Color String Research Articles

Particle production as a function of charged-particle flattenicity in pp collisions at s=13 TeV

This paper reports the first measurement of the transverse momentum (pT) spectra of primary charged pions, kaons, (anti)protons, and unidentified particles as a function of the charged-particle flattenicity in pp collisions at s=13 TeV. Flattenicity is a novel event shape observable that is measured in the pseudorapidity intervals covered by the V0 detector, 2.8<η<5.1 and −3.7<η<−1.7. According to QCD-inspired phenomenological models, it shows sensitivity to multiparton interactions and is less affected by biases toward larger pT due to local multiplicity fluctuations in the V0 acceptance than multiplicity. The analysis is performed in minimum-bias (MB) as well as in high-multiplicity events up to pT=20 GeV/c. The event selection requires at least one charged particle produced in the pseudorapidity interval |η|<1. The measured pT distributions, average pT, kaon-to-pion and proton-to-pion particle ratios, presented in this paper, are compared to model calculations using 8 based on color strings and EPOS LHC. The modification of the pT-spectral shapes in low-flattenicity events that have large event activity with respect to those measured in MB events develops a pronounced peak at intermediate pT (2<pT<8 GeV/c), and approaches the vicinity of unity at higher pT. The results are qualitatively described by , and they show different behavior than those measured as a function of charged-particle multiplicity based on the V0M estimator. © 2025 CERN, for the ALICE Collaboration 2025 CERN

Study of thermodynamic observables in Oxygen + Oxygen collisions at sNN = 7 TeV using color string percolation approach

Study of thermodynamic observables in Oxygen + Oxygen collisions at sNN = 7 TeV using color string percolation approach

Exploring the QGP phase above the deconfinement temperature in pp and A − A collisions at LHC energies

In the present work we have analyzed the transverse momentum spectra of charged particles in high multiplicity pp collisions at LHC energies s=5.02 and 13 TeV published by the ALICE Collaboration using the Color String Percolation Model. For heavy ions Pb-Pb at sNN=2.76 and 5.02 TeV along with Xe-Xe at sNN=5.44 TeV have been analyzed. The initial temperature is extracted both in low and high multiplicity events in pp collisions. For A−A collisions the temperature is obtained as a function of centrality. A universal scaling in the temperature from pp and A−A collisions is obtained when multiplicity is scaled by the transverse interaction area. From the measured energy density ε and the temperature the dimensionless quantity ε/T4 is obtained. Our results for Pb-Pb and Xe-Xe collisions show a sharp increase in ε/T4 above T ∼ 210 MeV and reaching the ideal gas of quarks and gluons value of ε/T4∼16 at temperature ∼230 MeV.

Emergent Flow Signal and the Colour String Fusion

In this study, we develop the colour string model of particle production, based on the multi-pomeron exchange scenario, to address the controversial origin of the flow signal measured in proton–proton inelastic interactions. Our approach takes into account the string–string interactions but does not include a hydrodynamic phase. We consider a comprehensive three-dimensional dynamics of strings that leads to the formation of strongly heterogeneous string density in an event. The latter serves as a source of particle creation. The string fusion mechanism, which is a major feature of the model, modifies the particle production and creates azimuthal anisotropy. Model parameters are fixed by comparing the model distributions with the ATLAS experiment proton–proton data at the centre-of-mass energy s=13 TeV. The results obtained for the two-particle angular correlation function, C(Δη,Δϕ), with Δη and Δϕ differences in, respectively, pseudorapidities and azimuthal angles between two particles, reveal the resonance contributions and the near-side ridge. Model calculations of the two-particle cumulants, c2{2}, and second order flow harmonic, v2{2}, also performed using the two-subevent method, are in qualitative agreement with the data. The observed absence of the away-side ridge in the model results is interpreted as an imperfection in the definition of the time for the transverse evolution of the string system.

Transverse momentum distributions of the identified particles in mini–bias non-single diffracted p＋p collisions at 200 GeV

The transverse momentum (pT) distributions of hadrons stem from the probability distributions of deconfined colored partons known as pT distributions. This provides insights into various stages of nuclear collisions, ranging from the initial partonic phase to the later stages, including the directly measurable hadronization process. The objective is to analyze the pT distributions of identified particles: π+, π−, K+, K−, K0s, p, p̄, Λ, Λ̄, Σ+, Σ−. These analyses are conducted in mini-bias non-single diffracted p+p collisions at an energy of 200GeV. The goal is to accurately determine the kinetic freezeout parameters and the extent of statistical nonextensivity. The measurements from the STAR experiment are merged with simulations using DPMJET, PYTHIA, and Sibyll.3d Monte–Carlo Event Generators. The predictions from these models and the actual measurements are compared using statistical distributions employing the Tsallis-type of non-extensive statistics. While Pythia8 displays a closer alignment with the data in certain instances, it was observed that none of the event generators could accurately replicate the data for all charged particles across the entire range of pT. We examined how the effective temperature correlates with the rest mass of different particles. Our analysis revealed that the freezeout process for heavier particles tends to occur at lower temperatures. This suggests that heavier particles might reach an equilibrium state relatively rapidly during the freezeout stage. Additionally, we observed a pattern where the non-extensive parameter q decreases as the mass of the produced particles increases. This implies that lighter particles tend to reach equilibrium after the heavier ones. Furthermore, the average transverse momentum (<pT>) is greater for heavier particles, leading to an enhanced radial flow compared to lighter particles. This rising trend also indicates the likelihood of mini-jet production, contributing to color string fragmentation that becomes more pronounced with the increasing mass of the particles.

Minimal center-of-mass energy required for QGP formation in pp and AA collisions

We discuss the conditions for QGP formation under the Color String Percolation Model. Since the observables in the percolation theory are sensitive to the system size, we expect the finite size effects take a relevant contribution to the estimation of the color string observables, such as the transition temperature or the center of mass energy needed for the QGP formation. We observe that pp collisions (small systems) require around 20 times bigger center of mass energy than heavy ion collisions. Our results are consistent with the experiments claiming that the QGP has been observed.

Soft and hard scales of the transverse momentum distribution in the color string percolation model

In color string models, the transverse momentum distribution (TMD) is obtained through the convolution of the Schwinger mechanism with the string tension fluctuations distribution. Considering a q-Gaussian distribution for these fluctuations, the TMD becomes a hypergeometric confluent function that adequately reproduces the characteristic scales at low and high p T values. In this approach, the hard scale of the TMD is a consequence of considering a heavy-tailed distribution for the string tension fluctuations whose width rises as , multiplicity or centrality increases. In this paper, we introduce broader information of the TMD in the color string percolation model by determining the color suppression factor, which now also depends on the parameters of the q-Gaussian. To this end, we analyze the reported data on pp and AA collisions at different center of mass energies, multiplicities, and centralities. In particular, for minimum bias pp collisions, we found that the q-Gaussian parameters and the effective temperature are monotonically increasing functions of the center of mass energy. Similar results are found for AA collisions as a function of the centrality at fixed . We summarize these results in a phase diagram that indicates the q-Gaussian parameters region allowing the quark–gluon plasma formation.

Interacting Colour Strings Approach in Modelling of Rapidity Correlations

In this paper, using the concept of multi-pomeron exchange, we develope a Monte Carlo model of interacting quark–gluon strings acting as particle-emitting sources aimed at describing inelastic proton–proton interactions at high energies. The implemented 3D (three-dimensional) dynamics of colour string formation resulted in their finite length in the rapidity space and in the fluctuating event-by-event spatial density. Thus, this results in string cluster formation because of the fusion mechanism and the appearance of long-range multiplicity and mean transverse momentum (mean-pT) correlations in rapidity. We study, via the pseudorapidity dependence, the sensitivity to the details of the 3D dynamical formation of strings for several observables such as the forward–backward correlation coefficient value, strongly intensive quantity, Σ, and the “almost” strongly intensive observable, the variance, σC2, of the distribution of the asymmetry coefficient, C. The strongly intensive quantity Σ is used in this study to suppress trivial statistical fluctuations in the number of particles emitting similar types of sources and to reveal the intrinsic fluctuations of a single source. We demonstrate the connection between Σ and such often used observables as cumulants, factorial cumulants, and σC2. We stress the importance of the contribution of “short” strings and the event asymmetry of the initial conditions on the long-range correlation measures. We argue that string cluster formation because of the fusion mechanism explains the collective effects seen in multiplicity and transverse momentum–multiplicity, ⟨pT⟩–N, long-range correlation functions.

Structure of the Medium Formed in Heavy Ion Collisions

We investigate the structure of the medium formed in heavy ion collisions using three different models: the Color String Percolation Model (CSPM), the Core–Shell-Color String Percolation Model (CSCSPM), and the Color Glass Condensate (CGC) framework. We analyze the radial distribution function of the transverse representation of color flux tubes in each model to determine the medium’s structure. Our results indicate that the CSPM behaves as an ideal gas, while the CSCSPM exhibits a structural phase transition from a gas-like to a liquid-like structure. Additionally, our analysis of the CGC framework suggests that it produces systems that behave like non-ideal gases for AuAu central collisions at RHIC energies and liquid-like structures for PbPb central collisions at LHC energies.

Production of Cumulative Pions and Percolation of Strings

Production of pions in high-energy collisions with nuclei in the kinematics prohibited for free nucleons (“cumulative pions”) is studied in the fusing color string model. The model describes the so-called direct mechanism for cumulative production. The other (spectator) mechanism dominates in production of cumulative protons, and is suppressed for pions. In the model, cumulative pions are generated by string fusion, which raises the maximal energy of produced partons above the level of the free nucleon kinematics. Momentum and multiplicity sum rules are used to determine the spectra in the deep fragmentation region. Predicted spectra of cumulative pions exponentially fall with the scaling variable x in the interval 1&lt;x&lt;3 with a slope between 5.1 and 5.6, which agrees well with the raw data obtained in the recent experiment at RHIC involving Cu–Au collisioins. However, the agreement is worse for the so-called unfolded data, presumably taking into account corrections due to the experimental setup and having rather a power-like form.

Understanding the QCD medium by the diffusion of charm quarks using a color string percolation model

We study the drag and diffusion coefficients of the charm quark in the deconfined matter produced in the ultra-relativistic collisions by taking the Color String Percolation Model (CSPM) approach. CSPM, being a QCD-inspired model, can give us essential information about the hot and dense system produced in ultra-relativistic collisions. With the information on initial percolation temperature and percolation density, we estimate the relaxation time ($\tau_{c}$), drag coefficient ($\gamma$), transverse momentum diffusion coefficient ($B_{0}$), and spatial diffusion coefficient ($D_{s}$) of charm quark inside a deconfined medium. Finally, we compare the obtained results with lattice QCD and with various other theoretical models. A good agreement can be observed between the results obtained from CSPM and lattice QCD.

Percolation leads to finite-size effects on the transition temperature and center-of-mass energy required for quark-gluon plasma formation

We investigate the finite-size effects on the transition temperature associated with the quark-gluon plasma (QGP) formation. From a percolation perspective, the onset of the QGP in high-energy collisions occurs when the spanning cluster of color strings emerges. The principal result presented here is the finite-size effects on the transition temperature expressed as a power law in terms of the nucleon number. We found that the transition temperature is higher for small systems than for large ones. It means that minimal triggering conditions events in pp collisions require about 20 times higher energies than AuAu-PbPb collisions. We also estimate the center-of-mass energy required for the QGP formation as a function of the nucleon number. Our results are consistent with the minimal center-of-mass energies at which the QGP has been observed.

Exploring jet transport coefficients by elastic scattering in the strongly interacting quark-gluon plasma

We study the interaction of leading jet partons in a strongly interacting quark-gluon plasma (sQGP) medium based on the effective dynamical quasi-particle model (DQPM). The DQPM describes the non-perturbative nature of the sQGP at finite temperature $T$ and baryon chemical potential $\mu_B$ based on a propagator representation of massive off-shell partons (quarks and gluons) whose properties (characterized by spectral functions with $T,\mu_B$ dependent masses and widths) are adjusted to reproduce the lQCD EoS for the QGP in thermodynamic equilibrium. We present the results for the jet transport coefficients, i.e. the transverse momentum transfer squared per unit length $\hat{q}$ as well as the energy loss per unit length $\Delta E =dE/dx$, in the QGP and investigate their dependence on the temperature $T$ and baryon chemical potential $\mu_B$ as well as on jet properties such as the leading jet parton momentum, mass, flavor, and the choice of the strong coupling constant. In this first study only elastic scattering processes of a leading jet parton with the sQGP partons are explored discarding presently the radiative processes (such as gluon Bremsstrahlung). We present a comparison of our results for the elastic energy loss in the sQGP medium with the pQCD results obtained by the BAMPS and LBT models as well as with other theoretical approaches such as lattice QCD and the LO-HTL and also with estimates of $\hat{q}/T^3$ by the color string percolation model (CSPM) and the JET and JETSCAPE Collaborations based on a comparison of hydrodynamical calculations with experimental heavy-ion data.

Content-Based Video Retrieval Based on Multifaceted Feature Extraction Using Statistical Methods

For content-dependent video recovery, this paper proposes a multifaceted feature extraction approach based on color string extraction, local texture characteristics, and amount of Absolute Difference, which extracts the features such as color components , texture components, and motion behavior. The color string function is derived using the string duration count, and the color histogram approach is used for detecting scene shifts. Based on scene shift recognition, the key-frames are retrieved. Based on the color string and local texture functions, the color and texture characteristics are derived from the key-frame. The Amount of Absolute Difference is measured, and the motion function of a video is derived using it. To compare the function vectors of the question and main frames of the video to be recovered, the Jeffrey's Divergence measure is implemented. The suggested approach has the greatest capture of both spatial and temporal aspects, and the recovery efficiency is increased by utilizing multifaceted features. The system suggested outperforms the current approaches.

Possible formation of a perfect fluid in pp, p–Pb, Xe–Xe and Pb–Pb collisions at the Large Hadron Collider energies: a color string percolation approach

Isothermal compressibility ($\kappa_{\rm T}$) is an important thermodynamic observable which gives information about the deviation of a system from perfect fluid behavior. In this work, for the first time we have estimated the isothermal compressibility of QCD matter formed in high energy hadronic and nuclear collisions using color string percolation model (CSPM), where we investigate the change in $\kappa_{\rm T}$ as a function of final state charged particle multiplicity and initial percolation temperature across various collision species. The estimated initial percolation temperature for different collision systems at different collision energies helps us to have a better understanding of the system at the initial phase of evolution. The comparison of the CSPM results for isothermal compressibility with that for the well known fluids, indicates that the matter formed in heavy-ion collisions might be the {\it closest perfect fluid} found in nature. This estimation complements the well-known observation of minimum shear viscosity to entropy density ratio for a possible QGP medium created in heavy-ion collision experiments. A threshold of pseudorapidity density of charged particles, $\langle dN_{\rm ch}/d\eta \rangle \geq 20 $ in the final state event multiplicity is observed, after which one may look for a possible QGP formation at the LHC energies.

Collective properties of hadrons in comparison of models prediction in pp collisions at 7 TeV

Analysis of the spectra of unidentified charged particles obtained by the CMS experiment in proton–proton collisions is reported in comparison with the simulation results of PYTHIA8.24 and EPOS-LHC models. The spectra obtained by the experiment were normalized to all non-single-diffractive (NSD) events using corrections for trigger and selection efficiency, acceptance, and branching ratios. The transverse-momentum (pT) spectra of the charged particles are measured in twelve equal bins of pseudorapidity (η) from 0.0 to 2.4 for pT from 0.1 to 2 GeV/c. The PYTHIA model reproduces the experimental data well in all bins of η especially in the region of high pT while the EPOS model predicts well in the intermediate pT regions. The intermediate regions where the EPOS model predicts well, broadens with increasing η.We used the Blast-wave model with Boltzmann–Gibbs statistics to study collective properties of the hadronic matter and for better comparison of the models’ prediction with the experimental data while determining the values of kinetic freeze-out temperature (T0) and transverse flow velocity (βT) for data and models. The values of T0 decrease with increasing η for data as well as for both the models. The transverse flow velocity has no clear trend with increasing η but a run through shows an increasing trend in the case of the data and the PYTHIA model but a decreasing trend in the case of the EPOS model. The multiplicity parameter N0 increases with increasing η and its values obtained by the fit function for the PYTHIA are closer to the ones obtained for data than the EPOS. It is concluded that none of the models completely describes the data in all bins of η over the entire pT range but the PYTHIA has better prediction than the EPOS model because the former has implied flow-like effects and formation of color string resulting from multiple hard sub-collisions between final and initial partons (color reconnection) from independent hard scatterings due to which the model predicts the data well.

The time substructure of jets and boosted object tagging

We propose the study of the time substructure of jets, motivated by the fact that the next generation of detectors at particle colliders will resolve the time scale over which jet constituents arrive. This effect is directly related to the fragmentation and hadronization process, which transforms partons into massive hadrons with a distribution of velocities. We review the basic predictions for the velocity distribution of jet hadrons, and suggest an application for this information in the context of boosted object tagging. By noting that the velocity distribution is determined by the properties of the color string which ends on the parton that initiates the jet, we observe that jets originating from boosted color singlets, such as Standard Model electroweak bosons, will exhibit velocity distributions that are boosted relative to QCD jets of similar jet energy. We find that by performing a simple cut on the corresponding distribution of charged hadron arrival times at the detector, we can discriminate against QCD jets that would otherwise give a false positive under a traditional spatial substructure-based boosted object tagger.

Jet Transport Coefficient at the Large Hadron Collider Energies in a Color String Percolation Approach

Within the color string percolation model (CSPM), jet transport coefficient, q^, is calculated for various multiplicity classes in proton-proton and centrality classes in nucleus-nucleus collisions at the Large Hadron Collider energies for a better understanding of the matter formed in ultra-relativistic collisions. q^ is studied as a function of final state charged particle multiplicity (pseudorapidity density at midrapidity), initial state percolation temperature and energy density. The CSPM results are then compared with different theoretical calculations from the JET Collaboration those incorporate particle energy loss in the medium.

Sudden increase in the degrees of freedom in dense QCD matter

In this paper, we analyzed charged particle transverse momentum spectra in high multiplicity events in proton–proton and nucleus–nucleus collisions at LHC energies from the ALICE experiment using the color string percolation model (CSPM). The color reduction factor and associated string density parameters are extracted for various multiplicity classes in [Formula: see text] collisions and centrality classes for heavy-ion collisions at various LHC energies to study the effect of collision geometry and collision energy. These parameters are used to extract the thermodynamical quantities temperature and the energy density of the hot nuclear matter. A universal scaling is observed in initial temperature when studied as a function of charged particle multiplicity scaled by transverse overlap area. From the measured initial energy density [Formula: see text] and the initial temperature T, a dimensionless quantity [Formula: see text] is constructed which is used to obtain the degrees of freedom (DOF) of the deconfined phase. A two-step behavior and a sudden increase in DOF of [Formula: see text]47 for the ideal gas, above the hadronization temperature (T [Formula: see text] 210[Formula: see text]MeV), are observed in case of heavy-ion collisions at LHC energies.

Thermodynamic and transport properties of matter formed in pp, p-Pb, Xe–Xe and Pb–Pb collisions at the Large Hadron Collider using color string percolation model

To have a better understanding of the matter formed in ultra-relativistic collisions, using the color string percolation model, we have estimated initial energy density, mean free path, squared speed of sound, shear viscosity to entropy density ratio (η/s), bulk viscosity to entropy density ratio and bulk modulus for pp, p-Pb, Xe–Xe and Pb–Pb collisions at the Large Hadron Collider (LHC). These observables are studied as a function of final state charged particle multiplicity density normalized by nuclear overlap area and initial state percolation temperature. The results from this work are compared with the results from well known QCD models and with the transport properties of matter found in day-to-day life. These observables allow us to conclude an array of important findings about the matter formed in high-energy collisions at the LHC. For the high-multiplicity events, the estimated η/s are comparable with that is observed for heavy-ion collisions, which is an indication of a strongly coupled quark gluon plasma. This makes LHC high-multiplicity pp collision events as probable candidates for the search of quark-gluon plasma droplets.