Searcharxiv⌕ Search

arXiv subjects

Krishna Rajagopal

Publications and source records attributed to Krishna Rajagopal.

At least 55 records · Page 3Linked to original sources
arXiv2020

Disentangling Jet Modification

Jet modification in heavy-ion collisions is an important probe of the nature and structure of the quark-gluon plasma (QGP) produced in these collisions and also encodes information about how the wakes that jets excite in a droplet of QGP form and relax. However, in experiment, one cannot know what a particular jet in a heavy ion collision would have looked like without quenching, making it difficult to interpret measurements in terms of individual jet modification. The goal of this Monte Carlo study is to gain insight into the modification of jet observables using the hybrid strong/weak coupling model of jet quenching as a test bed. In this Monte Carlo study (but not in experiment) it is possible to watch $\textit{the same jet}$ as it evolves in vacuum or in QGP. We use this ability to disentangle the effects of modification of individual jets in heavy ion collisions vs. the effects of differing selection bias on the distribution of two observables: fractional energy loss and groomed $ΔR$. We find that in the hybrid model the distribution of groomed $ΔR$ appears to be unmodified in a sample of jets selected after quenching, as in heavy ion collisions, and confirm that this lack of modification arises because of a selection bias toward jets that lose only a small fraction of their energy. If instead we select jets in a way that avoids this bias, and then follow these selected jets as they are quenched, we show that there is, in fact, a substantial modification of the $ΔR$ of individual jets. We show that this jet modification is principally due to the incorporation of particles coming from the wake that the parton shower excites in the plasma as a component of what an experimentalist reconstructs as a jet. The effects we discuss are substantial in magnitude, suggesting that our qualitative conclusions are more general than the Monte Carlo study in which we obtain them.

hep-ph↗
arXiv2020

QCD equation of state matched to lattice data and exhibiting a critical point singularity

We construct a family of equations of state for QCD in the temperature range 30 MeV $\leq T\leq$ 800 MeV and in the chemical potential range $0\leq μ_B \leq$ 450 MeV. These equations of state match available lattice QCD results up to $\mathcal{O}(μ_B^4)$ and in each of them we place a critical point in the 3D Ising model universality class. The position of this critical point can be chosen in the range of chemical potentials covered by the second Beam Energy Scan at RHIC. We discuss possible choices for the free parameters, which arise from mapping the Ising model onto QCD. Our results for the pressure, entropy density, baryon density, energy density and speed of sound can be used as inputs in the hydrodynamical simulations of the fireball created in heavy ion collisions. We also show our result for the second cumulant of the baryon number in thermal equilibrium, displaying its divergence at the critical point. In the future, comparisons between RHIC data and the output of the hydrodynamic simulations, including calculations of fluctuation observables, built upon the model equations of state that we have constructed may be used to locate the critical point in the QCD phase diagram, if there is one to be found.

hep-ph↗
arXiv2020

Jet substructure modification probes the QGP resolution length

We show the sensitivity of groomed jet substructure measurements to the finite resolution power of the QGP to disentangle multiple energetic partons, as produced by QCD jets, that traverse it simultaneously. We illustrate these effects by studying Soft Dropped observables within a hybrid strong/weak coupling model for jet-medium interactions. By analysing Monte-Carlo-generated jet data in heavy ion collisions, we show that the angular structure of these type of observables is sensitive to the value of the QGP resolution length.

hep-ph↗
arXiv2019

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 thermalizing 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.

hep-th↗
arXiv2019

Hydro+ in Action: Understanding the Out-of-Equilibrium Dynamics Near a Critical Point in the QCD Phase Diagram

Upcoming experimental programs will look for signatures of a possible critical point in the QCD phase diagram in fluctuation observables. To understand and predict these signatures, one must account for the fact that the dynamics of any critical fluctuations must be out-of-equilibrium: because of critical slowing down, the fluctuations cannot stay in equilibrium as the droplet of QGP produced in a collision expands and cools. Furthermore, their out-of-equilibrium dynamics must also influence the hydrodynamic evolution of the cooling droplet. The recently developed Hydro+ formalism allows for a consistent description of both the hydrodynamics and the out-of-equilibrium fluctuations, including the feedback between them. We shall explicitly demonstrate how this works, setting up a Hydro+ simulation in a simplified setting: a rapidity-independent fireball undergoing radial flow with an equation of state in which we imagine a critical point close to the $μ_B=0$ axis of the phase diagram. Within this setup, we show that we can quantitatively capture non-equilibrium phenomena, including critical fluctuations over a range of scales and memory effects. Furthermore, we illustrate the interplay between the dynamics of the fluctuations and the hydrodynamic flow of the fireball: as the fluid cools and flows, the dynamical fluctuations lag relative to how they would evolve if they stayed in equilibrium; there is then a backreaction on the flow itself due to the out-of-equilibrium fluctuations; and, in addition, the radial flow transports fluctuations outwards by advection. Within our model, we find that the backreaction from the out-of-equilibrium fluctuations does not yield dramatically large effects in the hydrodynamic variables. Further work will be needed in order to check this quantitative conclusion in other settings but, if it persists, this will considerably simplify future modelling.

hep-ph↗
arXiv2019

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 ultimately 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.

hep-ph↗
arXiv2018

Understanding wide jet suppression in data through the hybrid strong/weak coupling model

We explore a set of jet substructure observables that use grooming techniques such as the Soft Drop procedure by performing simulations with the hybrid strong/weak coupling model for jet quenching. The results obtained for the observables presented in this proceedings, namely the number of Soft Drop splittings, or $n_{\rm SD}$, and the sharing momentum distribution $z_g$ for different angular cuts between the two main branches in a jet, can be easily understood as arising from the fact that among all the jets with a given jet $p_T$, those jets which are wider in opening angle, meaning that they have a higher jet mass and come from showers featuring more splittings, tend to lose more energy than the narrower jets. We comment on the comparison to data from ALICE and CMS, and point out the caveats arising from the consideration of smearing effects due to the presence of a large fluctuating background.

hep-ph↗
arXiv2018

Finding the Scatterers in Hot Quark Soup

We present a brief report on a thought experiment in which an incident energetic parton traverses a brick of quark-gluon plasma (QGP), see arXiv:1808.03250 for the full report. We calculate the probability of detecting a parton showing up at a large angle with respect to its initial direction due to scattering with the constituents of QGP, using leading order perturbative QCD. We include all relevant channels, including the Rutherford-like channel as considered in early works, and those that are not Rutherford-like but become important at a large angle. The resulting probability distributions contain information about the short distance structure of QGP. Our results provide key theoretical input toward finding the scatterers within the QGP liquid, which in turn is the necessary first step toward using precise, high-statistics, suitably differential measurements of jet modification in heavy ion collisions to study the evolution of the properties of QGP with changing resolution scale.

nucl-th↗
arXiv2018

Charge-dependent Flow Induced by Magnetic and Electric Fields in Heavy Ion Collisions

We investigate the charge-dependent flow induced by magnetic and electric fields in heavy ion collisions. We simulate the evolution of the expanding cooling droplet of strongly coupled plasma hydrodynamically, using the iEBE-VISHNU framework, and add the magnetic and electric fields as well as the electric currents they generate in a perturbative fashion. We confirm the previously reported effect of the electromagnetically induced currents, that is a charge-odd directed flow $Δv_1$ that is odd in rapidity, noting that it is induced by magnetic fields (à la Faraday and Lorentz) and by electric fields (the Coulomb field from the charged spectators). In addition, we find a charge-odd $Δv_3$ that is also odd in rapidity and that has a similar physical origin. We furthermore show that the electric field produced by the net charge density of the plasma drives rapidity-even charge-dependent contributions to the radial flow $\langle p_T \rangle$ and the elliptic flow $Δv_2$. Although their magnitudes are comparable to the charge-odd $Δv_1$ and $Δv_3$, they have a different physical origin, namely the Coulomb forces within the plasma.

hep-ph↗
arXiv2018

A Simultaneous Description of Hadron and Jet Suppression in Heavy Ion Collisions

We present a global fit to all data on the suppression of high energy jets and high energy hadrons in the most central heavy ion collisions at the LHC for two different collision energies, within a hybrid strong/weak coupling quenching model. Even though the measured suppression factors for hadrons and jets differ significantly from one another and appear to asymptote to different values in the high energy limit, we obtain a simultaneous description of all these data after constraining the value of a single model parameter. We use our model to investigate the origin of the difference between the observed suppression of jets and hadrons and relate it, quantitatively, to the observed modification of the jet fragmentation function in jets that have been modified by passage through the medium produced in heavy ion collisions. In particular, the observed increase in the fraction of hard fragments in medium-modified jets, which indicates that jets with the fewest hardest fragments lose the least energy, corresponds quantitatively to the observed difference between the suppression of hadrons and jets. We argue that a harder fragmentation pattern for jets with a given energy after quenching is a generic feature of any mechanism for the interaction between jets and the medium that they traverse that yields a larger suppression for wider jets. We also compare the results of our global fit to LHC data to measurements of the suppression of high energy hadrons in RHIC collisions, and find that with its parameter chosen to fit the LHC data our model is inconsistent with the RHIC data at the $3σ$ level, suggesting that hard probes interact more strongly with the less hot quark-gluon plasma produced at RHIC.

hep-ph↗
arXiv2018

A simultaneous understanding of jet and hadron suppression

In the context of the hybrid strong/weak coupling model for jet quenching, we perform a global fit to hadron and jet data in the most central bins both at RHIC and LHC. The qualitative and quantitative success of the analysis is attributed to the fact that the model correctly captures the fact that wider jets lose, on average, more energy than the narrower ones, to which high energy hadrons belong. We show how one can understand the relative jet and hadron suppression by analyzing the jet fragmentation functions, and also discuss the role of plasma finite resolution effects.

hep-ph↗
arXiv2018

Searching for the QCD critical point via the rapidity dependence of cumulants

The search for a possible critical point in the QCD phase diagram is ongoing in heavy ion collision experiments at RHIC which scan the phase diagram by scanning the beam energy; a coming upgrade will increase the luminosity and extend the rapidity acceptance of the STAR detector. In fireballs produced in RHIC collisions, the baryon density depends on rapidity. By employing Ising universality together with a phenomenologically motivated freezeout prescription, we show that the resulting rapidity dependence of cumulant observables sensitive to critical fluctuations is distinctive. The dependence of the kurtosis (of the event-by-event distribution of the number of protons) on rapidity near mid-rapidity will change qualitatively if a critical point is passed in the scan. Hence, measuring the rapidity dependence of cumulant observables can enhance the prospect of discovering a critical point, in particular if it lies between two energies in the beam energy scan.

hep-ph↗
arXiv2018

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 ions ranges from highly energetic quarks and gluons described by perturbative QCD to a bath of strongly interacting gluons at lower energy scales. 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 a variety of different ways allows us to study the properties of QGP and the complex dynamics of multi-scale processes in QCD which 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 will be encountered.

hep-ph↗
arXiv2017

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 probes of the quark-gluon plasma (QGP) produced in heavy ion collisions come from the analysis of how the shape and energy of jets are modified by passage through QGP. We model an ensemble of back-to-back dijets to gain a qualitative understanding of how the shapes of the individual jets and the asymmetry in the energy of the pairs of jets are modified by passage through an expanding droplet of strongly coupled plasma, as modeled in a holographic gauge theory. We do so by constructing an ensemble of strings in the gravitational description of the gauge theory. We model QCD jets in vacuum using strings whose endpoints move "downward" into the gravitational bulk spacetime with some fixed small 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 model parameter such that the mean jet shape in our ensemble matches that measured in p-p collisions reasonably well. We send our strings through the plasma, choosing the second model parameter to get a reasonable suppression in the number of jets, and study how the mean jet shape and the dijet asymmetry are modified, comparing both to data from LHC heavy ion collisions.

nucl-th↗
arXiv2017

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, $L_{\rm res}$, 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 $L_{\rm res}$. 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, $L_{\rm res}$, and demonstrate that introducing a nonzero $L_{\rm res}$ 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. These effects are, however, small in magnitude, something that we confirm via checking for effects on missing-$p_T$ observables.

hep-ph↗
arXiv2017

Holographic Jet Shapes and their Evolution in Strongly Coupled Plasma

Recently our group analyzed how the probability distribution for the jet opening angle is modified in an ensemble of jets that has propagated through an expanding cooling droplet of plasma [1]. Each jet in the ensemble is represented holographically by a string in the dual 4+1- dimensional gravitational theory with the distribution of initial energies and opening angles in the ensemble given by perturbative QCD. In [1], the full string dynamics were approximated by assuming that the string moves at the speed of light. We are now able to analyze the full string dynamics for a range of possible initial conditions, giving us access to the dynamics of holographic jets just after their creation. The nullification timescale and the features of the string when it has nullified are all results of the string evolution. This emboldens us to analyze the full jet shape modification, rather than just the opening angle modification of each jet in the ensemble as in [1]. We find the result that the jet shape scales with the opening angle at any particular energy. We construct an ensemble of dijets with energies and energy asymmetry distributions taken from events in proton-proton collisions, opening angle distribution as in [1], and jet shape taken from proton-proton collisions and scaled according to our result. We study how these observables are modified after we send the ensemble of dijets through the strongly-coupled plasma.

nucl-th↗
arXiv2016

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

Building upon the hybrid strong/weak coupling model for jet quenching, we incorporate and study the effects of transverse momentum broadening and medium response of the plasma to jets on a variety of observables. For inclusive jet observables, we find little sensitivity to the strength of broadening. To constrain those dynamics, we propose new observables constructed from ratios of differential jet shapes, in which particles are binned in momentum, which are sensitive to the in-medium broadening parameter. We also investigate the effect of the back-reaction of the medium on the angular structure of jets as reconstructed with different cone radii R. Finally we provide results for the so called "missing-pt", finding a qualitative agreement between our model calculations and data in many respects, although a quantitative agreement is beyond our simplified treatment of the hadrons originating from the hydrodynamic wake.

hep-ph↗