Probing the Short-Distance Structure of the Quark-Gluon Plasma with Energy Correlators.

Energy-energy correlators (EECs) are promising observables to study the dynamics of jet evolution in the quark-gluon plasma (QGP) through its imprint on angular scales in the energy flux of final-state particles. We carry out the first complete calculation of EECs using realistic simulations of high-energy heavy-ion collisions and dissect the different dynamics underlying the final distribution through analyses of jet propagation in a uniform medium. The EECs of γ-jets in heavy-ion collisions are found to be enhanced by the medium response from elastic scatterings instead of induced gluon radiation at large angles. In the meantime, EECs are suppressed at small angles due to energy loss and transverse momentum broadening of jet shower partons. These modifications are further shown to be sensitive to the angular scale of the in-medium interaction, as characterized by the Debye screening mass. Experimental verification and measurement of such modifications will shed light on this scale and the short-distance structure of the QGP in heavy-ion collisions.

Spin Alignment of Vector Mesons in Heavy-Ion Collisions.

Polarized quarks and antiquarks in high-energy heavy-ion collisions can lead to the spin alignment of vector mesons formed by quark coalescence. Using the relativistic spin Boltzmann equation for vector mesons derived from Kadanoff-Baym equations with an effective quark-meson model for strong interaction and quark coalescence model for hadronizaton, we calculate the spin density matrix element ρ_{00} for ϕ mesons and show that anisotropies of local field correlations with respect to the spin quantization direction lead to ϕ meson's spin alignment. We propose that the local correlation or fluctuation of ϕ fields is the dominant mechanism for the observed ϕ meson's spin alignment and its strength can be extracted from experimental data as functions of collision energies. The calculated transverse momentum dependence of ρ_{00} agrees with STAR's data. We further predict the azimuthal angle dependence of ρ_{00} which can be tested in future experiments.

3D Structure of Jet-Induced Diffusion Wake in an Expanding Quark-Gluon Plasma.

The diffusion wake accompanying the jet-induced Mach cone provides a unique probe of the properties of quark-gluon plasma in high-energy heavy-ion collisions. It can be characterized by a depletion of soft hadrons in the opposite direction of the propagating jet. We explore the 3D structure of the diffusion wake induced by γ-triggered jets in Pb+Pb collisions at the LHC energy within the coupled linear Boltzmann transport and hydro model. We identify a valley structure caused by the diffusion wake on top of a ridge from the initial multiple parton interaction (MPI) in jet-hadron correlation as a function of rapidity and azimuthal angle. This leads to a double-peak structure in the rapidity distribution of soft hadrons in the opposite direction of the jets as an unambiguous signal of the diffusion wake. Using a two-Gaussian fit, we extract the diffusion wake and MPI contributions to the double peak. The diffusion wake valley is found to deepen with the jet energy loss as characterized by the γ-jet asymmetry. Its sensitivity to the equation of state and shear viscosity is also studied.

From Hydrodynamics to Jet Quenching, Coalescence, and Hadron Cascade: A Coupled Approach to Solving the R_{AA}⊗v_{2} Puzzle.

Hydrodynamics and jet quenching are responsible for the elliptic flow v_{2} and suppression of large transverse momentum (p_{T}) hadrons, respectively, two of the most important phenomena leading to the discovery of a strongly coupled quark-gluon plasma in high-energy heavy-ion collisions. A consistent description of the hadron suppression factor R_{AA} and v_{2}, especially at intermediate p_{T}, however, remains a challenge. We solve this long-standing R_{AA}⊗v_{2} puzzle by including quark coalescence for hadronization and final state hadron cascade in the coupled linear Boltzmann transport-hydro model that combines concurrent jet transport and hydrodynamic evolution of the bulk medium. We illustrate that quark coalescence and hadron cascade, two keys to solving the puzzle, also lead to a splitting of v_{2} for pions, kaons, and protons in the intermediate p_{T} region. We demonstrate for the first time that experimental data on R_{AA}, v_{2}, and their hadron flavor dependence from low to intermediate and high p_{T} in high-energy heavy-ion collisions can be understood within this coupled framework.

Search for the Elusive Jet-Induced Diffusion Wake in Z/γ-Jets with 2D Jet Tomography in High-Energy Heavy-Ion Collisions.

Diffusion wake is an unambiguous part of the jet-induced medium response in high-energy heavy-ion collisions that leads to a depletion of soft hadrons in the opposite direction of the jet propagation. New experimental data on Z-hadron correlation in Pb+Pb collisions at the Large Hadron Collider show, however, an enhancement of soft hadrons in the direction of both the Z and the jet. Using a coupled linear Boltzmann transport and hydro model, we demonstrate that medium modification of partons from the initial multiple parton interaction (MPI) gives rise to a soft hadron enhancement that is uniform in azimuthal angle while jet-induced medium response and soft gluon radiation dominate the enhancement in the jet direction. After subtraction of the contributions from MPI with a mixed-event procedure, the diffusion wake becomes visible in the near-side Z-hadron correlation. We further employ the longitudinal and transverse gradient jet tomography for the first time to localize the initial jet production positions in Z/γ-jet events in which the effect of the diffusion wake is apparent in Z/γ-hadron correlation even without the subtraction of the MPI contribution.

Jet quenching and medium response in high-energy heavy-ion collisions: a review.

Jet quenching has been used successfully as a hard probe to study properties of the quark-gluon plasma (QGP) in high-energy heavy-ion collisions at both the relativistic heavy-ion collider and the large hadron collider. We will review recent progresses in theoretical and phenomenological studies of jet quenching with jet transport models. Special emphasis is given to effects of jet-induced medium response on a wide variety of experimental observables and their implications on extracting transport properties of the QGP in heavy-ion collisions.

Gradient Tomography of Jet Quenching in Heavy-Ion Collisions.

Transverse momentum broadening and energy loss of a propagating parton are dictated by the space-time profile of the jet transport coefficient q[over ^] in a dense QCD medium. The spatial gradient of q[over ^] perpendicular to the propagation direction can lead to a drift and asymmetry in parton transverse momentum distribution. Such an asymmetry depends on both the spatial position along the transverse gradient and path length of a propagating parton as shown by numerical solutions of the Boltzmann transport in the simplified form of a drift-diffusion equation. In high-energy heavy-ion collisions, this asymmetry with respect to a plane defined by the beam and trigger particle (photon, hadron, or jet) with a given orientation relative to the event plane is shown to be closely related to the transverse position of the initial jet production in full event-by-event simulations within the linear Boltzmann transport model. Such a gradient tomography can be used to localize the initial jet production position for more detailed study of jet quenching and properties of the quark-gluon plasma along a given propagation path in heavy-ion collisions.

Bayesian Extraction of Jet Energy Loss Distributions in Heavy-Ion Collisions.

Based on the factorization in perturbative QCD, a jet cross section in heavy-ion collisions can be expressed as a convolution of the jet cross section in p+p collisions and a jet energy loss distribution. Using this simple expression and the Markov Chain Monte Carlo method, we carry out Bayesian analyses of experimental data on jet spectra to extract energy loss distributions for both single inclusive and γ-triggered jets in Pb+Pb collisions with different centralities at two colliding energies at the Large Hadron Collider. The average jet energy loss has a dependence on the initial jet energy that is slightly stronger than a logarithmic form and decreases from central to peripheral collisions. The extracted jet energy loss distributions with a scaling behavior in x=Δp_{T}/⟨Δp_{T}⟩ have a large width. These are consistent with the linear Boltzmann transport model simulations, in which the observed jet quenching is caused on the average by only a few out-of-cone scatterings.

An equation-of-state-meter of quantum chromodynamics transition from deep learning.

A primordial state of matter consisting of free quarks and gluons that existed in the early universe a few microseconds after the Big Bang is also expected to form in high-energy heavy-ion collisions. Determining the equation of state (EoS) of such a primordial matter is the ultimate goal of high-energy heavy-ion experiments. Here we use supervised learning with a deep convolutional neural network to identify the EoS employed in the relativistic hydrodynamic simulations of heavy ion collisions. High-level correlations of particle spectra in transverse momentum and azimuthal angle learned by the network act as an effective EoS-meter in deciphering the nature of the phase transition in quantum chromodynamics. Such EoS-meter is model-independent and insensitive to other simulation inputs including the initial conditions for hydrodynamic simulations.

Vortical Fluid and Λ Spin Correlations in High-Energy Heavy-Ion Collisions.

Fermions become polarized in a vortical fluid due to spin-vorticity coupling, and the polarization density is proportional to the local fluid vorticity. The radial expansion converts spatial vortical structures in the transverse plane to spin correlations in the azimuthal angle of final Λ hyperons' transverse momentum in high-energy heavy-ion collisions. Using a (3+1)D viscous hydrodynamic model with fluctuating initial conditions from a multiphase transport (AMPT) model, we reveal two vortical structures that are common in many fluid dynamic systems: a right-handed toroidal structure around each beam direction for transverse vorticity and pairing of longitudinal vortices with opposite signs in the transverse plane. The calculated azimuthal correlation of the transverse spin is shown to have a cosine form plus an offset due to the toroidal structure of the transverse vorticity around the beam direction and the global spin polarization. The longitudinal spin correlation in the azimuthal angle shows an oscillatory structure due to multiple vorticity pairs in the transverse plane. Mechanisms of these vortical structures, physical implications of hyperon spin correlations, dependence on colliding energy, rapidity, centrality, and sensitivity to the shear viscosity are also investigated.

Next-to-leading order QCD factorization for semi-inclusive deep inelastic scattering at twist 4.

Within the framework of a high-twist approach, we calculate the next-to-leading order (NLO) perturbative QCD corrections to the transverse momentum broadening in semi-inclusive hadron production in deeply inelastic e+A collisions, as well as lepton pair production in p+A collisions. With explicit calculations of both real and virtual contributions, we verify, for the first time, the factorization theorem at twist 4 in NLO for the nuclear-enhanced transverse momentum weighted differential cross section and demonstrate the universality of the associated twist-4 quark-gluon correlation function. We also identify the QCD evolution equation for the twist-4 quark-gluon correlation function in a large nucleus, which can be solved to determine the scale dependence of the jet transport parameter in the study of jet quenching.

Medium modification of γ jets in high-energy heavy-ion collisions.

Two puzzling features in the experimental study of jet quenching in central Pb+Pb collisions at the LHC are explained within a linearized Boltzmann transport model for jet propagation. A γ-tagged jet is found to lose about 15% of its initial energy while its azimuthal angle remains almost unchanged due to rapid cooling of the medium. The reconstructed jet fragmentation function is found to have some modest enhancement at both small and large fractional momenta as compared to that in the vacuum because of the increased contribution of leading particles to the reconstructed jet energy and induced gluon radiation and recoiled partons. A γ-tagged jet fragmentation function is proposed that is more sensitive to jet-medium interaction and the jet transport parameter in the medium. The effects of recoiled medium partons on the reconstructed jets are also discussed.

Berry curvature and four-dimensional monopoles in the relativistic chiral kinetic equation.

We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a four-dimensional Euclidean Berry monopole which gives an axial anomaly. By integrating out the zeroth component of the 4-momentum p, we reproduce the previous three-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields (FσρF[over ˜]σρ∼EσBσ). This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions.

Chiral anomaly and local polarization effect from the quantum kinetic approach.

A power expansion scheme is set up to determine the Wigner function that satisfies the quantum kinetic equation for spin-1/2 charged fermions in a background electromagnetic field. Vector and axial-vector current induced by magnetic field and vorticity are obtained simultaneously from the Wigner function. The chiral magnetic and vortical effect and chiral anomaly are shown as natural consequences of the quantum kinetic equation. The axial-vector current induced by vorticity is argued to lead to a local polarization effect along the vorticity direction in heavy-ion collisions.

Jets, Mach cones, hot spots, ridges, harmonic flow, dihadron, and γ-hadron correlations in high-energy heavy-ion collisions.

Within the AMPT Monte Carlo model, fluctuations in the initial transverse parton density are shown to lead to harmonic flows. The net back-to-back dihadron azimuthal correlation after subtraction of contributions from harmonic flows still has a double peak that is independent of the initial geometric triangularity and unique to the jet-induced Mach cone and expanding hot spots distorted by radial flow. The longitudinal structure of hot spots also leads to a nearside ridge in dihadron correlation with a large rapidity gap. By successively randomizing the azimuthal angle of the transverse momenta and positions of initial partons, one can isolate the effects of jet-induced medium excitation and expanding hot spots on the dihadron azimuthal correlation. The double peaks in the net dihadron and γ-hadron correlation are quantitatively different since the later is caused only by jet-induced Mach cone.

Mach cone induced by γ-triggered jets in high-energy heavy-ion collisions.

Medium excitation by jet shower propagation inside a quark-gluon plasma is studied within a linear Boltzmann transport and a multiphase transport model. Contrary to the naive expectation, it is the deflection of both the jet shower and the Mach-cone-like excitation in an expanding medium that is found to give rise to a double-peak azimuthal particle distribution with respect to the initial jet direction. Such a deflection is the strongest for hadron-triggered jets which are often produced close to the surface of a dense medium due to trigger bias and travel against or tangential to the radial flow. Without such trigger bias, the effect of deflection on γ-jet showers and their medium excitation is weaker. Comparative study of hadron and γ-triggered particle correlations can therefore reveal the dynamics of jet-induced medium excitation in high-energy heavy-ion collisions.

Tomography of high-energy nuclear collisions with photon-hadron correlations.

Within the next-to-leading order (NLO) perturbative QCD (PQCD) parton model, suppression of away-side hadron spectra associated with a high pT photon due to parton energy loss is studied in high-energy heavy-ion collisions. Because of the sharp falloff of the gamma-jet spectrum in momentum imbalance pTjet-pTgamma>0 in NLO PQCD, hadron spectra at large zT=pTh/pTgamma greater than approximately 1 are more susceptible to parton energy loss and therefore are dominated by surface emission of gamma-associated jets with almost no energy loss, whereas small zT hadrons mainly come from the volume emission of jets with reduced energy. These lead to different centrality dependence of the gamma-hadron suppression for different values of zT. Therefore, a complete measurement of the suppression of gamma-triggered hadron spectra allows a true tomographic study of the quark-gluon plasma in high-energy heavy-ion collisions.

Modified dihadron fragmentation functions in hot and nuclear matter.

Medium modification of dihadron fragmentation functions due to gluon bremsstrahlung induced by multiple partonic scattering is studied in both deep-inelastic scattering (DIS) off large nuclei and high-energy heavy-ion collisions within the same framework of twist expansion. The modification for dihadrons is found to closely follow that for single hadrons, leading to a weak nuclear suppression of their ratios in DIS experiments. A mild enhancement of the near-side correlation of two high transverse momentum hadrons with increasing centrality is found in heavy-ion collisions due to trigger bias and the rise in parton energy loss with centrality. Successful comparisons between theory and experiment for multihadron observables in both confining and deconfined media offer comprehensive evidence for partonic energy loss as the mechanism of jet modification in dense matter.

Dihadron tomography of high-energy nuclear collisions in next-to-leading order perturbative QCD.

Dihadron spectra in high-energy heavy-ion collisions are studied within the next-to-leading order perturbative QCD parton model with modified jet fragmentation functions due to jet quenching. High-p(T) back-to-back dihadrons are found to originate mainly from jet pairs produced close and tangential to the surface of the dense matter. However, a substantial fraction also comes from jets produced at the center with finite energy loss. Consequently, high-p(T) dihadron spectra are found to be more sensitive to the initial gluon density than the single hadron spectra that are more dominated by surface emission. A simultaneous chi(2) fit to both the single and dihadron spectra can be achieved within a range of the energy loss parameter E(0)=1.6-2.1 GeV/fm. Because of the flattening of the initial jet production spectra at square root s=5.5 TeV, high p(T) dihadrons are found to be more robust as probes of the dense medium.

Small shear viscosity of a quark-gluon plasma implies strong jet quenching.

We derive an expression relating the transport parameter q and the shear viscosity eta of a weakly coupled quark-gluon plasma. A deviation from this relation can be regarded as a quantitative measure of "strong coupling" of the medium. The ratio T{3}/q, where T is the temperature, is a more broadly valid measure of the coupling strength of the medium than eta/s, where s denotes the entropy density. Different estimates of q derived from existing Relativistic Heavy Ion Collider data are shown to imply radically different structures of the produced matter.