and diffusion ($\hat{e}_2$) coefficients]. The appli…
We present the first attempt to extract the "$x$" dependence of the parton distribution function (PDF) of the quark gluon plasma (QGP). In the absence of knowledge regarding the mass of a QGP constituent, we define the new variable $x_N$, the nucleonic momentum fraction, which represents the ratio of the momentum of the parton to that of a self-contained section of the plasma that has the mass of a nucleon. Calculations are compared to data for single hadron suppression in terms of the nuclear modification factor $R_{AA}$ and the azimuthal anisotropy parameter $v_{2}$, as a function of transve…
I report on some theoretical progress concerning the calculation of gluon bremsstrahlung for very high energy particles crossing a weakly-coupled quark-gluon plasma. (i) I advertise that two of the several formalisms used to study this problem, the BDMPS-Zakharov formalism and the AMY formalism (the latter used only for infinite, uniform media), can be made equivalent when appropriately formulated. (ii) A standard technique to simplify calculations is to expand in inverse powers of logarithms $\ln(E/T)$. I give an example where such expansions are found to work well for $ω/T \gtrsim 10$ where …
We calculate the evolution of a jet shower due to medium induced splittings in the deep LPM regime. Due to the characteristic energy dependence of the formation time $t_{\rm form}(ω)= \sqrt{ω/\hat{\bar{q}}}$, the radiative break-up process exhibits turbulent characteristics, allowing for analytic predictions of various inclusive properties of the medium induced cascade in an inertial range of energies $T \ll ω\ll E$, where $E$ is the energy of the jet and $T$ is the temperature of the medium.
The transverse momentum broadening coefficient $\hat{q}$ receives both soft, classical and radiative, quantum corrections. The former are responsible for a large O(g) correction, whereas the latter enter at relative order $α_s$, but are enhanced by a double logarithm of the length of the medium over the thermal wavelength. We analyze radiative corrections for a weakly-coupled quark-gluon plasma. We find that a thermal population of dynamical gluons changes the boundaries and reduces the size of the double-logarithmic phase space. It also provides new subdominant logarithmic corrections. We als…
Minijet thermalization and jet transport coefficients in QCD kinetic theory
SUBATECH UMR 6457 (IMT Atlantique, Université de Nantes, IN2P3/CNRS)（SUBATECH UMR 6457（IMT大西洋学院，南特大学，IN2P3/法国国家科学研究中心））；Institute of Theoretical Physics, TU Wien（维也纳工业大学理论物理研究所）；MIT Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Institute for Theoretical Physics, University of Heidelberg（海德堡大学理论物理研究所）
In the framework of Soft-Collinear Effective Theory, the jet quenching parameter, $\hat{q}$, has been evaluated by adding the effect of Glauber gluon interactions to the propagation of a highly-energetic collinear parton in a medium. The result, which holds in covariant gauges, has been expressed in terms of the expectation value of two Wilson lines stretching along the direction of the four-momentum of the parton. In this paper, we show how that expression can be generalized to an arbitrary gauge by the addition of transverse Wilson lines. The transverse Wilson lines are explicitly computed b…
We develop a new heavy quark transport model, QLBT, to simulate the dynamical propagation of heavy quarks inside the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. Our QLBT model is based on the linear Boltzmann transport (LBT) model with the ideal QGP replaced by a collection of quasi-particles to account for the non-perturbative interactions among quarks and gluons of the hot QGP. The thermal masses of quasi-particles are fitted to the equation of state from lattice QCD simulations using the Bayesian statistical analysis method. Combining QLBT with our advanced hybrid…
The high-energy behavior of tree-level scattering in finite-temperature QCD: estimates of theoretical systematic uncertainty in jet-medium Monte Carlo simulations
Department of Physics, University of Regina（里贾纳大学物理系）
We investigate the jet-quenching parameter $\hat{q}$ for the quark-gluon plasma (QGP) for $N_c=3$, defined nonperturbatively with the Wilson loop in the light-cone (LC) coordinate, at finite temperature $(T)$. Considering the effective static (heavy) quark-antiquark potential $V_{\bar{Q}Q}=σL+C-A/L$, where $L$ indicates the LC transverse separation between the quarks, we obtain $\hat{q}\approx8V_{\bar{Q}Q}/L^2$. The $T$ dependences for $L$ and other relevant parameters are extracted from the $T$-dependent instanton (trivial-holonomy caloron) length parameters and the lattice QCD data. By choos…
We give details of our study of whether high-energy gluon showers inside a QCD medium can be treated as a sequence of individual splitting processes $g \to gg$, or whether there is significant quantum overlap between where one splitting ends and the next begins (neglecting effects that can be absorbed into an effective value of the jet quenching parameter $\hat q$ that characterizes the medium). The study is carried out by imagining in-medium gluon shower development in the simplest theoretical situation, which includes imagining a very large, static, homogeneous medium and taking the large $N…
A bottom-up Einstein-Maxwell-Dilaton holographic model is used to compute, for the first time, the behavior of several transport coefficients of the hot and baryon-rich strongly coupled quark-gluon plasma at the critical point and also across the first-order phase transition line in the phase diagram. The observables under study are of the shear and bulk viscosities, baryon diffusion, thermal conductivity, the jet quenching parameter $\hat{q}$, as well as the heavy-quark drag force and Langevin diffusion coefficients. These calculations provide a phenomenologically promising estimate for these…
We study the phenomenon of transverse momentum broadening for a high-$p_T$ parton propagating through a weakly-coupled quark-gluon plasma undergoing boost-invariant longitudinal expansion. We propose a boost-invariant description for this phenomenon, in which the broadening refers to the angular variables $η$ (the pseudo-rapidity) and $ϕ$ (the azimuthal angle). The jet quenching parameter $\hat{q}$ which enters this description depends upon the proper time alone. We furthermore consider radiative corrections to $\hat q$. As in the case of a static medium, we find potentially large corrections …
Nuclei colliding at very high energy create a strong, quasi-classical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromo-electric and chromo-magnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. For exa…
The interplay of magnetic field and thermal vorticity in a relativistic ideal fluid might generate fluid vorticity during the fluid evolution provided the flow fields and the entropy density of the fluid is inhomogeneous \cite{Mahajan:2010}. Exploiting this fact and assuming large magnetic Reynolds number we study the evolution of generalised magnetic field ($\hat{B}$) which is defined as a combination of the usual magnetic field ($\vec{B}$) and relativistic thermal vorticity ($ω^{μν}$), in a 2(space)+1(time) dimensional isentropic evolution of Quark Gluon Plasma (QGP) with longitudinal boost …
We study the gluon cascade generated via successive medium-induced branchings by an energetic parton propagating through a dense QCD medium. We focus on the high-energy regime where the energy $E$ of the leading particle is much larger than the characteristic medium scale $ω_c=\hat q L^2/2$, with $\hat q$ the jet quenching parameter and $L$ the distance travelled through the medium. In this regime the leading particle loses only a small fraction $\simα_s(ω_c/E)$ of its energy and can be treated as a steady source of radiation for gluons with energies $ω\leω_c$. For this effective problem with …
Recent progress in open-heavy-flavor measurements and future experimental upgrades are bringing heavy-flavor physics into the precision era, allowing for strong quantitative constraints on the transport properties of heavy quarks in the quark-gluon plasma. Starting from the LIDO transport model, which combines a matrix-element based linearized-Boltzmann transport and diffusion-based Langevin equation, we have made two essential improvements to increase both the flexibility and physical accuracy of the model. First, we have absorbed the pQCD scatterings with small momentum transfers to the medi…
Using the CUJET3=DGLV+VISHNU jet-medium interaction framework, we show that dijet azimuthal acoplanarity in high energy $A+A$ collisions is sensitive to possible non-perturbative enhancement of the jet transport coefficient, $\hat{q}(T,E)$, in the QCD crossover temperature $T\sim 150-300$ MeV range. With jet-medium couplings constrained by global RHIC\& LHC $χ^2$ fits to nuclear modification data on $R_{AA}$, we compare predictions of the medium induced dijet transverse momentum squared, $Q_s^2\sim \langle \hat{q} L \rangle \sim Δϕ^2 E^2$, in two models of the temperature, $T$, and jet energy …
We derive the generalized Boltzmann equation (GBE) near equilibrium from the Kadanoff-Baym equation for quark excitation with ultrasoft momentum (~g^2T, g: coupling constant, T: temperature) in quantum chromodynamics (QCD) at extremely high T, and show that the equation is equivalent to the self-consistent equation derived in the resummed perturbation scheme used to analyze the quark propagator. We obtain the expressions of the dispersion relation, the damping rate, and the strength of a quark excitation with ultrasoft momentum by solving the GBE. We also show that the GBE enables us to obtain…
We use Soft Collinear Effective Theory (SCET) to analyze the transverse momentum broadening, or diffusion in transverse momentum space, of an energetic parton propagating through quark-gluon plasma. Since we neglect the radiation of gluons from the energetic parton, we can only discuss momentum broadening, not parton energy loss. The interaction responsible for momentum broadening in the absence of radiation is that between the energetic (collinear) parton and the Glauber modes of the gluon fields in the medium. We derive the effective Lagrangian for this interaction, and we show that the prob…
In relativistic heavy ion collisions, a highly occupied gluonic matter is created shortly after initial impact, which is in a non-thermal state and often referred to as the Glasma. Successful phenomenology suggests that the glasma evolves rather quickly toward the thermal quark-gluon plasma and a hydrodynamic behavior emerges at very early time $\sim \hat{o}(1)$ fm/c. Exactly how such "apparent thermalization" occurs and connects the initial conditions to the hydrodynamic onset, remains a significant challenge for theory as well as phenomenology. We briefly review various ideas and recent prog…
We calculate P(k_\perp), the probability distribution for an energetic parton that propagates for a distance L through a medium without radiating to pick up transverse momentum k_\perp, for a medium consisting of weakly coupled quark-gluon plasma. We use full or HTL self-energies in appropriate regimes, resumming each in order to find the leading large-L behavior. The jet quenching parameter \hat q is the second moment of P(k_\perp), and we compare our results to other determinations of this quantity in the literature, although we emphasize the importance of looking at P(k_\perp) in its entire…
Consider a high-energy parton showering as it traverses a QCD medium such as a quark-gluon plasma. Interference effects between successive splittings in the shower are potentially very important but have so far been calculated (even in idealized theoretical situations) only in soft emission or large-$N_{\rm c}$ limits, where $N_{\rm c}$ is the number of quark colors. In this paper, we show how one may remove the assumption of large $N_{\rm c}$ and so begin investigation of $N_{\rm c}{=}3$ without soft-emission approximations. Treating finite $N_{\rm c}$ requires (i) classifying different ways …
