arXiv subjects

Krishna Rajagopal

Publications and source records attributed to Krishna Rajagopal.

At least 19 recordsLinked to original sources

arXiv2026

Computationally Efficient Description of Medium Response to Jets in Heavy Ion Collisions

We develop an Efficient Wake procedure for computing the distribution of hadrons originating from jet wakes in heavy ion collisions - the hydrodynamic response of a droplet of quark-gluon plasma to the energy and momentum deposited in it by high-energy partons propagating through it. The procedure employs the linearity of linearized hydrodynamics and takes account of the effects of both longitudinal expansion and transverse radial flow on the hydrodynamic evolution of the wakes and on the resulting particle production at the freezeout hypersurface. It makes repeated use of template solutions to linearized hydrodynamics in a Bjorken flow background with no transverse flow, templates that need only be computed once, and uses suitable rotations and boosts to map fluctuations from these templates to fluctuations at a point on the freezeout hypersurface in a way that incorporates the effects of the radial flow. We benchmark this procedure by comparing its results to results obtained from full $(3+1)$-dimensional nonlinear hydrodynamics calculations, find reasonable agreement, and find that our Efficient Wake procedure yields a much better description of the distribution of hadrons originating from jet wakes than does the older oversimplified procedure employed in the Hybrid Model. And, the Efficient Wake procedure is computationally efficient: it is at least tens of thousands of times faster than full nonlinear hydrodynamics calculations. Hence, we anticipate that when our new procedure is implemented in Monte Carlo analyses of jets in heavy ion collisions, for example in the Hybrid Model, it will greatly improve the description of the soft component of many jet and jet substructure observables as compared to experimental data.

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arXiv2026

Heavy quark transport in quark-gluon plasma beyond the non-relativistic limit

The dynamics of heavy quarks in quark-gluon plasma (QGP) formed in heavy ion collisions provide a unique window to characterize its properties. Existing approaches to describe heavy quarks in medium rely either on quasiparticle-based models of QGP, or on assuming that the momentum transfer from the medium follows Gaussian statistics. However, neither of these assumptions can be taken for granted in QCD. In fact, in the prototypical theory that is strongly coupled $\mathcal{N}=4$ SYM, it has been long known there are no momentum-carrying quasiparticles, and furthermore, we have recently shown that the momentum transfer from the medium is far from being Gaussian [arXiv:2501.06289]. Since then, we showed that the asymmetry of said momentum transfer between energy loss and energy gain -- which affects all moments of the distribution, not only its Gaussian characteristics -- is, in fact, universal [arXiv:2504.21139]. Therefore, in order to connect the initial heavy quark production cross section with the final hadron spectrum in a way that is consistent with QFT principles, new methods are needed. In this talk, we present a new transport description of heavy quarks that encodes all of the non-Gaussian features of the momentum transfer from the medium, all of which can be defined and in principle calculated in QCD, without relying on any assumptions regarding the strength of the coupling. As a demonstrative example, we discuss heavy quark equilibration in $\mathcal{N}=4$ SYM. This paves the way towards extracting novel information about fundamental properties of QGP.

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arXiv2026

Short-Range Correlations Between Partons in a Proton

A principal lesson from recreating droplets of quark-gluon plasma (QGP) in heavy ion collisions is that it is a strongly coupled liquid, not a plasma of partons. The energy density and pressure of quarks and gluons confined within a proton are comparable to those of QGP at or just above the QCD transition temperature. Given this similarity between protons and QGP, we propose that the investigation of correlations between nearby partons within a proton must be a central goal for the future Electron-Ion Collider (EIC). Here, we ask how EIC measurements can discern such short-range correlations (SRCs) of quark pairs. Doing so would characterize the strongly coupled interior of a proton, augmenting the one-parton-at-a-time understanding of protons via (generalized) parton distribution functions, and could at the same time yield a key ingredient for the microscopic understanding of the liquid nature of QGP. Motivated by the experiments that have been used to demonstrate the existence of SRCs between nucleon pairs within a nucleus, we propose using EIC observables involving measurements of a jet and a pion, together with the scattered electron, to seek and quantify the possible existence of SRCs between quark pairs within a nucleon. The pronounced isospin dependence observed in the dominance of $np$ SRCs over $pp$ or $nn$ SRCs has played a central role in establishing the importance of SRCs among nucleons in nuclei. Analogously, the QCD attraction in the $ud$ diquark channel can make the $ud$ SRC stronger than the $uu$ and $dd$ SRCs, allowing a first observation of partonic SRCs.

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arXiv2026

Stochastic Dynamics of Heavy Quarks in Strongly Coupled Plasma

We study the stochastic dynamics of heavy quarks propagating through the strongly coupled plasma of $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory at nonzero temperature in terms of the corresponding Kolmogorov equation, which correctly describes their kinetic equilibration and the non-Gaussian fluctuations in their momenta without having to restrict their velocity to the non-relativistic regime. Leveraging the heavy quark limit, we show that the evolution of the momentum space distribution function can be reformulated as a Hamilton-Jacobi problem, and therefore can be solved in terms of first-order ordinary differential equations. We solve these evolution equations in an infinite thermal plasma with a constant temperature for initial conditions specified by spherically symmetric heavy quark momentum distributions with a phenomenologically motivated shape that is steeply falling at large momentum. To highlight the distinctive features of the kinetic equilibration process, we compare their solutions with Fokker-Planck dynamics with the same drag coefficient and fluctuations chosen by hand to guarantee equilibration. We find qualitatively similar dynamics at small momentum, and very different dynamics at large momentum, where, much like in jet quenching phenomena, the steepness of the momentum distribution gives a larger relevance to unlikely events in which a heavy quark loses little momentum in a given time step. Such events are much less unlikely in the Kolmogorov evolution than in Fokker-Planck evolution with the same mean energy loss, meaning that equilibration at large momentum is significantly delayed. Our results provide a systematic description of heavy quarks propagating through strongly coupled plasma from the ultra-relativistic to the non-relativistic regime and point the way towards implementation in phenomenological studies.

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arXiv2026

Looking at the Entropy in a Proton through a QGP Lens

We investigate the interplay between the thermodynamic (Gibbs) entropy of quark-gluon plasma (QGP) and the quantum entanglement entropy characteristic of confined hadronic states across the quark-hadron phase transition. In the deconfined regime, entropy is well described by the statistical mechanics of colored quarks and gluons. Upon hadronization, however, the macroscopic Gibbs entropy of the plasma cannot simply vanish; instead, it is reorganized into the configurational entropy of a gas of colorless hadrons together with quantum correlations among the confined partons within each hadron. We show that the entanglement entropy of the internal partonic wave functions inside hadrons provides a natural repository for this ``converted'' thermodynamic entropy, reconciling the apparent reduction of macroscopic entropy with the second law of thermodynamics. Either by extrapolating from known facts about deep inelastic scattering, or starting from model descriptions of the proton wave function, or starting from the Hagedorn spectrum of its resonances, we provide three estimates of the magnitude of the entanglement entropy carried by a proton, with very different uncertainties. All three estimates indicate that the internal entanglement entropy of the proton is similar in magnitude to the Gibbs entropy of the QGP droplet from which the proton formed as QGP cools through the quark-hadron transition, as for example throughout the universe microseconds after the Big Bang. These results suggest that entanglement entropy offers a bridge between the quantum information content of hadronic states and the thermodynamic entropy of the quark-gluon plasma, providing a new lens on the microscopic mechanism of confinement and the nature of the QCD phase transition.

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arXiv2026

A Breath of Fresh Air for Moli\`ere: Detecting Moli\`ere Scattering using Jet Substructure Observables in Oxygen Collisions

Ultra-relativistic oxygen-oxygen (OO) collisions are a promising arena in which to probe rare, large-angle, high momentum-transfer $2\rightarrow2$ Moli\`ere scatterings between energetic jet partons and quasiparticles in quark-gluon plasma (QGP). As a jet propagates through the droplet of QGP formed in the same collision, its constituents lose energy to and excite wakes in the medium, and may scatter off quark- and gluon-like quasiparticles in QGP. Using the hybrid strong/weak coupling model, we show that including Moli\`ere scatterings between jet partons and medium quasiparticles is essential to reproduce recent CMS measurements of charged-particle suppression in OO collisions with this model. We then present the first theoretical study of how jet-medium interactions modify the internal structure of jets in OO collisions. We find that Moli\`ere scatterings broaden the Soft Drop splitting angle $R_g$, enhancing the population of $R=0.4$ and $R=0.8$ jets with $R_g\gtrsim0.2$ in OO collisions relative to pp collisions. Energy-energy correlators (EECs) provide a complementary probe, exhibiting enhanced large-angle correlations within jets due to jet-induced wakes and Moli\`ere scattering. In both cases, we propose an experimental measurement where the relevant OO/pp ratio can, if enhanced above unity in future data as in our calculations, be a distinctive, model-independent, detection of hard scattering off QGP quasiparticles. We furthermore use our calculations of EECs to show how the angular scale corresponding to the deflection of jet or medium partons by Moli\`ere scattering is imprinted in the EEC for jets with radius $R_{\rm jet}\sim0.8$ in OO collisions. These results demonstrate that jet substructure measurements in OO collisions are promising avenues to probe the quasiparticles that emerge at short distances within an otherwise strongly coupled medium.

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arXiv2026

Sensitivity of Jet Observables to Moli\`ere Scattering Off Quasiparticles in Quark-Gluon Plasma

Quark-gluon plasma (QGP) is a strongly coupled liquid when viewed at length scales of order the inverse of its temperature and longer. However, when it is probed at short enough length scales, asymptotic freedom mandates the presence of quark- and gluon-like quasiparticles. Partons in jets can trigger perturbative, high momentum-exchange $2\rightarrow2$ Moli\`ere scatterings off quasiparticles in the medium, making jets useful probes of the microscopic structure of QGP. Prior to this work, soft strongly coupled momentum-exchanges between jet partons and the QGP droplet produced in a heavy-ion collision, as well as the wakes that jets excite in the droplet, had been accounted for in the Hybrid Model of jet quenching. Here, we present a full calculation of Moli\`ere scattering off a QGP quasiparticle which results in the deflection of the jet parton and the excitation of a parton from the thermal medium that recoils after being kicked, and describe how it is implemented in the Hybrid Model. The scattered jet and recoil partons continue to propagate through the QGP, lose energy and momentum, excite wakes, and may further re-scatter. Using the Hybrid Model, we study how Moli\`ere scatterings impact jet shapes and fragmentation functions, the Soft Drop angle $R_g$, jet girth $g$, and observables that focus on the number and angular distribution of subjets within jets. We demonstrate that photon-tagged jets provide a particularly sensitive probe: selecting events by the photon energy mitigates the selection bias inherent in inclusive jet measurements and enhances sensitivity to rare large-angle scatterings. We find that Moli\`ere scatterings broaden both the $R_g$ and $g$ distributions when jets significantly softer than the photon are included. Our results point the way towards distinctive model-independent experimental signatures of hard scattering of jet partons off quasiparticles in QGP.

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arXiv2025

Heavy Quark Energy Loss in the Hybrid Model

Heavy quarks offer an invaluable hard probe of the droplets of quark gluon plasma (QGP) formed in heavy ion collisions at the LHC and RHIC. Given their large mass, they are predominantly produced in hard scattering processes at the earliest moment of a collision and given their rarity they almost never annihilate with a heavy antiquark subsequently. This means that they experience, and probe, the entire history of the expanding, cooling, droplet of QGP from hydrodynamization through hadronization. Quantitative measurements of heavy quark final state observables therefore give us access to information about the transport properties of QGP as well as about medium modifications of hadronization. To date, the Hybrid strong/weak coupling Model of jet quenching has not included any implementation of the heavy-quark sector, which has made it impossible to confront its predictions with measurements of heavy quark and jet observables together, in a unified fashion. Here, we extend the Hybrid Model to investigate heavy quark observables for the first time. We introduce a strongly-coupled calculation of heavy-quark energy loss with the correct behavior when the heavy quarks are either ultrarelativistic or non-relativistic, Gaussian momentum broadening, and recombination of heavy quarks with medium partons using a local color neutralization model of hadronization. We compare our results for the suppression $R_{\rm AA}$ and azimuthal anisotropies $v_2$ of B- and D-mesons and $\Lambda_c$ baryons, the $R_{\rm AA}$ of B-tagged jets, as well as baryon-to-meson ratios, with available experimental data from ALICE, ATLAS and CMS.

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arXiv2025

Factorial cumulants of proton multiplicity near a critical point using maximum entropy freeze-out prescription

We present the first application of the maximum-entropy freeze-out prescription to calculate factorial cumulants of proton multiplicities near the conjectured QCD critical point in thermal equilibrium. We map the Gibbs free energy of the 3D Ising model to a parameterized class of possible EoS near QCD critical point. This equilibrium baseline highlights how factorial cumulants isolate critical fluctuations by subtracting trivial self-correlations, setting the stage for future out-of-equilibrium analyses. We identify the key non-universal aspects of the mapping to the Ising model that strongly control the characteristic properties, such as magnitude and location of the peaks of the factorial cumulants along the freeze-out curve.

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arXiv2025

First Demonstration that Quark-Gluon Plasma has a Nonzero Resolution Length

We report on our investigation in arXiv:2509.08881 of how recent jet substructure measurements constrain the resolution length $L_{\rm res}$ of the quark-gluon plasma formed in heavy-ion collisions. $L_{\rm res}$ is defined such that high-energy partons within a jet shower are resolved by the medium if and only if they are separated by a distance greater than $L_{\rm res}$. Using the Hybrid Model, we reproduce ALICE data on the scaled Soft Drop angle $\theta_g$ for $R=0.2$ charged-particle jets and ATLAS data on the Hard Group angle $\Delta R_{12}$ for $R=1$ jets reclustered from skinny $R = 0.2$ inclusive subjets. We find that the narrowing of the $\theta_g$-distribution in PbPb collisions observed by ALICE and the suppression of $R=1$ jets with multiple skinny subjets in PbPb collisions observed by ATLAS rule out $L_{\rm res} = \infty$, where each entire parton shower loses energy to the plasma coherently as if it were a single colored object. We then compare Hybrid Model calculations to ATLAS measurements of $R_{\rm AA}$ of $R=1$ jets reclustered from $R=0.2$ subjets, as a function of the Soft Drop angle $dR_{12}$ obtained by grooming all charged-particle tracks associated with each $R=1$ jet. We demonstrate, for the first time, that the ATLAS data is inconsistent with $L_{\rm res} = 0$, where the plasma resolves every splitting in a parton shower. Our results agree best with the data when QGP possesses a finite, nonzero $L_{\rm res}\sim (1-2)/(\pi T)$.

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arXiv2025

Constraining the Resolution Length of Quark-Gluon Plasma with New Jet Substructure Measurements

We show that recent measurements of substructure-dependent jet suppression constrain the value of the resolution length of the droplets of quark-gluon plasma (QGP) formed in heavy ion collisions. This resolution length, $L_{\rm res}$, is defined such that the medium can only resolve partons within a jet shower that are separated by more than $L_{\rm res}$. We first use Hybrid Model calculations to reproduce ALICE measurements of the scaled Soft Drop angle $\theta_g$ for anti-$k_t$ $R = 0.2$ jets reconstructed from charged-particle tracks. We find that the narrowing of the $\theta_g$-distribution in PbPb collisions compared to pp collisions that is seen in the ALICE data rules out a picture of fully coherent energy loss ($L_{\rm res} = \infty$) where each entire parton shower loses energy to the plasma as if it were a single unresolved colored object. We then use Hybrid Model calculations to reproduce ATLAS measurements of $dR_{12}$, the Soft Drop angle obtained by applying the Soft Drop grooming procedure to all charged-particle tracks in $R=1$ jets reconstructed from $R = 0.2$ skinny subjets. Our analysis demonstrates that the ATLAS measurements of $R_{\rm AA}$ for such $R = 1$ jets as a function of $dR_{12}$ are inconsistent with a picture of fully incoherent energy loss ($L_{\rm res} = 0$) in which every splitting in a parton shower is immediately resolved by the plasma. We find that our Hybrid Model calculations agree best with the ATLAS measurements if QGP has a finite, nonzero, resolution length $L_{\rm res}\sim (1-2)/(\pi T)$. For the first time, jet substructure measurements are constraining the resolution length of QGP from below, as well as from above.

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arXiv2025

Imaging the Jet-Induced Medium Response with Energy Correlators

Quark-gluon plasma (QGP), when viewed at length scales of order the inverse of its temperature, behaves as a strongly-coupled liquid. However, when it is probed with sufficiently high momentum transfer, asymptotic freedom mandates the presence of quark- and gluon-like quasi-particles. High energy partons within jets can trigger these high-momentum exchanges, making jets valuable probes for revealing the presence of such quasi-particles. Such elastic scatterings are implemented in the Hybrid Model, where a jet parton that scatters is deflected, kicking a medium parton, which recoils. Before and after a scattering, as one and then both partons propagate through the medium, they lose energy and momentum, exciting wakes in the QGP droplet. We use two-point and three-point energy-energy correlators (EECs) to reveal the relevant angular regions at which (modified) parton showers and wakes in the QGP each dominate, offering a new way with which to visualize and constrain the corresponding dynamics. We compare our calculations to recent CMS and ALICE measurements of two-point EECs of charged-particle tracks in jets produced in PbPb collisions. We show that our calculations are closest to the experimental measurements when elastic scattering is included and when the elastically scattered recoil-partons produce their own wakes. We also propose a new variant of the measurement that is especially sensitive to jet wakes.

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arXiv2025

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

We summarize and update using new NICER measurements the results of arXiv:2401.16253, in which we used various astrophysical neutron-star observations to set an upper bound on the CFL color-superconducting gap in a range of baryon chemical potentials $\mu_B \in [2.1,3.2]$, above those reached within neutron stars. We also corroborate the ``reasonable" constraint from arXiv:2401.16253 on the maximum value of the color-superconducting gap by performing a new Bayesian analysis using a prior that extends a two-segment Gaussian process connecting the whole density range between CEFT and pQCD.

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arXiv2025

Quantifying fluctuation signatures of the QCD critical point using maximum entropy freeze-out

A key question about the QCD phase diagram is whether there is a critical point somewhere on the boundary between the hadronic and quark-gluon plasma phases, and if so where. Heavy-ion collisions offer a unique opportunity to search for signatures of such a critical point by analyzing event-by-event fluctuations in particle multiplicities. To draw meaningful conclusions from experimental data, a theoretical framework is needed to link QCD thermodynamics with the particle spectra and correlations observed in detectors. The Equation of State (EoS) of QCD near a critical point can be related to the universal Gibbs free energy of the 3D Ising model using four currently unknown non-universal mapping parameters whose values are determined by the microscopic details of QCD. We utilize the maximum entropy approach to freeze-out the fluctuations in order to make estimates for factorial cumulants of proton multiplicities, assuming thermal equilibrium, for a family of EoS with a 3D Ising-like critical point, varying the microscopic inputs that determine the strength and structure of the critical features. We quantify the effect of the non-universal mapping parameters, and the distance between the critical point and the freeze-out curve, on the factorial cumulants of proton multiplicities.

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arXiv2025

Attractors Without Scaling: Adiabatic Hydrodynamization With and Without Inelastic Scattering

We study the process of hydrodynamization in kinetic theories of gluons undergoing boost-invariant expansion using the Adiabatic Hydrodynamization (AH) framework. We study both number-conserving and non-conserving theories, and find that including number non-conserving inelastic scattering processes restores many qualitative features of hydrodynamization in QCD EKT despite the simplicity of our model. In particular, introducing inelastic scattering results in a more realistic hydrodynamization time. With or without number non-conservation, we find that first-order hydrodynamics becomes applicable at the same time that a unique ground state emerges in the dynamical evolution of the one-particle distribution function. Furthermore, we find a set of low-effective-energy attractor modes which evolve adiabatically long before hydrodynamization, and find that the emergence of a gap between these ground state modes and the excited modes coincides with the time at which the system falls onto an attractor surface. Strikingly, this is the case even in the absence of pre-thermal scaling of the gluon distribution function, which has previously been strongly associated with pre-thermal attractor behavior. Finally, motivated by a generic feature we observe in the spectrum, we show that as the system hydrodynamizes, the rapid decoupling of non-hydrodynamic modes in boost-invariant kinetic theory can be understood with the AH framework in a model-independent fashion.

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arXiv2025

Holographic Heavy Quark Energy Loss in the Hybrid Model

To date, holographic calculations in strongly coupled plasma have provided separate descriptions for the rates of energy loss either for ultrarelativistic massless quarks and gluons or for infinitely massive quarks, with the latter calculation valid for $\sqrt{\gamma} < M/(\sqrt{\lambda}T)$, where $\gamma$ is the Lorentz boost factor for a heavy quark with velocity $v$ and mass $M$ moving through plasma with 't Hooft coupling $\lambda$ and temperature $T$. These two calculations should apply sequentially in the description of the energy loss of a heavy quark that starts out ultrarelativistic, loses energy, slows down, becomes non-relativistic at later times, and ultimately comes to rest and diffuses in the strongly coupled plasma. We provide an ansatz for uniquely incorporating both regimes to give an approximate but unified description of how a heavy quark that is initially ultrarelativistic loses energy all the way until it comes to rest. We implement this ansatz in the Hybrid Strong/Weak Coupling Model. With this new, consistent, treatment of heavy quark energy loss at strong coupling, we confront our predictions for the suppression and azimuthal anisotropies of D- and B-mesons, as well as B-tagged jets, with available experimental data.

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arXiv2025

Universal Equilibration Condition for Heavy Quarks

Kinetic equilibration at late times is physically required for heavy particles in a finite temperature medium. In Fokker-Planck dynamics, it is ensured by the Einstein relation between the drag and longitudinal momentum diffusion coefficients. However, in certain gauge field theories, this relation is violated at any nonzero heavy quark velocity. Recent work in strongly coupled $\mathcal{N}=4$ SYM gauge theory shows that the Kolmogorov equation for the heavy quark phase space distribution (that reduces to Fokker-Planck form upon truncating the momentum transfer probability distribution to second moments) does equilibrate even though the Fokker-Planck equation does not. Going beyond these (to date theory-specific) insights, we derive a universal equilibration condition for the kernel of the Kolmogorov equation and, consequently, for the momentum transfer probability distribution that holds in any quantum field theory with any coupling strength. This condition, which is the generalization of the Einstein relation to quantum field theories which feature non-Gaussian fluctuations, reveals that the asymmetry between energy loss and energy gain in the momentum transfer probability distribution takes a simple, theory-independent, form.

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arXiv2025

Connecting Pre-Thermal and Hydrodynamizing Attractors With Adiabatic Hydrodynamization

The far-from equilibrium dynamics of the pre-hydrodynamic quark-gluon plasma (QGP) formed in heavy ion collisions can be characterized by distinct stages, during each of which the system loses some memory of its initial condition, until only the hydrodynamic modes remain. However, even though it has been repeatedly observed, finding intuitive physical explanations of how and why attractor behavior occurs has remained a challenge. The Adiabatic Hydrodynamization (AH) framework provides exactly such an explanation, showing that the attractor solution can be thought of as the ground state of an analog to quantum mechanical adiabatic evolution, provided we identify appropriate coordinate rescalings. Using the example of a simplified QCD kinetic theory in the small-angle scattering limit, we show how AH can explain both the early pre-hydrodynamic attractor and the later hydrodynamizing attractor in a longitudinally expanding gluon gas in a unified framework. By doing this, we provide a unified description of, and intuition for, all the stages of what in QCD would be bottom-up thermalization, starting from a pre-hydrodynamic attractor and ending with hydrodynamization.

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