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Visualizing How the Structure of Large-Radius Jets Shapes Their Wakes

The ATLAS collaboration has introduced and implemented a strategy for selecting and analyzing large-radius jets composed of skinny $R=0.2$ subjets in heavy ion collisions at the LHC. We show how measurements of these jets teach us about the resolution length $L_{\rm res}$ of quark-gluon plasma (QGP) and can teach us how jet substructure shapes the wakes that jets excite in the QGP droplets through which they pass. We use Hybrid Model calculations to reproduce measurements of $R_{AA}$ for large-radius jets in PbPb collisions, and study their dependence on the angle between the two skinny subjets involved in the final reclustering step of an $R=1$ jet. We show how these observables can constrain the value of $L_{\rm res}$ and demonstrate that the ATLAS data rule out any picture in which an entire parton shower loses energy coherently as if it were a single entity. Determining the degree to which the QGP can resolve partons within a jet is central to the broader program of using jet quenching measurements to probe QGP. We make further use of this setup by analyzing the response of the medium to the passage of large-radius $R=2$ jets containing two skinny subjets in gamma-jet events. We introduce novel jet-shape observables that allow us to visualize the angular shape of the soft hadrons originating from the wakes that wide jets with two skinny subjets excite in a droplet of QGP, as a function of the angular separation between the subjets. We find that even when they are $\sim 0.8- 1$ radian apart, a single broad wake is produced. Only when the two subjets are even farther apart is the presence of two sub-wakes revealed. We show that the way in which jet structure shapes jet wakes can be visualized with similar clarity in experiments by using only those hadrons with low $p_T$. These observables thus offer a new and distinctive way of seeing jet wakes in heavy ion collision data.

FOS: Physical sciences

Overview of high-density QCD studies with the CMS experiment at the LHC

We review key measurements performed by CMS in the context of its heavy ion physics program, using event samples collected in 2010-2018 with several collision systems and energies. These studies provide detailed macroscopic and microscopic probes of the quark-gluon plasma (QGP) created at the LHC energies, a medium characterized by the highest temperature and smallest baryon-chemical potential ever reached in the laboratory. Numerous observables related to high-density quantum chromodynamics (QCD) were studied, leading to some of the most impactful and qualitatively novel results in the 40-year history of the field. Using a dedicated high-multiplicity trigger in the first pp run, CMS discovered that small collision systems can exhibit signs of collectivity, a generic phenomenon with significant implications and presently understood to affect essentially all soft physics processes. This observation opened new paths to understand how fluidity and plasma properties emerge in QCD matter as a function of system size. Measurements of jet quenching have reached a completely new level of detail by directly assessing, for the first time, the medium modification of parton showers, as opposed to simply observing leading hadrons or di-hadrons. The first fully reconstructed beauty hadron and heavy-flavor jet nuclear modifications were also measured. The large size of the event samples, the precision of the measurements, and the extension of the probed kinematical phase space, allowed many other hard probes of the QGP medium to be explored in detail, leading to multiple groundbreaking findings. In particular, the seminal measurements of bottomonium suppression patterns answer fundamental questions that have been actively pursued, both theoretically and experimentally, by the community since the mid-1980s. We conclude by outlining the opportunities offered by the continuation of this physics program at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Search for medium effects using jet axis decorrelation in inclusive jets from PbPb collisions at $\sqrt{{s}_{\text{NN}}}$ = 5.02 TeV

The jet axis decorrelation in inclusive jets is studied using lead-lead (PbPb) collisions at a center-of-mass energy per nucleon pair of 5.02 TeV. The jet axis decorrelation is defined as the angular difference between two definitions of the jet axis. It is obtained by applying two recombination schemes on all the constituents of a given jet reconstructed by the anti-kT sequential algorithm with a distance parameter of R = 0.4. The data set, corresponding to an integrated luminosity of 0.66 nb −1 , was collected in 2018 with the CMS detector at the CERN LHC. The jet axis decorrelations are examined across collision centrality selections and intervals of jet transverse momentum. A centrality dependent evolution of the measured distributions is observed, with a progressive narrowing seen in more central events. This narrowing could result from medium-induced modification of the internal jet structure or reflect color charge effects in energy loss. This new measurement probes jet substructure in previously unexplored kinematic domains and show great promise for providing new insights on the color charge dependence of energy loss to jet-quenching models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Dynamics of heavy quarks in strongly coupled $\mathcal{N}$ = 4 SYM plasma

We calculate the probability distribution P(k) for a heavy quark with velocity v propagating through strongly coupled N = 4 SYM plasma in the ’t Hooft limit (N c → ∞, λ = g 2 N c → ∞) at a temperature T to acquire a momentum k due to interactions with the plasma. This distribution encodes the well-known drag coefficient η D and the transverse and longitudinal momentum diffusion coefficients κ T and κ L . The jet quenching parameter $\hat{q}$ can be extracted from P(k) for v = 1. Going beyond these known Gaussian characteristics of P(k), our calculation determines all of the higher order and mixed moments to leading order in 1/$\sqrt{λ}$ for the first time. These non-Gaussian features of P(k) include qualitatively novel correlations between longitudinal energy loss and transverse momentum broadening at nonzero v. We show that all higher moments scale characteristically with an effective temperature of the boosted plasma in the heavy quark rest frame, and we demonstrate that these non-Gaussian characteristics can be sizable in magnitude and even dominant in physically relevant situations. We use these results to derive a Kolmogorov equation for the evolution of the probability distribution for the total momentum of a heavy quark that propagates through strongly coupled plasma. This evolution equation accounts for all higher order correlations between transverse momentum broadening and longitudinal energy loss, which we have calculated from first principles. It reduces to a Fokker-Planck equation when truncated to only include the effects of η D , κ T and κ L . Remarkably, while heavy quarks do not reach kinetic equilibrium with the plasma if evolved with this Fokker-Planck equation, by showing that the Boltzmann distribution is a static solution of the all-order Kolmogorov equation that we have derived we demonstrate that heavy quarks do reach kinetic equilibrium if evolved with this equation. Our results thus provide a dynamically complete framework for understanding the thermalization of a heavy quark that may be initially far from equilibrium in the strongly coupled N = 4 SYM plasma — as well as new insight into heavy quark transport and equilibration in quark-gluon plasma.

Holography and Hydrodynamics

Evidence of medium response to hard probes using correlations of Z bosons with hadrons in heavy ion collisions

The first measurement of pseudorapidity and azimuthal angle distributions relative to the momentum vector of a Z boson for low transverse momentum ($p_\mathrm{T}$) charged hadrons in lead-lead (PbPb) collisions is presented. By studying the hadrons produced in an event with a high-$p_\mathrm{T}$ Z boson (40 $\lt$ $p_\mathrm{T}$ $\lt$ 350 GeV), the analysis probes how the quark-gluon plasma (QGP) medium created in these collisions affects the parton recoiling opposite to the Z boson. Utilizing PbPb data at a nucleon-nucleon center-of-mass energy $\sqrt{s_{_\mathrm{NN}}}$ = 5.02 TeV from 2018 with an integrated luminosity of 1.67 nb$^{-1}$ and proton-proton (pp) data at the same energy from 2017 with 301 pb$^{-1}$, the distributions are examined in bins of charged-hadron $p_\mathrm{T}$. A significant modification of the distributions for charged hadrons in the range 1 $\lt$ $p_\mathrm{T}$ $\lt$ 2 GeV in PbPb collisions is observed when compared to reference measurements from pp collisions. The data provide new information about the correlation between hard and soft particles in heavy ion collisions, which can be used to test predictions of various jet quenching models. The results are consistent with expectations of a hydrodynamic wake created when the QGP is depleted of energy by the parton propagating through it. Based on comparisons of PbPb data with pp references and predictions from theoretical models, this Letter presents the first evidence of medium-recoil and medium-hole effects caused by a hard probe.

CMS

Azimuthal anisotropies of charged particles with high transverse momentum in Pb + Pb collisions at $\sqrt{s_{\textrm{NN}}}$ = 5.02 TeV with the ATLAS detector

A measurement is presented of elliptic (𝑣 2 ) and triangular (𝑣 3 ) azimuthal anisotropy coefficients for charged particles produced in Pb + Pb collisions at $\sqrt{s_{\textrm{NN}}}$ = 5.02 TeV using a dataset corresponding to an integrated luminosity of 0.44nb −1 collected with the ATLAS detector at the LHC in 2018. The values of 𝑣 2 and 𝑣 3 are measured for charged particles over a wide range of transverse momentum (𝑝 T ), 1–400 GeV, and Pb + Pb collision centrality, 0–60%, using the scalar-product and multiparticle cumulant methods. These methods are sensitive to event-by-event fluctuations and nonflow effects in the measurements of azimuthal anisotropies. Positive values of 𝑣 2 are observed up to a 𝑝 T of approximately 100 GeV from both methods across all centrality intervals. Positive values of 𝑣 3 are observed up to approximately 25 GeV using both methods, though the application of the three-subevent technique to the multiparticle cumulant method leads to significant changes at the highest 𝑝 T . At high 𝑝 T (𝑝 T ⪆ 10 GeV), charged particles are dominantly from jet fragmentation. These jets, and hence the measurements presented here, are sensitive to the path-length dependence of parton energy loss in the quark-gluon plasma produced in Pb + Pb collisions.

Collective flow

Search for the jet-induced diffusion wake in the quark-gluon plasma via measurements of jet-track correlations in photon-jet events in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV with the ATLAS detector

This paper presents a measurement of jet-track correlations in photon-jet events, using 1.72 nb −1 of Pb+Pb data at $\sqrt{s_{NN}}$ = 5.02TeV recorded with the ATLAS detector at the LHC. Events with energetic photon-jet pairs are selected, where the photon and jet are approximately back-to-back in azimuth. The angular correlation between jets and charged-particle tracks with transverse momentum (𝑝 T ) in the range 0.5–2.0 GeV in the hemisphere opposite to the jet, |Δ⁢𝜙(jet,track)|>𝜋/2, is measured as a function of their relative pseudorapidity difference, |Δ⁢𝜂(jet,track)|. In central Pb+Pb collisions, these correlations are predicted to be sensitive to the diffusion wake in the quark-gluon plasma resulting from the lost energy of high-𝑝T partons traversing the plasma, with a characteristic modification as a function of |Δ⁢𝜂(jet,track)|. The correlations are examined with different selections on the jet-to-photon 𝑝 T ratio to select events with different degrees of energy loss. No diffusion wake signal is observed within the current sensitivity and upper limits at 95% confidence level on the diffusion wake amplitude are reported.

heavy flavor physics

Measurement of In-Medium Jet Modification Using Direct Photon + Jet and 𝜋 0 + Jet Correlations in 𝑝 + 𝑝 and Central Au + Au Collisions at $\sqrt{s_{NN}}$ = 200 GeV

The STAR Collaboration presents measurements of the semi-inclusive distribution of charged-particle jets recoiling from energetic direct-photon (𝛾 dir ) and neutral-pion (𝜋 0 ) triggers in 𝑝 + 𝑝 and central Au + Au collisions at $\sqrt{s_{NN}}$ =2 00 GeV over a broad kinematic range, for jet resolution parameters 𝑅 = 0.2 and 0.5. Medium-induced jet yield suppression is observed to be larger for 𝑅 = 0.2 than for 0.5, reflecting the angular range of jet energy redistribution due to quenching. The predictions of model calculations incorporating jet quenching are not fully consistent with the observations. Furthermore, these results provide new insight into the physical origins of jet quenching.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Constraining color-charge effects of partonic energy loss with jet-axis-based inclusive jet substructure measurement

This study investigates the color-charge dependence of parton energy loss in the quark-gluon plasma (QGP) medium and the associated relative modifications of quark and gluon jet fractions compared to vacuum, using jet axis decorrelation observables. Recent CMS jet axis decorrelation measurements in PbPb collisions at 5.02 TeV are interpreted using Pythia simulations with varied quark/gluon jet compositions and emulated color-charge dependent energy loss. A template-fit procedure is employed to estimate the limits on gluon jet fractions in the published CMS data and average shift in jet momentum due to quenching for quark- and gluon-initiated jets traversing the QGP. The extracted gluon jet fractions and the estimated quark and gluon energy losses based on this study of jet axis decorrelations are found to be consistent with other model calculations based on inclusive observables. This work illustrates the use of jet substructure measurements for providing constraints on the color-charge dependence of parton energy loss and offers valuable insights for jet quenching models.

jet quenching

Minimizing Selection Bias in Inclusive Jets in Heavy-Ion Collisions with Energy Correlators

The first-ever measurement of energy correlators within inclusive jets produced in heavy-ion collisions, revealed by the CMS Collaboration, shows a clear enhancement at large angles relative to the proton-proton (p-p) baseline. However, interpreting this enhancement is complicated due to selection bias from energy loss, which also distorts the energy correlator heavy-ion to p-p ratio in the hadronization region, hindering our understanding of parton/hadron dynamics in a colored medium. In this Letter, we introduce a new ratio of energy correlator observables that removes the leading effects of selection bias from the two-point energy correlator spectrum (E2C). PYTHIA and HERWIG simulations show that the impact of selection bias in the E2C is reduced by an order of magnitude, while sensitivity to any other medium modifications is retained. This quantity can be obtained directly from the experimental measurements presented by CMS, as illustrated in an accompanying note [C. Andres and J. Holguin, arXiv:2409.07526].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Probing cold nuclear matter with energy correlators

The future electron-ion collider (EIC) will produce the first-ever high energy collisions between electrons and a wide range of nuclei, opening a new era in the study of cold nuclear matter. Quarks and gluons produced in these collisions will propagate through the dense nuclear matter of nuclei, imprinting its structure into subtle correlations in the energy flux of final state hadrons. In this article, we apply recent developments from the field of jet substructure, namely the energy correlator observables, to decode these correlations and provide a new window into nuclear structure. The energy correlators provide a calibrated probe of the scale dependence of vacuum quantum chromodynamics (QCD), enabling medium modifications to be imaged and interpreted as a function of scale. Using the eHIJING parton shower to simulate electron-nucleus collisions, we demonstrate that the size of the nucleus is imprinted as an angular scale in the correlators, with a magnitude that is visible for realistic EIC kinematics. We can observe the size difference between the proposed EIC nuclear targets 3 He, 4 He, 12 C, 40 Ca, 64 Cu, 197 Au, and 238 U, showing that the energy correlators can image femtometer length scales using asymptotic energy flux. Our approach offers a unified view of jet substructure across collider experiments, and provides numerous new theoretical tools to unravel the complex dynamics of QCD in extreme environments, both hot and cold.

Electron-ion collisions

Jet cone radius dependence of R AA and v 2 at PbPb 5.02 TeV from JEWEL+T R ENTo+v-USPhydro

We combine, for the first time, event-by-event T R ENTo initial conditions with the relativistic viscous hydrodynamic model v-USPhydro and the Monte Carlo event generator JEWEL to make predictions for the nuclear modification factor R AA and jet azimuthal anisotropies v n { 2 } in $\sqrt{s_{NN}}$ = 5.02 TeV PbPb collisions for multiple centralities and values of the jet cone radius R. The R-dependence of R AA and v 2 { 2 } strongly depends on the presence of recoiling scattering centers. We find a small jet v 3 { 2 } in mid-central collisions and consistent results in wide jet p T regions and centralities with ATLAS data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

System-size dependence of charged-particle suppression in ultrarelativistic nucleus-nucleus collisions

High-energy partons lose energy while propagating through the hot, strongly interacting medium produced in ultrarelativistic nucleus-nucleus collisions, leading to a suppression of particle production at high transverse momentum (p T ). The dependence of this energy loss on the size of the colliding nuclear system has yet to be firmly established experimentally. This Letter presents a systematic study of charged-particle suppression across four different nucleus-nucleus collision systems using nuclear modification factors (R AA ) measured by the CMS Collaboration at the CERN LHC. Previous CMS measurements of R AA in oxygen-oxygen, xenon-xenon, and lead-lead collisions are recast with identical p T intervals and are complemented by the first measurement of the charged-particle R AA in neon-neon collisions at $\sqrt{S_{NN}}$ = 5.36 Te V . The neon-neon data correspond to an integrated luminosity of 0.76 nb −1 . The R AA in all collision systems examined show similar qualitative trends as a function of p T , but have a magnitude which is ordered with the nucleon number A. The R AA feature a downward slope at low p T , a local minimum at around 5–7 Ge V , and an upward slope with increasing p T . The R AA are also compared in terms of A 1/3 , which is proportional to the nuclear radius. Models including only initial-state nuclear effects fail to reproduce the observed trends, whereas energy loss models reproduce the trends in the region p T > 9.6 Ge V .

CMS

Fiber Sorbents – A Versatile Platform for Sorption-Based Gas Separations

Increasing demand for high-purity fine chemicals and a drive for process intensification of large-scale separations have driven significant work on the development of highly engineered porous materials with promise for sorption-based separations. While sorptive separations in porous materials offer energy-efficient alternatives to longstanding thermal-based methods, the particulate nature of many of these sorbents has sometimes limited their large-scale deployment in high-throughput applications such as gas separations, for which the necessary high feed flow rates and gas velocities accrue prohibitive operational costs. These processability limitations have been historically addressed through powder shaping methods aimed at the fabrication of structured sorbent contactors based on pellets, beads or monoliths, commonly obtained as extrudates. These structures overcome limitations such as elevated pressure drops commonly recorded across powder adsorption beds but often accrue thermal limitations arising from elevated particle density and aggregation, which ultimately cap their maximum separation performance. Furthermore, the harsh mechanical strain to which powder particles are subjected during contactor fabrication, in the form of extrusion/compression forces, can result in partial pore occlusion and framework degradation, further limiting their performance. Here, we present the development of porous fiber sorbents as an alternative sorbent contactor design capable of addressing sorbent processability limitations while enabling an array of performance-maximizing heat integration capabilities. This new sorbent form factor leverages pre-existing know-how from hollow fiber spinning to produce fiber-shaped sorbent contactors through the phase inversion of known polymers in a process known as dry-jet/wet quenching. The process of phase inversion allows microporous sorbent particles to be latched onto a macroporous polymer matrix under mild processing conditions, thus making it compatible with soft porous materials prone to amorphization under traditional pelletization conditions. Sorbent fibers can be created with different geometries through control of the spinning apparatus and process, offering the possibility to produce monolithic and hollow fibers alike, the latter of which can be integrated with thermalization fluid flows. In this Account, we summarize our progress in the field of fiber sorbents from both design and application standpoints. We further guide the reader through the evolution of this field from the early inceptive work on zeolite hollow fibers to recent developments on MOF fibers. We highlight the versatile nature of fiber sorbents, both from the composition, fabrication and structure points of view, and further demonstrate how fiber sorbents offer alternative paths in tackling new and challenging chemical separation challenges like direct air capture (DAC), with a final perspective on the future of the field.

36 MATERIALS SCIENCE

Observation of Suppressed Charged-Particle Production in Ultrarelativistic Oxygen-Oxygen Collisions

A hot and dense state of nuclear matter, known as the quark-gluon plasma, is created in collisions of ultrarelativistic heavy nuclei. Highly energetic quarks and gluons, collectively referred to as partons, lose energy as they travel through this matter, leading to suppressed production of particles with large transverse momenta (𝑝 T ). Conversely, high-𝑝 T particle suppression has not been seen in proton-lead collisions, raising questions regarding the minimum system size required to observe parton energy loss. Oxygen-oxygen (OO) collisions examine a region of effective system size that lies between these two extreme cases. The CMS detector at the CERN LHC has been used to quantify charged-particle production in inclusive OO collisions for the first time via measurements of the nuclear modification factor (𝑅 AA ). The 𝑅 AA is derived by comparing particle production to expectations based on proton-proton (𝑝⁢𝑝) data and has a value of unity in the absence of nuclear effects. The data for OO and 𝑝⁢𝑝 collisions at a nucleon-nucleon center-of-mass energy $\sqrt{s_{NN}}$ = 5.36 TeV correspond to integrated luminosities of 6.1 nb −1 and 1.02 pb −1 , respectively. The 𝑅 AA is below unity with a minimum of 0.69 ± 0.04 around 𝑝 T = 6 GeV. The data exhibit better agreement with theoretical models incorporating parton energy loss as compared to baseline models without energy loss.

FOS: Physical sciences

Modified coherence and the transverse extent of jets

We present a study of the transverse size of parton showers and their diminishing interaction with the medium in the high virtuality stage of jet evolution. We consider the process of a hard quark produced in deep inelastic scattering off a large nucleus. Single gluon radiation from this quark, in the absence of scattering, is rederived using wave packets. This allows for a derivation of the quantum uncertainty size of the hard quark, at the point of splitting. This uncertainty size is then incorporated within a Monte Carlo shower routine yielding transverse shower sizes noticeably larger than the classical antenna size of the shower. No clear relation is found between the full uncertainty size of the shower and the virtuality of the originating parton. The single gluon emission from the hard quark is then reanalyzed for the case of single rescattering off the remainder of the nucleus. A relation is derived between the jet transport coefficient $\hat{𝑞}$ and the gluon Transverse momentum-dependent parton distribution function (gTMDPDF). Solving this relation, for a simple case, clearly demonstrates the weakening of $\hat{𝑞}$ with the virtuality of the hard splitting parton.

jet quenching

Hard-photon-triggered jets in 𝑝−𝑝 and 𝐴−𝐴 collisions

An investigation of high-transverse-momentum (high-𝑝 𝑇 ) photon-triggered jets in proton-proton (𝑝−𝑝) and ion-ion (𝐴−𝐴) collisions at $\sqrt{s_{NN}}$=0.2 and 5.02TeV is carried out, using the multistage description of in-medium jet evolution. Monte Carlo simulations of hard scattering and energy loss in heavy-ion collisions are performed using parameters tuned in a previous study of the nuclear modification factor (𝑅 𝐴⁢𝐴 ) for inclusive jets and high-𝑝𝑇 hadrons. We obtain a good reproduction of the experimental data for photon-triggered jet 𝑅 𝐴⁢𝐴 , as measured by the ATLAS detector, the distribution of the ratio of jet to photon 𝑝 𝑇 (𝑋 𝐽⁢𝛾 ), measured by both CMS and ATLAS, and the photon-jet azimuthal correlation as measured by CMS. We obtain a moderate description of the photon-triggered jet 𝐼 𝐴⁢𝐴 , as measured by STAR. A noticeable improvement in the comparison is observed when one goes beyond prompt photons and includes bremsstrahlung and decay photons, revealing their significance in certain kinematic regions, particularly at 𝑋 𝐽⁢𝛾 >1. Moreover, azimuthal angle correlations demonstrate a notable impact of bremsstrahlung photons on the distribution, emphasizing their role in accurately describing experimental results. This work highlights the success of the multistage model of jet modification to straightforwardly predict (this set of) photon-triggered jet observables. This comparison, along with the role played by bremsstrahlung photons, has important consequences on the inclusion of such observables in a future Bayesian analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

An Extreme X-ray Disk Wind in the Black Hole Candidate IGR J17091-3624

Chandra spectroscopy of transient stellar-mass black holes in outburst has clearly revealed accretion disk winds in soft, disk-dominated states, in apparent anti-correlation with relativistic jets in low/hard states. These disk winds are observed to be highly ionized. dense. and to have typical velocities of approx 1000 km/s or less projected along our line of sight. Here. we present an analysis of two Chandra High Energy Transmission Grating spectra of the Galactic black hole candidate IGR J17091-3624 and contemporaneous EVLA radio observations. obtained in 2011. The second Chandra observation reveals an absorption line at 6.91+/-0.01 keV; associating this line with He-like Fe XXV requires a blue-shift of 9300(+500/-400) km/ s (0.03c. or the escape velocity at 1000 R(sub schw)). This projected outflow velocity is an order of magnitude higher than has previously been observed in stellar-mass black holes, and is broadly consistent with some of the fastest winds detected in active galactic nuclei. A potential feature at 7.32 keV, if due to Fe XXVI, would imply a velocity of approx 14600 km/s (0.05c), but this putative feature is marginal. Photoionization modeling suggests that the accretion disk wind in IGR J17091-3624 may originate within 43,300 Schwarzschild radii of the black hole, and may be expelling more gas than accretes. The contemporaneous EVLA observations strongly indicate that jet activity was indeed quenched at the time of our Chandra observations. We discuss the results in the context of disk winds, jets, and basic accretion disk physics in accreting black hole systems

King, A. L.