High Energy Partons Research Articles

Jet thermalization in QCD kinetic theory

We perform numerical studies in the framework of QCD kinetic theory to investigate the energy and angular profiles of a high energy parton — as a proxy for a jet produced in heavy ion collisions — passing through a Quark-Gluon Plasma (QGP). We find that the fast parton loses energy to the plasma mainly via a radiative turbulent quark and gluon cascade that transports energy locally from the jet down to the temperature scale where dissipation takes place. In this first stage of the system time evolution, the angular structure of the turbulent cascade is found to be relatively collimated. However, when the lost energy reaches the plasma temperature it is rapidly transported to large angles w.r.t. the jet axis and thermalizes. We investigate the contribution of the soft jet constituents to the total jet energy. We show that for jet opening angles of about 0.3 rad or smaller, the effect is negligible. Conversely, larger opening angles become more and more sensitive to the thermal component of the jet and thus to medium response. Our result showcases the importance of the jet cone size in mitigating or enhancing the details of dissipation in jet quenching observables.

Several Topics on Transverse Momentum-Dependent Fragmentation Functions

The hadronization of a high-energy parton is described by fragmentation functions which are introduced through QCD factorizations. While the hadronization mechanism per se remains uknown, fragmentation functions can still be investigated qualitatively and quantitatively. The qualitative study mainly concentrates on extracting genuine features based on the operator definition in quantum field theory. The quantitative research focuses on describing a variety of experimental data employing the fragmentation function given by the parameterizations or model calculations. With the foundation of the transverse-momentum-dependent factorization, the QCD evolution of leading twist transverse-momentum-dependent fragmentation functions has also been established. In addition, the universality of fragmentation functions has been proven, albeit model-dependently, so that it is possible to perform a global analysis of experimental data in different high-energy reactions. The collective efforts may eventually reveal important information hidden in the shadow of nonperturbative physics. This review covers the following topics: transverse-momentum-dependent factorization and the corresponding QCD evolution, spin-dependent fragmentation functions at leading and higher twists, several experimental measurements and corresponding phenomenological studies, and some model calculations.

The LPM effect in sequential bremsstrahlung: 1/ {mathrm{N}}_{mathrm{c}}^2 corrections

An important question concerning in-medium high-energy parton showers in a quark-gluon plasma or other QCD medium is whether consecutive splittings of the partons in a given shower can be treated as quantum mechanically independent, or whether the formation times for two consecutive splittings instead have significant overlap. Various previous calculations of the effect of overlapping formation times have either (i) restricted attention to a soft bremsstrahlung limit, or else (ii) used the large-Nc limit (where Nc = 3 is the number of quark colors). In this paper, we make a first study of the accuracy of the large-Nc limit used by those calculations of overlap effects that avoid a soft bremsstrahlung approximation. Specifically, we calculate the 1/ {N}_{mathrm{c}}^2 correction to previous Nc = ∞ results for overlap g → gg → ggg of two consecutive gluon splittings g → gg. At order 1/ {N}_{mathrm{c}}^2 , there is interesting and non-trivial color dynamics that must be accounted for during the overlap of the formation times.

Hard gluon evolution in the last stage of the bottom-up thermalization

The study of how fast thermalization in heavy ion collisions occurs has been one of the central topics in the heavy ion community. In the weak coupling picture this thermalization occurs from ‘the bottom up’: high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. In this scheme we apply a model on parton energy loss to discuss the effects of medium expansion on the thermalization problem and estimate the average transverse momentum diffusivity for thermalization in a Bjorken expanding medium.

Hard gluon evolution in warming medium

We describe the energy distribution of hard gluons travelling through a dense quark–gluon plasma whose temperature increases linearly with time, within a probabilistic perturbative approach. The results were applied to the thermalization problem in heavy ion collisions. In the weak coupling picture this thermalization occurs from “the bottom up”: high energy partons, formed early in the collision, radiate low energy gluons which then proceed to equilibrate among themselves, forming a thermal bath that brings the high energy sector to equilibrium. We see that, in this scenario, the dynamic we describe must set in around t sim 0.5 fm/c after the collision in order to reach a fully thermalized state at t sim 1 fm/c. We then look at the entropy density and average temperature of the soft thermal bath, as the system approaches (local) thermal equilibrium.

The Problem of overlapping formation times: In-medium virtual corrections for QCD

High energy particles traversing through medium primarily lose energy by showering through hard bremsstrahlung and pair production. These splitting processes are coherent over large distances in the very high energy limit, leading to suppression from the Landau-Pomeranchuk-Migdal (LPM) effect. Avoiding soft-emission approximations, we study the cases where the coherence lengths of two consecutive splittings overlap (which is important for calculating corrections to LPM effect in QCD). In this work, we will show how to compute in-medium virtual corrections to the leading order LPM emission rates for QCD. These loop corrections will be necessary for calculating properties of in-medium high energy parton showers. To simplify the calculations, we will focus on the all-gluon case and work in the large-Nc limit of QCD, where Nc is the number of colors.

Anisotropic momentum broadening in the 2+1D glasma: Analytic weak field approximation and lattice simulations

In heavy ion collisions, transverse momentum broadening quantifies the modification of a hard probe due to interactions with the quark-gluon plasma (QGP). We calculate momentum broadening in the Glasma, which is the highly non-isotropic precursor stage of the QGP right after the collision. We show that the Glasma leads to anisotropic momentum broadening: high energy partons accumulate more momentum along the beam axis than transverse to it. The physical origin of anisotropic broadening can be traced back to differences in the shapes of chromo-electric and chromo-magnetic flux tubes in the Glasma. We provide semi-analytic results for momentum broadening in the dilute Glasma and numerical results from real-time lattice simulations of the non-perturbative dense Glasma.

Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large- N QCD to N=3 via the SU(N) analog of Wigner 6‐j symbols

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 that four gluons can form a color singlet and (ii) calculating medium-induced transitions between those singlets, for which we find application of results for the generalization of Wigner 6-$j$ symbols from angular momentum to SU($N_{\rm c}$). Throughout, we make use of the multiple scattering ($\hat q$) approximation for high-energy partons crossing quark-gluon plasmas, and we find that this approximation is self-consistent only if the transverse-momentum diffusion parameter $\hat q$ for different color representations satisfies Casimir scaling (even for strongly-coupled, and not just weakly-coupled, quark-gluon plasmas). We also find that results for $N_{\rm c}{=}3$ depend, mathematically, on being able to calculate the propagator for a coupled non-relativistic quantum harmonic oscillator problem in which the spring constants are operators acting on a 5-dimensional Hilbert space of internal color states. Those spring constants are represented by constant $5{\times}5$ matrices, which we explicitly construct. We are unaware of any closed form solution for this type of harmonic oscillator problem, and we discuss prospects for using numerical evaluation.

Strong- vs. weak-coupling pictures of jet quenching: a dry run using QED

High-energy partons (E ≫ T ) traveling through a quark-gluon plasma lose energy by splitting via bremsstrahlung and pair production. Regardless of whether or not the quark-gluon plasma itself is strongly coupled, an important question lying at the heart of philosophically different approaches to energy loss is whether the high-energy partons of an in-medium shower can be thought of as a collection of individual particles, or whether their coupling to each other is also so strong that a description as high-energy “particles” is inappropriate. We discuss some possible theorists’ tests of this question for simple situations (e.g. an infinite, non-expanding plasma) using thought experiments and first-principles quantum field theory calculations (with some simplifying approximations). The physics of in-medium showers is substantially affected by the Landau-Pomeranchuk-Midgal (LPM) effect, and our proposed tests require use of what might be called “next-to-leading order” LPM results, which account for quantum interference between consecutive splittings. The complete set of such results is not yet available for QCD but is already available for the theory of large-Nf QED. We therefore use large-Nf QED as an example, presenting numerical results as a function of Nfα, where α is the strength of the coupling at the relevant high-energy scale characterizing splittings of the high-energy particles.

In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers

The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-emission approximations. In this particular paper, we show (i) how the “instantaneous” interactions of Light-Cone Perturbation Theory must be included in the calculation to account for effects of longitudinally-polarized gauge bosons in intermediate states, and (ii) how to compute virtual corrections to LPM emission rates, which will be necessary in order to make infrared-safe calculations of the characteristics of in-medium QCD showering of high-energy partons. In order to develop these topics in as simple a context as possible, we will focus in the current paper not on QCD but on large-Nf QED, where Nf is the number of electron flavors.

Neutral meson production and correlation with charged hadrons in pp and Pb-Pb collisions with the ALICE experiment at the LHC

Among the probes used to investigate the properties of the Quark-Gluon Plasma, the measurement of the energy loss of high-energy partons can be used to put constraints on energy-loss models and to ultimately access medium characteristics, such as the energy density or the temperature. The study of two-particle correlations allows us to obtain very different constraints compared to the nuclear modification factor. In particular, the correlation of charged hadrons with high energy π0 or direct photons is believed to give a measurement of the parton energy loss and insights into the medium-induced modification of the fragmentation process. High energy neutral pions are reconstructed using the ALICE electromagnetic calorimeters EMCal and PHOS, and the charged particles are detected by the main tracking detectors ITS and TPC. In these proceedings, the measurement of neutral mesons at s=2.76TeV in pp collisions are presented, as well as the measurements of azimuthal π0-hadron correlations in pp and Pb-Pb collisions at s=2.76TeV, and the extracted per-trigger yield modification factor (IAA). Comparisons with theoretical model calculations are also added.

Neutral meson production in pp, p–Pb and Pb–Pb collisions with ALICE at the LHC

The ALICE experiment is mainly devoted to the study of QGP expected to be created in heavy-ion collisions at the LHC. In the early stage of such collisions, partons can be scattered and photons can be produced in energetic hard processes. High energy partons will interact with the QGP, and from the measurement of the particles originated from the parton fragmentation in vacuum, one can infer transport properties of the QGP. Therefore, study of high-pT hadrons production is important to constrain the properties of the hot and dense medium. The strong suppression of the high-pT hadrons in heavy-ion collisions has been explained by the energy loss of the partons in medium and it can be investigated experimentally via the nuclear modification factor of hadrons.ALICE measured neutral mesons (π0 and η) at mid-rapidity in a wide pT range in pp, p-Pb and Pb-Pb collisions. Neutral mesons are reconstructed via complementary methods, using the electromagnetic calorimeters, PHOS and EMCal, and by the central tracking system, identifying photons converted to e+e− pairs in the material of the inner barrel detectors (ITS and TPC). Measurement of neutral meson spectra in pp collisions at s=0.9,2.76,7 and 8 TeV provides valuable comparison data for pQCD calculations and allows to study scaling properties of hadron production at the LHC energies. The study of neutral mesons production in p-Pb collisions helps to disentangle initial and final state effects on the suppression itself. The latest results of neutral meson measurement in pp, p-Pb and Pb-Pb collisions will be shown in this paper.

Jets in heavy ion collisions

High energy collisions of heavy nuclei permit the study of nuclear matter at temperatures and energy densities so high that the fundamental theory for strong interactions, QCD, predicts a phase transition to a plasma of quarks and gluons. This matter, called a Quark Gluon Plasma (QGP), has been studied experimentally for the last decade and has been observed to be a strongly interacting liquid with a low viscosity. High energy partons created early in the collision interact with the QGP and provide unique probes of its properties. Hard partons fragment into collimated sprays of particles called jets and have been studied through measurements of single particles, correlations between particles, and measurements of fully reconstructed jets. These measurements demonstrate partonic energy loss in the QGP and constrain the QGP’s properties. Measurements of the jet structure give insight into the mechanism of this energy loss. The information we have learned from studies of jets and challenges for the field will be reviewed.

Experiment summary

The measurement of the production of particles coming from hard scattering processes covers a fundamental role in the characterization of the system formed in heavy-ion collisions, allowing to probe the microscopic processes underlying the interaction of high energy partons with the medium. An impressive amount of measurements related to jet, quarkonia, open heavy flavor, and electroweak signal production in nucleus-nucleus as well as p(d)-nucleus collisions was delivered by experiments at RHIC and LHC in past years. In these proceedings, the main experimental results presented during the Hard Probes conference are summarized.

Radiative energy loss and radiative p⊥-broadening of high-energy partons in QCD matter

I give a self-contained review on radiative p⊥-broadening and radiative energy loss of high-energy partons in QCD matter. The typical p⊥2 of high-energy partons receives a double logarithmic correction due to the recoiling effect of medium-induced gluon radiation. Such a double logarithmic term, averaged over the path length of the partons, can be taken as the radiative correction to the jet quenching parameter qˆ and hence contributes to radiative energy loss. This has also been confirmed by detailed calculations of energy loss by radiating two gluons.

Jet measurements by ALICE at LHC

Jets are collimated sprays of particles originating from fragmentation of high energy partons produced in a hard collision. They are an important diagnostic tool in studies of the Quark Gluon Plasma (QGP). The modification of the jet fragmentation pattern and its structure is a signature for the influence of hot and dense matter on the parton fragmentation process. Jet measurements in proton-proton collisions provide a baseline for similar measurements in heavy-ion collisions, while studies in proton-nucleus system allow to estimate cold nuclear matter effects. Here we present jet studies in different colliding systems (p–p, p–Pb, Pb–Pb) performed by the ALICE collaboration at LHC energies. Results on jet spectra, cross sections, nuclear modification factors, jet structure and other kinematic observables will be presented.

Energy loss in unstable quark-gluon plasma

The momentum distribution of quark-gluon plasma at the early stage of a relativistic heavy-ion collision is anisotropic and consequently the system, which is assumed to be weakly coupled, is unstable due chromomagnetic plasma modes. We consider a high-energy parton which flies across such an unstable plasma, and the energy transfer between the parton and the medium is studied as an initial value problem. In the case of equilibrium plasmas, the well-known formula of collisional energy loss is reproduced. The unstable plasma case is much more complex, and the parton can lose or gain energy depending on the initial conditions. The extremely prolate and extremely oblate systems are considered as examples of unstable plasmas, and two classes of initial conditions are discussed. When the initial chromodynamic field is uncorrelated with the color state of the parton, it typically looses energy, and the magnitude of the energy loss is comparable to that in an equilibrium plasma of the same density. When the initial chromodynamic field is induced by the parton, it can be either accelerated or decelerated depending on the relative phase factor. With a correlated initial condition, the energy transfer grows exponentially in time and its magnitude can much exceed the absolute value of energy loss in an equilibrium plasma. The energy transfer is also strongly directionally dependent. Consequences of our findings for the phenomenology of jet quenching in relativistic heavy-ion collisions are briefly discussed.

Radiative energy loss and radiative p ⊥-broadening of high-energy partons in QCD matter

We study the connection between radiative energy loss and radiative p_T-broadening of a high-energy quark or gluon passing through QCD matter. The generalized Baier-Dokshitzer-Mueller-Peigne-Schiff-Zakharov (BDMPS-Z) formalism is used to calculate energy loss due to multiple gluon emission. With L the length of the matter and l_0 the size of constituents of the matter we find a double logarithmic correction proportional to ln^2(L/l_0) to parton energy loss due to two-gluon emission. We also show that the radiative energy loss per unit length -dE/dz = alpha_s N_c < p_T^2 >/12 by carrying out a resummation of the double logarithmic terms. Here, the transverse momentum broadening <p_T^2> is obtained by resumming terms proportional to alpha_s ln^2(L/l_0) in Ref. [11]. Our result agrees with that by the renormalization of qhat proposed in Refs. [13,14].

Momentum transport away from a jet in an expanding nuclear medium

We study the transport dynamics of momenta deposited from jets in ultrarelativistic heavy-ion collisions. Assuming that the high-energy partons traverse expanding quark-gluon fluids and are subject to lose their energy and momentum, we simulate dijet asymmetric events by solving relativistic hydrodynamic equations numerically without linearization in the fully (3+1)-dimensional coordinate. Mach cones are formed and strongly broadened by radial flow of the background medium. As a result, the yield of low-$p_{T}$ particles increases at large angles from the jet axis and compensates the dijet momentum imbalance inside the jet-cone. This provides an intimate link between the medium excitation by jets and results in dijet asymmetric events observed by the CMS Collaboration.

Lattice study of the jet quenching parameter.

We present a first-principle computation of the jet quenching parameter, which describes the momentum broadening of a high-energy parton moving through the deconfined state of QCD matter at high temperature. Following an idea originally proposed by Caron-Huot, we explain how one can evaluate the soft contribution to the collision kernel characterizing this real-time phenomenon, analyzing certain gauge-invariant operators in a dimensionally reduced effective theory (electrostatic QCD), which can be studied nonperturbatively via simulations on a Euclidean lattice. Our high-precision numerical computations at two different temperatures indicate that soft contributions to the jet quenching parameter are large. After discussing the systematic uncertainties involved, we present a quantitative estimate for the jet quenching parameter in the temperature range accessible at heavy-ion colliders, and compare it to results from phenomenological models as well as to strong-coupling computations based on the holographic correspondence.