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High-multiplicity Events of Proton-proton Collisions at LHC Exhibit Features of Relativistic Heavy-i
Premomoy Ghosh
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DOI: 10.22661/AAPPSBL.2019.29.2.20

High-multiplicity Events of Proton-proton Collisions
at LHC Exhibit Features of Relativistic Heavy-ion Collisions

PREMOMOY GHOSH*
VARIABLE ENERGY CYCLOTRON CENTRE, KOLKATA 700 064, INDIA
(DATED: MARCH 25, 2019)

* Electronic address: prem@vecc.gov.in

Quark-Gluon Plasma (QGP), an exotic phase of partonic matter that is believed to have existed a few microseconds after the Big Bang, could be created in the laboratory as "Little Bangs" through relativistic AuAu collisions at the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). In extracting the discovery-signals of the QGP in heavy-ion collisions at RHIC, the proton-proton (pp) collision data at the same energy, considered as elementary interactions, served as the baseline. The pp collisions at the Large Hadron Collider (LHC), at a larger center-of mass energy of collisions, however, exhibit anomalous features of particle production - the events with high multiplicities replicate some of the characteristic properties of particle production in the Little Bangs. This brief article aims to highlight some of those features.

INTRODUCTION

Following an indication in PbPb collisions at CERN at the center-of mass energy, = 17 GeV the formation of QGP [1] in the laboratory could be unambiguously detected [2-5] at RHIC in AuAu collisions at = 130 and 200 GeV. The two prime signals that helped in discovering QGP in heavy-ion collisions in the laboratory are 1) the azimuthal anisotropic flow of the produced particles revealing collective behavior of the source of the particles and 2) the suppression of high-pT particles, confirming formation of the dense partonic medium. The data of the pp collisions at the same energy served as the baseline in extracting the signal of suppression of high-pT particles. The formation of QGP implies thermodynamic equilibrium of the system of de-confined partons. Theoretically, in relativistic heavy-ion collisions, the local thermodynamic equilibrium is assumed to obtain the equation of state, which is needed for the space-time evolution of the system in the framework of relativistic hydrodynamics. The hydrodynamic models, by successful reproduction of the measured distribution of the final-state invariant yields in heavy-ion collisions, depict the dynamics of particle production mechanisms. In most of the topical models of particle production, the formation of QGP and subsequently an equilibrated hadronic phase before the freeze out of the final state particles is expected only in heavy-ion collisions, while the proton-proton (pp) collision is considered as the elementary interaction. These models do not support formation of any medium in pp collisions. In this scenario, certain features of produced particles in high-multiplicity events of pp collisions at the Large Hadron Collider (LHC) at CERN resemble those of heavy-ion collisions at RHIC, and subsequently at LHC, which are attributed to the collective behavior of a hydrodynamic medium. It is, however, important to note that the suppression of high-pT particles or any other confirmative signal of formation of dense partonic medium in high-multiplicity pp events has not yet been observed, which prevents us from being able to make a conclusion on the QGP-like origin of the observed "collective behavior" of high- multiplicity pp events. The ambiguity in interpreting the azimuthal anisotropic flow-like behavior in the pp data invites several non-hydrodynamic models, which also can describe the observed features, at least qualitatively. This article, however, refrains from detailed discussion on all those models and focuses on certain observed features of high-multiplicity pp events that resemble those of hydrodynamic origin in heavy-ion collisions.

AZIMUTHAL ANISOTROPY

The unexpected behavior of particle production in pp collisions at the LHC era was first revealed [6] in terms of long range near side angular correlations in high-multiplicity events at = 7 TeV. Further studies [7-9] at = 5, 7 and 13 TeV extracted the elliptic flow coefficient, v2 and mass ordering of v2(pT) for identified charged particles [9]. It is worth mentioning here that similar hydro-like behavior has been observed in other small collisional systems, e.g., the proton-nucleus (pA) [10-15], also, at the LHC and very recently at RHIC. Further discussion on the pA results, however, is beyond the scope of this article.

The two-particle angular correlation function of pT-inclusive charged particles is obtained from Δ管, Δ distribution (where Δ管 and Δ are the differences in the pseudo-rapidity () and azimuthal angle () of the two particles) and for a given multiplicity event-class is given by:

 

Fig. 1: 2-D two-particle angular correlation functions for pp 7 TeV minimum bias events (upper panels, a and b) and for high multiplicity Ntrk < 110) events (lower panel, c and d). The figure has been published in Ref. [6].

 

(1)

where, <N> is the average multiplicity over all events of the multiplicity class,

(2)

is the signal distribution and is calculated by counting particle pairs within same event. The background distribution is obtained from uncorrelated particle pairs from mixed events and is given by:

(3)

N (N - 1) and N2 in Eq. 2 and Eq. 3 are respective normalization factors. For the minimum-bias data, the events are classified in several multiplicity bins and finally the correlation function is obtained by taking the average over all multiplicity bins.

The long-range (|Δ管| ≫ 0) two-particle azimuthal correlations study reveals a "ridge" structure in relativistic heavy-ion collisions in CuCu [16] and AuAu [16-20] collisions at RHIC and in PbPb collisions at LHC energies [21-26]. It is suggested that the hydrodynamic collective flow of a strongly interacting and expanding medium [27-29] is responsible for the "ridge" structure in the relativistic heavy ion systems. Figure 1 shows the "ridge" structure in a high multiplicity pp events-sample at = 7 TeV. Theoretically, the appearance of a "ridge" structure in high-multiplicity pp events at 7 TeV has been shown [30] to be expected in a hydrodynamic approach, based on flux tube initial conditions.

 

Fig. 2: The v2sub{2} and v3sub{2} of charged particles as a function of charged particle multiplicity Ntrkof fline in pp collisions at = 5, 7 and 13 TeV, pPb collisions at = 5 TeV, and PbPb collisions at = 2.76 TeV, after correcting for back-to-back jet correlations estimated from low-multiplicity data. The figure has been published in Ref. [9].

 

Fig. 3: v2 as a function of pT for inclusive charged hadrons, Ks0 and () in high-multiplicity pp events at = 13 TeV. The figure has been published in Ref. [9].

The quantification [9] of the observed long-range correlations in high-multiplicity pp events in terms of Fourier harmonics of azimuthal anisotropy (v2 is the elliptic flow and v3 is the traingular flow) and their properties help in strengthening the claim of the hydrodynamic origin of the long-range correlations. The CMS experiment has measured two- and multi-particle correlations of identified and inclusive charged particles for several classes of different multiplicity in pp collisions at = 5, 7 and 13 TeV. In extracting collective or flow-like correlations, suppressing the non-flow component, the azimuthal anisotropy Fourier harmonics from long-range azimuthal correlation should be free from contribution from short-range correlations. The v2sub and v3sub values extracted from long-range two-particle correlations, after subtracting contributions from back-to-back jet correlations estimated using low-multiplicity data, have been compared with the pPb and PbPb data at = 5 and 2.76 TeV, respectively. As can be seen in the Figure 2, multiplicity dependence of both v2sub and v3sub values in pp collisions follow a similar trend as in pPb and PbPb collisions. Though v2sub values for pp collisions are smaller as compared to pPb and PbPb collisions, v3sub values for all three collision systems are comparable.

The mass ordering of v2(pT) for identified charged particles as observed in heavy-ion collisions at RHIC [31, 32] and in pPb collisions [33, 34] at LHC has been revealed [9] in high-multiplicity pp events of 13 TeV pp data also. As shown in the Figure 3, in the lower pT -region of v2 as a function of pT for charged particles - hadrons (mostly pions, 𝜋), Ks0 and (), the lighter particle species exhibit stronger azimuthal anisotropy.

The charged particle multiplicity (in terms of Ntrkof fline) dependent second harmonic, v2{n}, extracted from the multi-particle cumulant method for pp collisions at = 13 TeV show similar behavior [35] as observed in pPb and PbPb collisions at LHC. The v2{4} and v2{6} values for high-multiplicity pp events have been reported [9] to be consistent with each other, which provides a stronger indication of the collective origin of the long-range correlations.

Several other theoretical and phenomenological studies [36-41] indicate the possibility of a hydro-like collective medium in high-multiplicity pp events. We will discuss a few more data-driven studies that extract signals for collectivity.

RADIAL FLOW

The collective behavior of particle production in high-multiplicity pp events has been observed also in terms of strong transverse radial flow extracted [40] from the identified charged particle yields [42] by the hydrodynamics-motivated Boltzmann - Gibbs blast-wave (BGBW) model [43]. The blast-wave model analysis does not involve full hydrodynamic calculations. The model assumes instantaneous freeze out of all the particle species at a kinetic freeze out temperature (Tkin) and with common transverse radial flow velocity (<>) from the freeze out surface of a locally thermalized system, expanding with a common velocity field. Assuming a hard-sphere particle source of uniform density, the transverse momentum spectra, in the BGBW model is given by:

(4)

where ρ = tanh-1 , I0 and K1 are modified Bessel functions.

The flow velocity profile is given by,

(5)

where s is the surface velocity and r/R is the relative radial position in the thermal source. The average transverse flow velocity, <> is given by,

The BGBW model satisfactorily describes the pT-spectra of the RHIC heavy ions data [44, 45] extracting the kinetic freeze-out parameters, Tkin and <> by simultaneous fit to the pT spectra of pions, kaons and protons for the pT-range up to pT = 1.2 GeV/c. A centrality and energy dependence study [45] for AuAu collisions reveals that the <> increases and the Tkin decreases with both the center-of-mass energy of collisions and the centrality. It may be noted that the blast-wave analysis [46] of the transverse mass spectra of pions, kaons and protons from central heavy-ion collisions data at fixed-target experiments at SPS energies - 200 A GeV SS and 158, have also provided evidence of collective transverse flow. On the other hand, a multiplicity dependent study of pp data at = 200 GeV at RHIC in terms of the BGBW model analysis didn't reveal any appreciable values of Tkin and <>.

The CMS experiment at the LHC has measured pT-spectra [42] of pions (𝜋), kaons (K), and protons p and (p) over the rapidity range |y| < 1 for the pp collisions at = 0.9, 2.76 and 7 TeV for several event classes selected on the basis of mean number of charged particles, <Nch> in the pseudo-rapidity interval, || < 2.4 or, in other words, as a function of pseudorapidity density, d <Nch>/d管, reflecting "centrality" in pp collisions. The measured pT-ranges are (0.1 to 1.2) GeV/c for 𝜋, (0.2 to 1.05) GeV/c for K and (0.35 - 1.7) GeV/c for p and p. The analysis [40] of the multiplicity dependent identified particle spectra data extracted values for and Tkin which are comparable with those for AA and pA data are depicted in Figures 4 and 5, respectively.

 

Fig. 4: The and centrality ( dnch/d管) dependence of mean transverse radial velocity, <>, as obtained by simultaneous fits in the BGBW framework to the published [41] spectra of 𝜋, K and p(p) in pp collisions at LHC is compared with results from similar analysis for AuAu collisions at RHIC [45], PbPb and pPb collisions at LHC [47, 48]. The figure has been published in Ref. [40].

Satisfactory simultaneous fits to the BGBW description of the transverse momentum spectra of 𝜋, K and p(p) in high multiplicity events in pp collisions at = 0.9, 2.76 and 7 TeV at LHC, along with appreciable values of Tkin and , indicate the formation of collective medium in high-multiplicity events in pp collisions at LHC. The dependency of Tkin and on multiplicity, equivalent to the dependency on centrality in heavy-ion collisions, is quite similar to the heavy-ion data where the collectivity has been established as due to the formation of a thermalised partonic medium.

 



Fig. 5: Same as Figure 4 for the kinetic freeze-out temperature, Tkin. The figure has been published in Ref. [40].

INVERSE SLOPE PARAMETER

The mT (for a particle of mass m, mT = (m2+pT2)1/2) spectra corresponding to low - pT (usually < 2 GeV/c) particles in heavy-ion collisions are usually satisfactorily fitted with the exponential function of the form:

(6)

where Teffective, known as the inverse slope parameter, contains information of the temperature of the source of the particles at the freeze out, as well as of the effect due to the transverse expansion of the system.

Increase in the inverse slope parameter, Teffective with mass, m, for the most commonly measured and identified particles (𝜋, K, p and p), has been observed in heavy-ion collisions [49, 50] as well as in the recent pPb collisions [51] at the LHC. The phenomenon is attributed to the collective transverse flow of the medium formed in the collision. For high-multiplicity pp events, the mT-spectra for identified charged particles were obtained [52] from the pT-spectra [42] from different multiplicity classes of pp events at = 7 TeV.

 

Fig. 6: The inverse slope parameter Teffective as a function of mass of identified particles (m𝜋 = 0.14, mK = 0.495, mp(p) = 0.938 GeV/c2) as obtained from transverse momentum spectra from non-single diffractive events of pp collisions as measured by the CMS experiment [42] at = 7 TeV. <Nch> is the mean multiplicity of the charged particles. The lines in the figure are drawn connecting the points just to guide the eyes. The figure has been published in Ref. [52].

In reference [52], the mT-spectra of identified particles were fitted with Eq. 6 for the overlapped range (0.475 < pT < 1.025) of pT-spectra at = 7 TeV [42]. The increase of the Teffective with a mass of identified charged particles for event classes of high <Nch> reiterated (Fig. 6) the finding of collective medium in high-multiplicity pp collisions.

SUMMARY AND OUTLOOK

Certain features of high-multiplicity events of pp collisions at LHC energies that resemble those of the relativistic heavy-ion collisions have been discussed. These features in heavy-ion collisions are successfully described by hydrodynamic models and are considered to be characteristic signals of the formation of thermalized partonic matter, the QGP. Substantial resemblance in terms of signals related to the collective behavior of particle production leads one to infer that the high-multiplicity pp events form collective medium of particle production. Of course, characterization of such collective medium still remains inconclusive and in absence of observation of high-pT particle suppression in high-multiplicity pp events, one cannot conclude on formation of thermalized, dense partonic medium, like the one formed in relativistic heavy-ion collisions. At the same time, however, the non-observance may be attributed to the limitations in measurement of path-length dependent energy-loss of high-pT particles in a small system formed, if any, in pp collisions.

It is worth repeating here that although several existing models of particle production - hydrodynamic [30, 53-55] and non-hydrodynamic [56-58] - could describe the observed features of high-multiplicity events of small collision systems, at least qualitatively, the detailed discussion on the models is avoided as the focus of this article has been on the similarities between data of high-multiplicity pp events and relativistic heavy-ion collisions. Furthermore, there doesn't exist a single version of a particular model, hydrodynamic or non-hydrodynamic, that provides satisfactory quantitative description of the majority of the observed features. Absolute identification of the origin of these features thus remains far from the reach, with the availability of only qualitative reproduction of partial features of the data by different particle production models with diverse physics considerations.

The exhibited features of particle production in pp collisions were "unexpected" in accordance with the topical models of particle production. It, however, does not mean that the idea of collective properties or even the formation of partonic matter in pp collisions was triggered with the observation of the discussed features in high-multiplicity pp collisions at the LHC. Long before the availability of LHC pp data, even prior to the experimental confirmation [2-5] of the occurrence of Little Bangs at RHIC, the lattice quantum chromodynamics (LQCD-based prediction) [59] of the first order phase transition in proton-antiproton (pp) collisions was motivated by the experimental finding of the flattening of the transverse momentum spectrum with increasing multiplicity at = 540 GeV. The de-confinement and formation of a hydrodynamic medium in pp collisions at = 1800 GeV at TeVatron at Fermilab also have been studied [60, 61]. In fact, the so-called unexpected behavior of the data of pp collisions at the LHC has just revived a rather old but subdued school of thought [59-63] regarding the creation of the quark-gluon plasma phase in pp collisions. Further details on the search of collectivity or de-confined partonic matter in pp collisions prior to the LHC experiments may be found in the review article in ref. [64].

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Dr. Premomoy Ghosh is a Senior Scientist at Variable Energy Cyclotron Centre (VECC), Department of Atomic Energy. He is heading the Experimental High Energy Physics Section at VECC. Dr. Ghosh is a member of the ALICE Experiment at LHC, CERN. He is actively involved in phenomenological works of Quark Gluon Plasma and hot and dense hadronic system. His current research interest is thermalization of matter created in collisions of small systems. (proton+proton, etc.)

 
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