Azimuthal anisotropy is studied by taking into account the ridges created by semi-hard scattering, which is sensitive to the initial spatial configuration in non-central heavy-ion collisions. No rapid thermalization is required. Although hydrodynamics is not used in this study, the validity of hydrodynamical expansion is not excluded at later time after equilibration is achieved. Phenomenological properties of the bulk and ridge behaviors are used as inputs to determine the elliptic flow of pion and proton at low p_T. At intermediate p_T the recombination of shower partons with thermal partons becomes more important. The phi dependence arises from the variation of the in-medium path length of the hard parton that generates the shower. The p_T dependence of v_2 is therefore very different at intermediate p_T compared to that at low p_T. Quark number scaling of v_2 is shown to be only approximately valid at low p_T, but is broken at intermediate p_T, even though recombination is the mechanism of hadronization in all p_T regions considered.
Hadron correlations in jets, ridges and opposite dijets at all $p_T$ above 2 GeV/c are discussed. Since abundant data are available from RHIC at intermediate $p_T$, a reliable hadronization scheme at that $p_T$ range is necessary in order to relate the semihard partonic processes to the observables. The recombination model is therefore first reviewed for that purpose. Final-state interaction is shown to be important for the Cronin effect, large B/M ratio and forward production. The effect of semihard partons on the medium is then discussed with particular emphasis on the formation of ridge wit…
The formation of ridges induced by semihard scattering in nuclear collisions is included in the description of single-particle distributions for both pion and proton at low transverse momenta. The ridge component is characterized by an azimuthal dependent factor that is derived in the study of the ridge structure in two-particle correlation distributions involving triggers. It is shown that the inclusive ridge can reproduce the observed data on $v_2(p_T)$ if the base component underlying the ridge has no azimuthal dependence. A common description of pion and proton spectra is given in the reco…
The azimuthal angular dependence of the nuclear modification factor R_{AA}(p_T, phi,N_{part}) recently obtained by PHENIX is related at low p_T to the trigger phi dependence of the ridge yield as measured by STAR in a framework in which the azimuthal anisotropy is driven by semihard scattering near the surface. Careful consideration of the initial geometry leads to the determination of a surface segment in which the production of semihard partons are responsible for the phi dependence of the inclusive distribution on the one hand, and for the angular correlation in ridge phenomenology on the o…
We calculate the triple- and quadruple-gluon inclusive distributions with arbitrary rapidity and azimuthal angle dependences in the gluon saturation regime by using glasma diagrams. Also, we predict higher-dimensional ridges in triple- and quadruple-hadron correlations for p-p and p-Pb collisions at LHC, which have yet to be measured. In p-p and p-Pb collisions at the top LHC energies, gluon saturation is expected to occur since smaller Bjorken-$x$ values are being probed. Glasma diagrams, which are enhanced at small-$x$, include the gluon saturation effects, and they are used for calculating …
Correlation studies exhibit a ridge-like feature in rapidity and azimuthal angle, with and without a jet trigger. We ask whether the feature in untriggered correlations can be a consequence of transverse flow and viscous diffusion.
Ridge formation in near-side correlation in heavy-ion collisions is studied in the framework of a phenomenological model, called Correlated Emission Model (CEM). Successive soft emissions due to jet-medium interaction lead to the enhancement of thermal partons which follow the local flow directions. The correlation between the flow direction and the semihard parton direction is the major factor that causes the ridge formation to depend on the trigger direction relative to the reaction plane. With the use of a few parameters we have been able to reproduce the data on the ridge yields as functio…
Nuclear collisions exhibit long-range rapidity correlations not present in proton-proton collisions. Because the correlation structure is wide in relative pseudorapidity and narrow in relative azimuthal angle, it is known as the ridge. Similar ridge structures are observed in correlations of particles associated with a jet trigger (the hard ridge) as well as correlations without a trigger (the soft ridge). Earlier we argued that the soft ridge arises when particles formed in an early Glasma stage later manifest transverse flow. We extend this study to address new soft ridge measurements. We th…
We review the models suggested, to date, as an explanation for the so called "ridge" phenomenon, an elongation in rapidity of 2-particle correlations seen at RHIC and LHC energies. We argue that these models can be divided into two phenomenologically distinct classes: "Hotspot+flow" driven correlations, where initial state correlations created by structures local in configuration space are collimated by transverse flow, and models where the azimuthal correlation is created through local partonic interactions in a high gluon density initial state. We further argue that the key to distinguish th…
Recombination is a hadronization process that converts partons to hadrons at late time, but the description has no quantitative significance without some meaningful input on the parton distributions at earlier time. Thus observations of particle spectra and correlations have definitive implications on the partonic processes at all transverse momenta. After presenting a general review of the subject at the Workshop, I selected two topics in nuclear collisions for more detailed discussion, which are summarized here. One is on the azimuthal anisotropy at low $p_T$ due to hard or semihard scatteri…
The ridge signal, which is long-ranged in rapidity, in the di-hadron correlations in high-multiplicity p-p and p-A collisions opened up a whole new research area in high-energy QCD. Although the ridge had been observed in A-A collisions and interpreted as a result of the radial flow of quark-gluon plasma, it had not appeared until recently in the data of small collision systems such as p-p and p-A, nor had it been predicted theoretically or seen in the event generators. There are two competing approaches that attempt to explain the systematics of the di-hadron ridge signal; hydrodynamics and g…
Pseudorapidity and azimuthal three-particle correlations are studied based on a correlated-cluster model of multiparticle production. The model provides a common framework for correlations in proton-proton and heavy-ion collisions allowing easy comparison with the measurements. It is shown that azimuthal cluster correlations are definitely required in order to understand three-particle correlations in the near-side ridge effect. This is similar to the explanation of the ridge phenomenon found in our previous analysis of two-particle correlations and generalizes the model to higher-order correl…
Azimuthal anisotropy in heavy-ion collisions is studied by taking into account the ridges generated by semi-hard scattering of intermediate-momentum partons, which can be sensitive to the initial spatial configuration of the medium in non-central collisions. In a simple treatment of the problem where the recombination of only thermal partons is considered, analytical formulas can be derived that yield results in accord with the data on v_2 for p_T <1-2 GeV/c. Centrality dependence is described by a geometrical factor. Ridge phenomenology is used to determine the initial slopes of v_2 at low p_…
The production of hadrons in heavy-ion collisions at RHIC in the low transverse-momentum ($p_T$) region is investigated in the recombination model with emphasis on the effects of minijets on the azimuthal anisotropy. Since the study is mainly on the hadronization of partons at late time, the fluid picture is not used to trace the evolution of the system. The inclusive distributions at low $p_T$ are determined as the recombination products of thermal partons. The $p_T$ dependencies of both pion and proton have a common exponential factor apart from other dissimilar kinematic and resonance facto…
Correlation measurements indicate that excess two particle correlations extend over causally disconnected rapidity ranges. Although, this enhancement is broad in relative rapidity $η=η_1 - η_2$, it is focused in a narrow region in relative azimuthal angle $ϕ=ϕ_1 - ϕ_2$. The resulting structure looks like a ridge centered at $η= ϕ=0$. Similar ridge structures are observed in correlations of particles associated with a jet trigger (the hard ridge) and in correlations without a trigger (the soft ridge). The long range rapidity behavior requires that the correlation originates in the earliest stag…
A review is given on the subject of hadron production at intermediate $p_T$ in heavy-ion collisions. The underlying dynamical processes are inferred from interpreting the data in the framework of recombination. Ridge formation with or without triggers is found to play an important role in nearly all observables in that $p_T$ region. Correlation data would be hard to interpret without taking ridges into account. The semi-hard partons that create the ridges may even be able to drive elliptic flow without fast thermalization.
Within the AMPT Monte Carlo model, hot spots in the initial transverse parton density are shown to lead to harmonic flows which all contribute to dihadron azimuthal correlation. The net back-to-back dihadron correlation after subtraction of harmonic flows still has a double-peak that is independent of the initial geometric triangularity at a fixed impact-parameter and unique to the structure of jet-induced Mach cone and expanding hot spots dragged by radial flow. The longitudinal structure of hot spots also leads to a near-side ridge in dihadron correlation with a large rapidity gap. By succes…
Here I review the transverse momentum distributions of identified hadrons produced in Au-Au collisions at RHIC and Pb-Pb collisions at LHC in the framework of recombination model. Minijets play an important role in generating shower partons in the intermediate $p_T$ region. At LHC, the resultant soft shower partons are even found to dominate over the thermal partons in the non-strange sector. The azimuthal anisotropy of the produced hadrons could also be explained as the consequence of the effects of minijets. Harmonic analysis of the $ϕ$ dependence leads to $v_n(p_T, b)$ that can be well prod…
The azimuthal anisotropy due to path-length dependent jet energy loss is studied in a simple jet absorption model that include event by event fluctuating Glauber geometry. Significant anisotropy coefficients v_n are observed for n=1,2 and 3, but they are very small for n>3. These coefficients are expected to result in a "ridge" for correlations between two independently produced jets. The correlations between the orientation of the n^{th}-order anisotropy induced by jet absorption (Φ_n^{QP}) and the n^{th}-order participant plane (Φ_n^{PP}) responsible for harmonic flow are studied. Tight corr…
For heavy-ion collisions at RHIC a scaling behavior is found in the dependencies on azimuthal angle $ϕ$ and impact parameter $b$ for pion production at high $p_T$ essentially independent of the hadronization process. The scaling variable is in terms of a dynamical path length $ξ$ that takes into account detailed properties of geometry, medium density and probability of hard scattering. It is shown in the recombination model how the nuclear modification factor depends on the average $\barξ(ϕ,b)$. The data for $π^0$ production at $p_T=$ 4-5 and 7-8 GeV/c at RHIC are shown to exhibit the same sca…
We calculate the inclusive gluon correlation function for arbitrary number of gluons with full rapidity and transverse momentum dependence for the initial glasma state of the p-p, p-A and A-A collisions. The formula we derive via superdiagrams generates cumulants for any number of gluons. Higher order cumulants contain information on correlations between multiple gluons, and they are necessary for calculations of higher dimensional ridges as well as flow coefficients from multi-particle correlations.
An event generator is constructed on the basis of a model of multiple scattering of partons so that the trajectory of a parton traversing a dense and expanding medium can be tracked. The parameters in the code are adjusted to fit the Δϕazimuthal distribution on the far side when the trigger momentum is in the non-perturbative region, p_T(trigger)<4 GeV/c. The dip-bump structure for 1<p_T(assoc)<2.5 GeV/c is reproduced by averaging over the exit tracks of deflected jets. An essential characteristic of the model, called Markovian Parton Scattering (MPS) model, is that the scattering angle is ran…
The creation of partons with transverse momenta around 10 GeV/c in Pb-Pb collisions at LHC is expected to be so copious that the parton density may be high enough for neighboring jet cones to overlap. If the shower partons in adjacent jets can recombine to form trigger particles, the distribution of hadrons on the away side should be distinguishable from that due to the recoil of a single harder parton that can produce a similar trigger particle by fragmentation. The two-particle azimuthal correlation on the away side is generated by simulation of the two trigger types. Moments of the correlat…
In this paper we present with full details a systematic quantification, on an even-by-event basis, of the hard probe response to the geometry and fluctuations of the hot QCD matter created in heavy ion collisions at both the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The azimuthal anisotropy of jet quenching is extracted and decomposed as harmonic responses (for n=1,2,3,4,5,6) to the corresponding harmonics in the fluctuating initial condition. We show that such jet response harmonics are sensitive to the jet quenching models as well as to the bulk matter initi…
Autocorrelation of two pions produced in heavy-ion collisions at intermediate $p_T$ is calculated in the framework of the recombination model. The differences of the pseudo-rapidities and azimuthal angles of the two pions are related to the angle between two shower partons in a jet. It is shown how the autocorrelation distribution reveals the properties of jet cone of the shower partons created by high-$p_T$ partons in hard collisions.
In this paper we study the jet response (particularly azimuthal anisotropy) as a hard probe of the harmonic fluctuations in the initial condition of central heavy ion collisions. By implementing the fluctuations via cumulant expansion for various harmonics quantified by $ε_n$ and using the geometric model for jet energy loss, we compute the response $χ^h_n=v_n/ε_n$. Combining these results with the known hydrodynamic response of the bulk matter expansion in the literature, we show that the hard-soft azimuthal correlation arising from their respective responses to the common geometric fluctuati…
We develop a framework of coupled transport equations for open heavy flavor and quarkonium states, in order to describe their transport inside the quark-gluon plasma. Our framework is capable of studying simultaneously both open and hidden heavy flavor observables in heavy-ion collision experiments and can account for both, uncorrelated and correlated recombination. Our recombination implementation depends on real-time open heavy quark and antiquark distributions. We carry out consistency tests to show how the interplay among open heavy flavor transport, quarkonium dissociation and recombinati…
In this brief review of the observable effects of minijets in heavy-ion collisions the main points emphasized are that the quadruple moment $v_2(p_T,b)$ and the hadronic ($π$ and $p$) spectra at low $p_T$ can both be reproduced by minijet contributions to the recombination of thermal and shower partons. Without using hydrodynamics the minijet approach does not trace the evolution of the expanding system. The thermal distribution of the medium partons at the time of hadronization is assumed, but rapid thermalization initially is not required so as to allow minijets to leave their footprints on …
We employ the Boltzmann equation for describing hadron production from a quark-gluon plasma (QGP) in ultrarelativistic heavy-ion collisions. We propose resonance formation in quark-antiquark scattering as the dominant meson-production channel, which, in particular, ensures that energy is conserved in the recombination process. This, in turn, facilitates a more controlled extension of hadronization to low transverse momenta ($p_T$), and to address the experimentally observed transition from a hydrodynamic regime to constituent quark-number scaling (CQNS). Based on input distributions for strang…
