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Rajagopal, Krishna

Publications and source records attributed to Rajagopal, Krishna.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

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↗
DOE OSTI2024

Astrophysical Equation-of-State Constraints on the Color-Superconducting Gap

We demonstrate that astrophysical constraints on the dense-matter equation of state place an upper bound on the color-superconducting gap in dense matter above the transition from nuclear matter to quark matter. Pairing effects in the color-flavor locked quark matter phase increase the pressure at high density, and if this effect is sufficiently large then the requirements of causality and mechanical stability make it impossible to reach such a pressure in a way that is consistent with what is known at lower densities. The intermediate-density equation of state is inferred by considering extensions of chiral effective field theory to neutron star densities, and conditioning these using current astrophysical observations of neutron star radius, maximum mass, and tidal deformability (PSR J⁢0348+0432, PSR J1624-2230, PSR J⁢0740+6620, GW170817). At baryon number chemical potential μ = 2.6 GeV we find a 95% upper limit on the color-flavor locked pairing gap Δ of 457 MeV using overly conservative assumptions and 216 MeV with more reasonable assumptions. Furthermore, this constraint may be strengthened by future astrophysical measurements as well as by future advances in high-density QCD calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Predictions for the sPHENIX physics program

sPHENIX is a next-generation detector experiment at the Relativistic Heavy Ion Collider, designed for a broad set of jet and heavy-flavor probes of the Quark-Gluon Plasma created in heavy ion collisions. In anticipation of the commissioning and first data-taking of the detector in 2023, a RIKEN-BNL Research Center (RBRC) workshop was organized to collect theoretical input and identify compelling aspects of the physics program. Here this paper compiles theoretical predictions from the workshop participants for jet quenching, heavy flavor and quarkonia, cold QCD, and bulk physics measurements at sPHENIX.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Disentangling jet modification in jet simulations and in Z+jet data

The selection of jets in heavy-ion collisions based on their p T after jet quenching is known to bias towards jets that lost little energy in the quark-gluon plasma. In this work, we study and quantify the impact of this selection bias on jet substructure observables so as to isolate effects caused by the modification of the substructure of jets by quenching. We do so at first in a simplified Monte Carlo study in which it is possible to identify the same jet before and after quenching. We show explicitly that jets selected based on their quenched (i.e. observable) p T have substantially smaller fractional energy loss than those selected based on the p T that they would have had in the absence of any quenching. This selection bias has a large impact on jet structure and substructure observables. As an example, we consider the angular separation ΔR of the hardest splitting in each jet, and find that the ΔR distribution of the (biased) sample of jets selected based upon their quenched p T is almost unmodified by quenching. In contrast, quenching causes dramatic modifications to the ΔR distribution of a sample of jets selected based upon their unquenched p T , with a significant enhancement at larger ΔR coming from the soft particles originating from the wake of the jet in the quark-gluon plasma. The jets which contribute to this enhancement are those which have lost the most energy and which were, therefore, left out of the sample selected after quenching. In a more realistic study, we then show that the same qualitative effects can all be observed in Z+jet events. Selecting jets in such events based on either the jet p T or the Z-boson p T provides an experimentally accessible way to quantify the effects of selection biases in jet observables and separate them from the modification of jet substructure caused by quenching. Selecting Z+jet events based upon the jet p T yields a ΔR distribution that appears almost unmodified whereas selecting Z+jet events based upon the Z-boson p T reveals a significant modification to the ΔR-distribution caused by quenching, once again arising from the wakes of those jets that lose more energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Jet wake from linearized hydrodynamics

We explore how to improve the hybrid model description of the particles originating from the wake that a jet produced in a heavy ion collision leaves in the droplet of quark-gluon plasma (QGP) through which it propagates, using linearized hydrodynamics on a background Bjorken flow. Jet energy and momentum loss described by the hybrid model become currents sourcing linearized hydrodynamics. By solving the linearized hydrodynamic equations numerically, we investigate the development of the wake in the dynamically evolving droplet of QGP, study the effect of viscosity, scrutinize energy-momentum conservation, and check the validity of the linear approximation. We find that linearized hydrodynamics works better in the viscous case because diffusive modes damp the energy-momentum perturbation produced by the jet. We calculate the distribution of particles produced from the jet wake by using the Cooper-Frye prescription and find that both the transverse momentum spectrum and the distribution of particles in azimuthal angle are similar in shape in linearized hydrodynamics and in the hybrid model. Their normalizations are different because the momentum-rapidity distribution in the linearized hydrodynamics analysis is more spread out, due to sound modes. Since the Bjorken flow has no transverse expansion, we explore the effect of transverse flow by using local boosts to add it into the Cooper-Frye formula. After including the effects of transverse flow in this way, the transverse momentum spectrum becomes harder: more particles with transverse momenta bigger than 2 GeV are produced than in the hybrid model. Although we defer implementing this analysis in a jet Monte Carlo, as would be needed to make quantitative comparisons to data, we gain a qualitative sense of how the jet wake may modify jet observables by computing proxies for two example observables: the lost energy recovered in a cone of varying open angle, and the fragmentation function. We find that linearized hydrodynamics with transverse flow effects added improves the description of the jet wake in the hybrid model in just the way that comparison to data indicates is needed. Our study illuminates a path to improving the description of the wake in the hybrid model, highlighting the need to take into account the effects of both transverse flow and the broadening of the energy-momentum perturbation in spacetime rapidity on particle production.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Fluctuation dynamics near the QCD critical point

The evolution of nonhydrodynamic slow processes near the QCD critical point is explored with the novel hydro+ framework, which extends the conventional hydrodynamic description by coupling it to additional explicitly evolving slow modes describing long wavelength fluctuations. Here, their slow relaxation is controlled by critical behavior of the correlation length and is independent from gradients of matter density and pressure that control the evolution of the hydrodynamic quantities. In this exploratory study, we follow the evolution of the slow modes on top of a simplified QCD matter background, allowing us to clearly distinguish and study, both separately and in combination, the main effects controlling the dynamics of critical slow modes. In particular, we show how the evolution of the slow modes depends on their wave number, the expansion of and advection by the fluid background, and the behavior of the correlation length. Nonequilibrium contributions from the slow modes to bulk matter properties that affect the bulk dynamics (entropy, pressure, temperature, and chemical potential) are discussed and found to be small.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Coupling constant corrections in a holographic model of heavy ion collisions with nonzero baryon number density

Sufficiently energetic collisions of heavy ions result in the formation of a droplet of a strongly coupled liquid state of QCD matter known as quark-gluon plasma. By using gauge-gravity duality (holography), a model of a rapidly hydrodynamizing and thermal- izing process like this can be constructed by colliding sheets of energy density moving at the speed of light and tracking the subsequent evolution. In this work, we consider the dual gravitational description of such collisions in the most general bulk theory with a four-derivative gravitational action containing a dynamical metric and a gauge field in five dimensions. Introducing the bulk gauge field enables the analysis of collisions of sheets which carry nonzero “baryon” number density in addition to energy density. Introducing the four-derivative terms enables consideration of such collisions in a gauge theory with finite gauge coupling, working perturbatively in the inverse coupling. While the dynamics of energy and momentum in the presence of perturbative inverse-coupling corrections has been analyzed previously, here we are able to determine the effect of such finite coupling corrections on the dynamics of the density of a conserved global charge, which we take as a model for the dynamics of nonzero baryon number density. In accordance with expectations, as the coupling is reduced we observe that after the collisions less baryon density ends up stopped at mid-rapidity and more of it ends up moving near the lightcone.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Molière scattering in quark-gluon plasma: finding point-like scatterers in a liquid

By finding rare (but not exponentially rare) large-angle deflections of partons within a jet produced in a heavy ion collision, or of such a jet itself, experimentalists can find the weakly coupled short-distance quark and gluon particles (scatterers) within the strongly coupled liquid quark-gluon plasma (QGP) produced in heavy ion collisions. This is the closest one can come to probing QGP via a scattering experiment and hence is the best available path toward learning how a strongly coupled liquid emerges from an asymptotically free gauge theory. The short-distance, particulate, structure of liquid QGP can be revealed in events in which a jet parton resolves, and scatters off, a parton from the droplet of QGP. The probability for picking up significant transverse momentum via a single scattering was calculated previously, but only in the limit of infinite parton energy which means zero angle scattering. Here, we provide a leading order perturbative QCD calculation of the Molière scattering probability for incident partons with finite energy, scattering at a large angle. We set up a thought experiment in which an incident parton with a finite energy scatters off a parton constituent within a “brick” of QGP, which we treat as if it were weakly coupled, as appropriate for scattering with large momentum transfer, and compute the probability for a parton to show up at a nonzero angle with some energy. We include all relevant channels, including those in which the parton that shows up at a large angle was kicked out of the medium as well as the Rutherford-like channel in which what is seen is the scattered incident parton. The results that we obtain will serve as inputs to future jet Monte Carlo calculations and can provide qualitative guidance for how to use future precise, high statistics, suitably differential measurements of jet modification in heavy ion collisions to find the scatterers within the QGP liquid.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Heavy Ion Collisions: The Big Picture and the Big Questions

Heavy ion collisions quickly form a droplet of quark–gluon plasma (QGP) with a remarkably small viscosity. We give an accessible introduction to how to study this smallest and hottest droplet of liquid made on Earth and why it is so interesting. The physics of heavy ion collisions ranges from highly energetic quarks and gluons described by perturbative QCD to a bath of strongly interacting gluons at lower energy scales. Furthermore, these gluons quickly thermalize and form QGP, while the energetic partons traverse this plasma and end in a shower of particles called jets. Analyzing the final particles in various ways allows us to study the properties of QGP and the complex dynamics of multiscale processes in QCD that govern its formation and evolution, providing what is perhaps the simplest form of complex quantum matter that we know of. Much remains to be understood, and throughout the review big open questions are encountered.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Resolution effects in the hybrid strong/weak coupling model

Within the context of a hybrid strong/weak coupling model of jet quenching, we study the consequences of the fact that the plasma produced in a heavy ion collision cannot resolve the substructure of a collimated parton shower propagating through it with arbitrarily fine spatial resolution. We introduce a screening length parameter, L res , proportional to the inverse of the local temperature in the plasma, estimating a range for the value of the proportionality constant via comparing weakly coupled QCD calculations and holographic calculations appropriate in strongly coupled plasma. We then modify the hybrid model so that when a parton in a jet shower splits, its two offspring are initially treated as unresolved, and are only treated as two separate partons losing energy independently after they are separated by a distance L res . This modification delays the quenching of partons with intermediate energy, resulting in the survival of more hadrons in the final state with p T in the several GeV range. We analyze the consequences of different choices for the value of the resolution length, L res , and demonstrate that introducing a nonzero L res results in modifications to the jet shapes and jet fragmentations functions, as it makes it more probable for particles carrying a small fraction of the jet energy at larger angles from the jet axis to survive their passage through the quark-gluon plasma. Furthermore, these effects are, however, small in magnitude, something that we confirm via checking for effects on missing- p T observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Evolution of the mean jet shape and dijet asymmetry distribution of an ensemble of holographic jets in strongly coupled plasma

Some of the most important experimentally accessible probes of the quark- gluon plasma (QGP) produced in heavy ion collisions come from the analysis of how the shape and energy of sprays of energetic particles produced within a cone with a specified opening angle (jets) in a hard scattering are modified by their passage through the strongly coupled, liquid, QGP. We model an ensemble of back-to-back dijets for the purpose of gaining a qualitative understanding of how the shapes of the individual jets and the asymmetry in the energy of the pairs of jets in the ensemble are modified by their passage through an expanding cooling droplet of strongly coupled plasma, in the model in a holographic gauge theory that is dual to a 4+1-dimensional black-hole spacetime that is asymptotically anti-de Sitter (AdS). We build our model by constructing an ensemble of strings in the dual gravitational description of the gauge theory. We model QCD jets in vacuum using strings whose endpoints are moving “downward” into the gravitational bulk spacetime with some fixed small angle, an angle that represents the opening angle (ratio of jet mass to jet energy) that the QCD jet would have in vacuum. Such strings must be moving through the gravitational bulk at (close to) the speed of light; they must be (close to) null. This condition does not specify the energy distribution along the string, meaning that it does not specify the shape of the jet being modeled. We study the dynamics of strings that are initially not null and show that strings with a wide range of initial conditions rapidly accelerate and become null and, as they do, develop a similar distribution of their energy density. We use this distribution of the energy density along the string, choose an ensemble of strings whose opening angles and energies are distributed as in perturbative QCD, and show that we can then fix one of the two model parameters such that the mean jet shape for the jets in the ensemble that we have built matches that measured in proton-proton collisions reasonably well. This is a novel way for hybridizing relevant inputs from perturbative QCD and a strongly coupled holographic gauge theory in the service of modeling jets in QGP. We send our ensemble of strings through an expanding cooling droplet of strongly coupled plasma, choosing the second model parameter so as to get a reasonable value for $R$ $^{AA}_{jet}$, the suppression in the number of jets, and study how the mean jet shape and the dijet asymmetry are modified, comparing both to measurements from heavy ion collisions at the LHC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Angular structure of jet quenching within a hybrid strong/weak coupling model

Within the context of a hybrid strong/weak coupling model of jet quenching, we study the modification of the angular distribution of the energy within jets in heavy ion collisions, as partons within jet showers lose energy and get kicked as they traverse the strongly coupled plasma produced in the collision. To describe the dynamics transverse to the jet axis, we add the effects of transverse momentum broadening into our hybrid construction, introducing a parameter K≡qˆ/T3K≡q^/T3 that governs its magnitude. We show that, because of the quenching of the energy of partons within a jet, even when K ≠ 0 the jets that survive with some specified energy in the final state are narrower than jets with that energy in proton-proton collisions. For this reason, many standard observables are rather insensitive to K. We also propose a new differential jet shape ratio observable in which the effects of transverse momentum broadening are apparent. We also analyze the response of the medium to the passage of the jet through it, noting that the momentum lost by the jet appears as the momentum of a wake in the medium. After freezeout this wake becomes soft particles with a broad angular distribution but with net momentum in the jet direction, meaning that the wake contributes to what is reconstructed as a jet. Thus, this effect must be included in any description of the angular structure of the soft component of a jet. We show that the particles coming from the response of the medium to the momentum and energy deposited in it leads to a correlation between the momentum of soft particles well separated from the jet in angle with the direction of the jet momentum, and find qualitative but not quantitative agreement with experimental data on observables designed to extract such a correlation. Generally, by confronting the results that we obtain upon introducing transverse momentum broadening and the response of the medium to the jet with available jet data, we highlight the importance of these processes for understanding the internal, soft, angular structure of high energy jets.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Evolution of the Jet Opening Angle Distribution in Holographic Plasma

We use holography to analyze the evolution of an ensemble of jets, with an initial probability distribution for their energy and opening angle as in proton-proton (pp) collisions, as they propagate through an expanding cooling droplet of strongly coupled plasma as in heavy ion collisions. We identify two competing effects: (i) each individual jet widens as it propagates and (ii) because wide-angle jets lose more energy, energy loss combined with the steeply falling perturbative spectrum serves to filter wide jets out of the ensemble at any given energy. Even though every jet widens, jets with a given energy can have a smaller mean opening angle after passage through the plasma than jets with that energy would have had in vacuum, as experimental data may indicate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

On the evolution of jet energy and opening angle in strongly coupled plasma

We calculate how the energy and the opening angle of jets in N = 4 SYM theory evolve as they propagate through the strongly coupled plasma of that theory. We define the rate of energy loss dE jet /dx and the jet opening angle in a straightforward fashion directly in the gauge theory before calculating both holographically, in the dual gravitational description. In this way, we rederive the previously known result for dE jet /dx without the need to introduce a finite slab of plasma. We obtain a striking relationship between the initial opening angle of the jet, which is to say the opening angle that it would have had if it had found itself in vacuum instead of in plasma, and the thermalization distance of the jet. Via this relationship, we show that N = 4 SYM jets with any initial energy that have the same initial opening angle and the same trajectory through the plasma experience the same fractional energy loss. We also provide an expansion that describes how the opening angle of the N = 4 SYM jets increases slowly as they lose energy, over the fraction of their lifetime when their fractional energy loss is not yet large. In conclusion, we close by looking ahead toward potential qualitative lessons from our results for QCD jets produced in heavy collisions and propagating through quark-gluon plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗