A very recent paper by the CMS collaboration \cite{cms_ridge} has created large discussion in the media, which call it important but did not explain why, in some places even calling it "unundestandable". While it is of course too soon to know what causes the correlations in question, a very similar observation in heavy ion collisions at RHIC has rather simple explanation related to explosion of high energy density matter. Perhaps this observation is the first hint for an explosive behavior in pp, which was anticipated and looked for for decades, yet never been seen.
We discuss the physics of the ridge -- azimuthally collimated long range rapidity correlations -- in high multiplicity proton-proton and proton-nucleus collisions. We outline some of the theoretical discussions in the literature that address the systematics of these ridge correlations.
We demonstrate that the recent measurement of azimuthally collimated, long range rapidity ("ridge") correlations in $\sqrt{s}=13$ TeV proton-proton (p+p) collisions by the ATLAS collaboration at the LHC are in agreement with expectations from the color glass condensate effective theory of high energy QCD. The observation that the integrated near side yield as a function of multiplicity is independent of collision energy is a natural consequence of the fact that multiparticle production is driven by a single semi-hard saturation scale in the color glass condensate framework. We argue further th…
The CMS collaboration has recently reported the appearance of a same-side "ridge" structure in two-particle angular correlations from 7 TeV p-p collisions. The ridge in p-p collisions at 7 TeV has been compared to a ridge structure in more-central Au-Au collisions at 0.2 TeV interpreted by some as evidence for a dense, flowing QCD medium. In this study we make a detailed comparison between 0.2 TeV p-p correlations and the CMS results. We find that 7 TeV minimum-bias jet correlations are remarkably similar to those at 0.2 TeV, even to the details of the same-side peak geometry. Extrapolation of…
A phenomenological analysis is presented of recent two-particle angular correlation data on relative pseudorapidity ($η$) and azimuth reported by the Compact Muon Solenoid (CMS) Collaboration for $\sqrt{s}$ = 7 TeV proton-proton collisions. The data are described with an empirical jet-like model developed for similar angular correlation measurements obtained from heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC). The same-side (small relative azimuth), $η$-extended correlation structure, referred to as the {\em ridge}, is compared with three phenomenological correlation struct…
We look at the new two-particle Bose-Einstein correlation (BEC) function accompanied by the color-electric flux model which can explain the "ridge" behavior in enhanced angular correlation between two identical pions at very broad rapidity with high multiplicity. We argue that such an investigation could probe both the size and the temperature of the source of two pions emitted into a narrow range of azimuthal angles. We can confirm the ev- idence for quark-gluon phase due to interaction of outgoing pions (having high transverse momenta) with the medium in thermal bath in proton-proton collisi…
The CMS data on the multiplicity distributions are compared with the results from the 8.142 version of the PYTHIA MC event generator with the default tuning and realistic impact parameter profile. The agreement is reasonable. However, it seems to be difficult to improve further this agreement by tuning the parameters determining the multiple parton interactions.
We show that the "ridge" phenomenon in the two-particle angular correlation function, as observed by the CMS experiment, can be reproduced by implementing an impact parameter dependent azimuthal correlation of the scattering planes of individual partonic interactions. Such an approach is motivated by the observation that even for moderate impact parameters a substantial number of partonic interactions may be produced, while at the same time the protons are sufficiently far apart to create a preferential direction in azimuth. A re-tune of the Pythia6 Z2 tune based on underlying event and minimu…
In a recent article (arXiv:1210.3890), we showed that high multiplicity di-hadron proton- proton (p+p) data from the CMS experiment are in excellent agreement with computations in the Color Glass Condensate (CGC) Effective Field Theory (EFT). This agreement of the theory with several hundred data points provides a non-trivial description of both nearside ("ridge") and away-side azimuthal collimations of long range rapidity correlations in p+p collisions. Our prediction in arXiv:1210.3890 for proton-lead (p+Pb) collisions is consistent with results from the recent CMS p+Pb run at $\sqrt{s}_{\rm…
The observation of long range ridge-like structure in the near-side region of the two particle $Δη-Δϕ$ correlations as measured by LHC experiments in high multiplicity p$-$p collisions indicated towards the presence of collective effects which are similar to that observed in p$-$A(nucleon-nucleus) and A$-$A (nucleus-nucleus) collisions. The two particle correlation between the charged particles in $Δη-Δϕ$ for p$-$p collisions at $\sqrt{s}$ = 7 TeV and 13 TeV is studied using Pythia 8 event generator within the framework of final-state partonic color reconnection effects as well as the microsco…
The recently reported effect of long-range near-side angular correlations at LHC occurs for large multiplicities of particles with $1\,GeV\,<p_T\,<\,3\,GeV$. To understand the effect several possibilities have been discussed. In the letter we propose a simple qualitative mechanism which corresponds to gluon bremstralung of quarks moving with acceleration appropriate to the quark--anti-quark string. The smallness of azimuthal angle difference $Δϕ$ along with large $Δη$ at large multiplicities in this interval of $p_T$ are natural in the mechanism. The mechanism predicts also bremstralung photon…
An unexpected result at the RHIC and the LHC is the observation that high-multiplicity hadronic events in heavy-ion and proton-proton collisions are distributed as two "ridges", approximately flat in rapidity and opposite in azimuthal angle. We propose that the origin of these events is due to the inelastic collisions of aligned gluonic flux tubes that underly the color confinement of the quarks in each proton. We predict that high-multiplicity hadronic ridges will also be produced in the high energy photon-photon collisions accessible at the LHC in ultra-peripheral proton-proton collisions or…
The CMS collaboration at the LHC has reported a remarkable and unexpected phenomenon in very high-multiplicity high energy proton-proton collisions: a positive correlation between two particles produced at similar azimuthal angles, spanning a large range in rapidity. We suggest that this "ridge"-like correlation may be a reflection of the rare events generated by the collision of aligned flux tubes connecting the valence quarks in the wave functions of the colliding protons. The "spray" of particles resulting from the approximate line source produced in such inelastic collisions then gives ris…
An energy independent scaling of the near-side ridge yield at a given multiplicity has been observed by the ATLAS and the CMS collaborations in p+p collisions at s = 7 and 13 TeV. Such a striking feature of the data can be successfully explained by approaches based on initial state momentum space correlation generated due to gluon saturation. In this paper, we try to examine if such a scaling is also an inherent feature of the approaches that employ strong final state interaction in p+p collisions. We find that hydrodynamical modeling of p+p collisions using EPOS 3 shows a violation of such sc…
In this study, the momentum-kick model is used to understand the ridge behaviours in dihadron $Δη$--$Δφ$ correlations recently reported by the LHC in high-multiplicity proton-proton (pp) collisions. The kick stand model is based on a momentum kick by leading jets to partons in the medium close to the leading jets. The medium where partons move freely is assumed in the model regardless of collision systems. This helps us apply the method to small systems like pp collisions in a simple way. Also, the momentum transfer is purely kinematic and this provides us a strong way to approach the ridge be…
In this paper we report the effect of the jet-medium interplay as implemented in EPOS 3 on the ridge like structure observed in high multiplicity p-Pb collisions at $\sqrt{s_{NN}} = $ 5.02 TeV. EPOS 3 takes into account hydrodynamically expanding bulk matter, jets and the jet-medium interaction. The basis of this model is multiple scatterings where each scattering finally produces flux tube / string. In the higher multiplicity event classes where the flux tube/string density is higher, there is a finite probability that the strings will pick up quarks and antiquarks (or diquarks) from the bulk…
We discuss the possibility of quantum entanglement for pairs of charged particles produced in high-energy $pp$-collisions at the LHC. Using a framework of interacting Wilson lines, we calculate 2-D and 1-D two-particle angular correlation functions in terms of the differences of the pseudorapidities and azimuthal angles of the produced particles. The calculated near-side angular correlation shows a localized maximum around $Δϕ\approx 0$, though it is less pronounced compared to the peak observed by the CMS Collaboration. We argue that this soft correlation is universal and insensitive to the s…
An interpretation of the ridge phenomenon found in pp collisions at 7 TeV is given in terms of enhancement of soft partons due to energy loss of semihard jets. A description of ridge formation in nuclear collisions can directly be extended to pp collisions, since hydrodynamics is not used, and azimuthal anisotropy is generated by semihard scattering. Both the p_T and multiplicity dependencies are well reproduced. Some suggestions are made about other observables.
A few-body proton image, expected to be derivable from QCD in the renormalization group procedure for effective particles, is used within the Monte Carlo Glauber model to calculate the anisotropy coefficients in the initial collision-state of matter in high-energy high-multiplicity proton-proton interaction events. We estimate the ridge-like correlations in the final hadronic state by assuming their proportionality to the initial collision-state anisotropy. In our estimates, some distinct few-body proton structures appear capable of accounting for the magnitude of p-p ridge effect, with potent…
Measurements of two-particle angular correlations of inclusive charged particles as well as identified strange hadron in pp and pPb collisions are presented over a wide range in pseudorapidity and full azimuth. The data were collected using the CMS detector at the LHC, with nucleon-nucleon center-of-mass energy of 5.02 TeV for pPb collisions and 5, 7, 13 TeV for pp collisions. The results are compared to semi-peripheral PbPb collision data at center-of-mass energy of 2.76 TeV, covering similar charged-particle multiplicity ranges of the events. For high-multiplicity pp and pPb events, a clear …
We show that the key features of the CMS result on the ridge correlation seen for high multiplicity events in sqrt(s)=7TeV proton-proton collisions at the LHC can be understood in the Color Glass Condensate framework of high energy QCD. The same formalism underlies the explanation of the ridge events seen in A+A collisions at RHIC, albeit it is likely that flow effects may enhance the magnitude of the signal in the latter.
One of the remarkable features of high-multiplicity hadronic events in proton-proton collisions at the LHC is the fact that the produced particles appear as two "ridges", opposite in azimuthal angle $ϕ$, with approximately flat rapidity distributions. This phenomena can be identified with the inelastic collision of gluonic flux tubes associated with the QCD interactions responsible for quark confinement in hadrons. In this paper we analyze the ridge phenomena when the collision involves a flux tube connecting the quark and antiquark of a high energy real or virtual photon. We discuss gluonic t…
Charged multiplicity distribution in a pseudo-rapidity window is formulated under the assumption that the charge conservation is satisfied in the full phase space. At first, we analyze measured charged particle multiplicity distributions in pseudo-rapidity windows in LHC by CMS and ALICE collaborations with the two probability distributions. One is the convolution of negative binomial and Poisson distributions, and the other is the Glauber-Lachs formula. Each distribution is considered as an analogy of the quantum optics. Next, we analyze the data with the double GL formulae for $|η|<2.4$ at 7…
The near-side ridge structure in the (Delta phi)-(Delta eta) correlation observed by the CMS Collaboration for pp collisions at 7 TeV at LHC can be explained by the momentum kick model in which the ridge particles are medium partons that suffer a collision with the jet and acquire a momentum kick along the jet direction. Similar to the early medium parton momentum distribution obtained in previous analysis for nucleus-nucleus collisions at 0.2 TeV, the early medium parton momentum distribution in pp collisions at 7 TeV exhibits a rapidity plateau as arising from particle production in a flux t…
We present persistently amassing evidence that the CMS and ATLAS Collaborations may indeed be already registering supersymmetry events at the Large Hadron Collider (LHC). Our analysis is performed in the context of a highly phenomenologically favorable model named No-Scale F-SU(5), which represents the unification of the F-lipped SU(5) Grand Unified Theory (GUT), two pairs of hypothetical TeV-scale vector-like supersymmetric multiplets derived out of F-Theory, and the dynamically established boundary conditions of No-Scale supergravity. We document highly suggestive correlations between the fi…
We investigate long range rapidity correlations of pairs of prompt photon and jet in the Color Glass Condensate (CGC) framework in proton-proton and proton-nucleus collisions at RHIC and the LHC. We show that photon-jet correlations exhibit long-range azimuthal collimation at near-side for low transverse momenta of the produced photon and jet in high-multiplicity events. These ridge-like features are strikingly similar to the observed ridge effect for di-hadron correlations at RHIC and the LHC. We show that correlations in the relative rapidity and the relative azimuthal angle between pairs of…
This study aims to analyze the data on multiplicity distributions and Bose-Einstein correlations collected at the LHC by the ATLAS and CMS Collaborations using a double-generalized Glauber-Lachs formula (D-GGL) and double-negative binomial distribution (D-NBD). From this investigation, it can be inferred that the D-GGL formula performs as effectively as the D-NBD. Moreover, our results show that the parameters estimated in multiplicity distributions (MD) (P(n)) are related to those contained in the BEC formula.
Experiments at the Large Hadron Collider (LHC) have measured multiplicity distributions in proton-proton collisions at a new domain of center-of-mass energy ($\sqrt {s}$) in limited pseudorapidity intervals. We analyze multiplicity distribution data of proton-proton collisions at LHC energies as measured by the Compact Muon Solenoid (CMS) experiment in terms of characteristic parameters of the Negative Binomial Distribution (NBD) function that has played a significant role in describing multiplicity distribution data of particle production in high energy physics experiments, in the pre-LHC ene…
The ALICE and CMS data on the multiplicity distributions are compared with the lower energy data and with the results from the 8.142 version of the PYTHIA MC event generator with two tunings. The ALICE data for moments are used to calculate the factorial cumulants. It is suggested that the data on moments or cumulants are well suited to specify the optimal tuning of the model parameters.
In the colour string picture with fusion and percolation it is shown that long range azimuthal-rapidity correlations (ridge) can arise from the superposition of many events with exchange of clusters of different number of strings and not from a single event. Relation of the ridge with the flow harmonics coefficients is derived. By direct Monte-Carlo simulations, in the technique previously used to calculate these coefficients, ridge correlations are calculated for AA, pA and pp collisions. The azimuthal anisotropy follows from the assumed quenching of the emitted particles in the strong colour…
The azimuthal collimation of di-hadrons with large rapidity separations in high multiplicity p+p collisions at the LHC is described in the Color Glass Condensate (CGC) effective theory [1] by N_c^2 suppressed multi-ladder QCD diagrams that are enhanced α_S^(-8) due to gluon saturation in hadron wavefunctions. We show that quantitative computations in the CGC framework are in good agreement with data from the CMS experiment on per trigger di-hadron yields and predict further systematics of these yields with varying trigger pT and charged hadron multiplicity. Radial flow generated by re-scatteri…
The CMS experiment at the Large Hadron Collider has recently presented data on the average transverse momentum of protons, kaons and pions as a function of particle multiplicity. We relate the particle multiplicity to saturation momentum using recently published computations of the interaction radius determined from the theory of the Color Glass Condensate. We show that the pp and the pA experimental data scale in terms of these saturation momenta. Computing transverse momentum spectra for identified particles using Boltzmann-type distributions and relating different associated multiplicities …
We present an evidence of strong radial flow in high-multiplicity pp collisions. We analyze the CMS data on the inclusive spectra of the charged pions, kaons and protons in the LHC $\sqrt{s}=7$ TeV collisions. For $<N_{\mathrm{tracks}} >\gtrsim 75$ we demonstrate the consistency of the hydrodynamic description with the (idealized) Gubser's flow. Using a one parameter fit of the model to experimental data, we obtain the initial fireball size to be of the order of 1 fm. At smaller multiplicities, the fit cannot be performed which shows a limitation of the hydrodynamic approach and provides us wi…
Experimental findings of CMS on properties of jets and underlying events at high multiplicities in proton-proton interactions at 7 TeV are interpreted as an indication of increasing role of central collisions with small impact parameters. We find an indication that the rates of different hard processes observed by CMS and ALICE universally depend on underlying event charged-particles multiplicity until it becomes four times more than average. It is shown that the increase of the overlap area of colliding protons is not sufficient for explanation of the rate of jet production in events with cha…
A new approach to phenomenological description of the charged particle multiplicity distributions in proton-(anti)proton and electron-positron collisions is presented. The observed features of the data are interpreted on the basis of stochastic-physical ideas of multiple production. Besides the processes of parton immigration and absorption, two and three patron incremental and decremental recombinations are considered. The complex behaviour of the multiplicity distributions at different energies is described by four parametric generalized hypergeometric distribution (GHD). Application of the …
We present a microscopic model for collective effects in high multiplicity proton--proton collisions, where multiple partonic subcollisions give rise to a dense system of strings. From lattice calculations we know that QCD strings are transversely extended, and we argue that this should result in a transverse pressure and expansion, similar to the flow in a deconfined plasma. The model is implemented in the PYTHIA8 Monte Carlo event generator, and we find that it can qualitatively reproduce the long range azimuthal correlations forming a near-side ridge in high multiplicity proton--proton even…
We analyze the structure of the high multiplicity events observed by the CMS collaboration at the LHC. We argue that the bulk of the observed correlations is due to the production of a pair of jets with p_t > 15 GeV/c. We also suggest that high multiplicity events are due to a combination of three effects: high underlying multiplicity for collisions at small impact parameters, upward fluctuations of the gluon density in the colliding protons, and production of hadrons in the fragmentation of dijets. The data analysis is suggested which may clarify the underlying dynamics of the high multiplici…
Recently exact numerical results from the evolution equation for parton multiplicities in QCD jets have been obtained. A comparison with various approximate results is presented. A good description is obtained not only of the jet multiplicities measured at LEP-1 but also of the hadron multiplicities for $cms$ energies above 1.6 GeV in \epem annihilation. The solution suggests that a final state hadron can be represented by a jet in the limit of small (nonperturbative) $k_\perp$ cut-off $Q_0$. In this description using as adjustable parameters only the QCD scale $Λ$ and the cut-off $Q_0$, the c…
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…
In this paper, transverse momentum spectra of pi+, K+ and p measured at fix event-multiplicities and \sqrt s = 0.9, 2.76 and 7 TeV collision energies by the CMS Collabotaion are shown to fit the Tsallis-distribution. It is found that the power of the distribution shows a double-logarithmic dependence on the event-multiplicity N, while the T parameter depends linearly on N. A similar double-logarithmic dependence of the q parameter of pi0 spectra on the collision energy \sqrt{s} is found too. It is also shown that event-by-event fluctuations of the multiplicity N and the total E_T energy going …
The similarities between string percolation and Glasma results are emphasized, special attention being paid to rapidity long range correlations, ridge structure and elliptic flow. As the string density of high multiplicity pp collisions at LHC energies has similar value as the corresponding to Au-Au semi-central collisions at RHIC we also expect in pp collisions long rapidity correlations and ridge structure, extended more than 8 units in rapidity.
Analysis of the charged multiplicity in proton-proton inelastic interactions at the LHC energies in the setting of Dual Parton Model is presented. Data from the CMS experiment and the data simulated at different energies in various pseudo-rapidity windows using the event generator PYTHIA8are analysed and compared with the calculations from the model. Each inelastic scattering is assumed to follow the Poisson distribution. The theoretical Koba-Nielsen-Olesen (KNO) scaling of the multiplicity distributions is studied and compared with previously published experimental results at $\sqrt{s}$ = 0.9…
One of the most promising probes to study deconfined matter created in high energy nuclear collisions is the energy loss of (heavy) quarks. It has been shown in experiments at the Relativistic Heavy Ion Collider (RHIC) that even charm and bottom quarks, despite their high mass, experience a remarkable medium suppression in the Quark Gluon Plasma. In this exploratory investigation we study the energy loss of heavy quarks in high multiplicity proton-proton collisions at LHC energies. Although the colliding systems are smaller than compared to those at RHIC (p+p vs. Au+Au) the higher energy might…
In this contribution we review recent progress with fixed-order QCD predictions for the production of a vector boson in association with jets at hadron colliders, using the programs BlackHat and SHERPA. We review general features of next-to-leading-order (NLO) predictions for the production of a massive vector boson in association with four jets. We also discuss how precise descriptions of vector-boson production can be applied to the determination of backgrounds to new physics signals. Here we focus on data-driven backgrounds to a missing-energy-plus-jets search performed by CMS. Finally, we …
The first moment <p_T> of the charged-particle transverse momentum spectrum and its correlation with the charged-particle multiplicity N_{ch} provide vital information about the underlying particle production mechanism. The ALICE collaboration recently reported that <p_T> versus N_{ch} in Pb+Pb collisions is smaller than in p+p and p+Pb collisions. Other interesting features of data is rather flatness of <p_T> at high N_{ch} in Pb+Pb and p+Pb collisions in seemingly striking contrast to the case of p+p collisions. With a detailed calculation, we show all these peculiar features in a wide range…
Using the negative binomial distribution (NBD) and the generalized Glauber-Lachs (GGL) formula, we analyze the data on charged multiplicity distributions in the several pseudorapidity intervals |η| < η_c at 0.2 - 7 TeV by UA5 and ALICE Collaborations. We confirm that the KNO scaling holds among the multiplicity distributions with η_c = 0.5 at \sqrt{s} = 0.2 - 2.36 TeV and estimate the energy dependence of a parameter 1/k in NBD and parameters 1/k and γ(the ratio of the average value of the coherent hadrons to that of the chaotic hadrons) in the GGL formula. Using empirical formulae for the par…
In the Color Glass Condensate formalism, charged hadron p_{T} distributions in p+p collisions are studied by considering an energy-dependent broadening of nucleon's density distribution. Then, in the Glasma flux tube picture, the n-particle multiplicity distributions at different pseudo-rapidity ranges are investigated. Both of the theoretical results show good agreement with the recent experimental data from ALICE and CMS at \sqrt{s}=0.9, 2.36, 7 TeV. The predictive results for p_{T} and multiplicity distributions in p+p and p+Pb collisions at the Large Hadron Collider are also given in this …
We analyse the transverse momentum $p_{\mathrm{T}}$ spectra of strange particles \Kslxi produced in $\textsf{Pb+Pb}$ collision at $\sqrt{s_{NN}}= 2.76$ TeV, $\textsf{p+Pb}$ collision at $\sqrt{s_{NN}}= 5.02$ TeV, and $\textsf{p+p}$ collision at $\sqrt{s_{NN}}= 7$ TeV in different multiplicity events measured by the \textit{CMS} experiment at the Large Hadron Collider. The $p_{\mathrm{T}}$ spectra of strange particles are fitted by Tsallis statistics and Boltzmann statistics, respectively. The fitting parameters are studied as a function of the multiplicity events for all systems. The Tsallis t…
The status of CMS jet simulations and physics analysis in heavy ion collisions is presented. Jet reconstruction and high transverse momentum particle tracking in the high multiplicity environment of heavy ion collisions at the LHC using the CMS calorimetry and tracking system are described. The Monte Carlo tools used to simulate jet quenching are discussed.
Using the negative binomial distribution (NBD) and the generalized Glauber-Lachs (GGL) formula, we analyze the data on charged multiplicity distributions with pseudo-rapidity cutoffs η_c at 0.9, 2.36, and 7 TeV by ALICE Collaboration and at 0.2, 0.54, and 0.9 TeV by UA5 Collaboration. We confirm that the KNO scaling holds among the multiplicity distributions with η_c = 0.5 at \sqrt{s} = 0.2\sim2.36 TeV and estimate the energy dependence of a parameter 1/k in NBD and parameters 1/k and γ(the ratio of the average value of the coherent hadrons to that of the chaotic hadrons) in the GGL formula. U…
Moments play a crucial role in investigating the characteristics of charged particle multiplicities in high energy interactions. The success of any model which describes the multiplicity data can be understood well by studying the normalised and factorial moments of that distribution.~The Tsallis model is one of the most successful models which describes the multiplicity spectra, transverse momentum ($p_T$) spectra very precisely in high energy interactions.~In our previous work we have used the Tsallis $q$-statistics to describe the multiplicity distributions in leptonic and hadronic collisio…
We study the impact parameter dependence of inelasticity in the framework of an updated geometrical model for multiplicity distribution. A formula in which the inelasticity is related to the eikonal is obtained. This framework permits a calculation of the multiplicity distributions as well as the inelasticity once the eikonal function is given. Adopting a QCD inspired parametrization for the eikonal, in which the gluon-gluon contribution dominates at high energy and determines the asymptotic behavior of the cross sections, we find that the inelasticity decreases as collision energy is increase…
An extension of the rope hadronization model, which has previously provided good descriptions of hadrochemistry in high multiplicity pp collisions, is presented. The extension includes a dynamically generated transverse pressure, produced by the excess energy from overlapping strings. We find that this model can qualitatively reproduce soft features of Quark Gluon Plasma in small systems, such as higher $\langle p_\perp \rangle$ for heavier particles and long range azimuthal correlations forming a ridge. The effects are similar to those obtained from a hydrodynamic expansion, but without assum…
