Color String Research Articles

Stopped Nucleons in Configuration Space

In this note, using the colour string model, we study the configuration space distribution of stopped nucleons in heavy-ion collisions. We find that the stopped nucleons from the target and the projectile end up separated from each other by the distance increasing with the collision energy. In consequence, for the center of mass energies larger than 6 or 10 GeV (depending on the details of the model) it appears that the system created is not in thermal and chemical equilibrium, and the net baryon density reached is likely not much higher than that already present in the colliding nuclei.

Emergent dimensions and branes from large- N confinement

$\mathcal{N}=1$ $SU(N)$ super-Yang-Mills theory on $\mathbb{R}^3\times S^1$ is believed to have a smooth dependence on the circle size $L$. Making $L$ small leads to calculable non-perturbative color confinement, mass gap, and string tensions. For finite $N$, the small-$L$ low-energy dynamics is described by a three-dimensional effective theory. The large-$N$ limit, however, reveals surprises: the infrared dual description is in terms of a theory with an emergent fourth dimension, curiously reminiscent of T-duality in string theory. Here, however, the emergent dimension is a lattice, with momenta related to the $S^1$-winding of the gauge field holonomy, which takes values in $\mathbb{Z}_N$. Furthermore, the low-energy description is given by a non-trivial gapless theory, with a space-like $z=2$ Lifshitz scale invariance and operators that pick up anomalous dimensions as $L$ is increased. Supersymmetry-breaking deformations leave the long-distance theory scale-invariant, but change the Lifshitz scaling exponent to $z=1$, and lead to an emergent Lorentz symmetry at small $L$. Adding a small number of fundamental fermion fields leads to matter localized on three-dimensional branes in the emergent four-dimensional theory.

Transport coefficient to trace anomaly in the clustering of color sources approach

From our previously obtained shear viscosity to entropy density ratio ($\eta/s$) in the framework of clustering of color sources (Color String Percolation Model: CSPM), we calculate the jet quenching parameter $\hat {q}$ and trace anomaly $\Delta = (\varepsilon -3\it p)/T^{4}$ as a function of temperature. It is shown that the scaled $\hat {q}/T^{3}$ is in agreement with the recent JET Collaboration estimates. The inverse of $\eta/s$ is found to represent $\Delta$. The results for $\Delta$ are in excellent agreement with Lattice Quantum Chromo Dynamics (LQCD) simulations. From the trace anomaly and energy density $\epsilon$, the equation of state is obtained as a function of temperature and compared with LQCD simulations. It is possible that there is a direct connection between the $\eta/s$ and $\Delta$. Thus the estimate of transport coefficient $\eta/s$ provides $\hat {q}$ and $\Delta$ as a function of temperature. Both $\Delta$ and $\eta/s$ describe the transition from a strongly coupled QGP to a weakly coupled QGP.

Scaling behaviours of the pT spectra for identified hadrons in pp collisions

We extend the scaling behaviour observed in the inclusive charged hadron transverse momentum (pT) distributions to the pT spectra of pions, kaons and protons produced in proton–proton (pp) collisions with center of mass energies () at 0.9, 2.76 and 7 TeV. This scaling behaviour arises when a linear transformation, is applied on the pion, kaon or proton pT spectra. The scaling parameter K depends on and is determined by a new method, the quality factor method, which does not rely on the shape of the scaling function. We argue that the pions, kaons and protons originate from different distributions of clusters which are formed by strings overlapping, and the scaling behaviours of these identified particles pT spectra could be understood with the colour string percolation model in a quantitative way simultaneously.

Hadronization scheme dependence of long-range azimuthal harmonics in high energy p + A reactions

We compare the distortion effects of three popular final-state hadronization schemes. We show how hadronization modifies the initial-state gluon correlations in high energy p + A collisions. The three models considered are (1) LPH: local parton–hadron duality, (2) CPR: collinear parton–hadron resonance independent fragmentation, and (3) LUND: color string hadronization. The strong initial-state azimuthal asymmetries are generated using the GLVB model for non-abelian gluon bremsstrahlung, assuming a saturation scale Qsat=2 GeV. Long-range elliptic and triangular harmonics for the final hadron pairs are compared based on the three hadronization schemes. Our analysis shows that the process of hadronization causes major distortions of the partonic azimuthal harmonics for transverse momenta at least up to pT=3 GeV. In particular, they appear to be greatly reduced for pT<1÷2 GeV.

Ridge from strings

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 fields inside string clusters. It is confirmed that in pp collisions the ridge structure only appears in rare events with abnormally high multiplicity. Comarison with the experimental data shows a good agreement. Also a good agreement is found for pPb collisions. For AA collisions a reasonable agreement is found for both near-side and away-side angular correlations although it worsens at intermediate angles.

De-Confinement and the Clustering of Color Sources

A brief review of the color string percolation model (CSPM) is presented. The clustering of color sources provides a framework of the the partonic interactions in the initial stage of the collisions. The CSPM has described several observables in agreement with the experimental results e.g. multiplicity, elliptic flow at RHIC and LHC energies. The thermodynamical quantities temperature and the Equation Of State (EOS) are obtained in agreement with the Lattice Quantum Chromo Dynamics (LQCD) calculations. The shear viscosity to entropy density ratio (·=s) is obtained at RHIC and LHC energies. It is also observed that the inverse of ·=s is equivalent to trace anomaly ¢ = ( i 3P)=T 4 in excellent agreement with the recent LQCD calculations.

Content Based Image Retrieval Using Colour Strings Comparison

Content Based Image Retrieval (CBIR) is a technique that enables a user to extract an image based on a query, from a database containing a large amount of images. A very fundamental issue in designing a content based image retrieval system is to select the image features that best represent the image contents in a database. In this paper, our proposed method mainly concentrated on database classification and efficient image representation. We present a method for content based image retrieval based on support vector machine classifier. In this method the feature extraction was done based on the colour string coding and string comparison. We succeed in transferring the images retrieval problem to strings comparison. Thus the computational complexity is decreases obviously. The image database used in our experiment contains 1800 colour images from Corel photo galleries. This CBIR approach has significantly increased the accuracy in obtaining results for image retrieval.

Color reconnection and flow-like patterns in pp collisions

Data collected at the LHC are confronted with the possible existence of flow in pp collisions. Here we present a study inside the framework of PYTHIA 8, showing that it contains implicit flow-like effects coming from multiple hard subcollisions and color string formation between initial and final partons from independent hard scatterings: color reconnection. We present studies with strange hadron observables in pp collisions at 7 TeV. Studies have been done both for minimum bias and multiplicity intervals in events with and without color reconnection to isolate the flow-like effect.

Turbulent pattern formation and diffusion in the early-time dynamics in relativistic heavy-ion collisions

We propose a picture of turbulent pattern formation in the relativistic heavy-ion collision, which follows an efficient process to break color strings and dispose energy in the whole phase space. We perform numerical simulations using the SU(2) pure Yang-Mills theory in a non-expanding box to observe a dynamical phenomenon in the transverse plane akin to the domain growth in time-dependent spin systems.

Long-range rapidity correlations in high energy AA collisions in Monte Carlo model with string fusion

The magnitude of long-range correlations between observables in two separated rapidity windows, proposed as a signature of the string fusion and percolation phenomenon, is studied in the framework of non-Glauber Monte Carlo string-parton model, based on the picture of elementary collisions of color dipoles. The predictions, obtained with and without string fusion, demonstrate effects of color string fusion on the observables in Pb-Pb collisions at the LHC: decrease of n-n correlation coeffcient with centrality and negative pt-n correlations, if a suffciently effective centrality estimator is applied. In general case it is shown that the values of n-n and pt-n correlation coeffcients strongly depend on the method of collision centrality fixation. In contrast, the predictions obtained for pt-pt correlation have almost no effect of centrality determination method and the corresponding experimental data would produce the strong limitation on the transverse radius of a string.

Modeling of exclusive parton distributions and long-range rapidity correlations in proton-proton collisions at the LHC energies

Soft pp interactions are considered in the framework of the phenomenological model with color strings formation. Under the assumption, that the elementary collision is realized as interaction of two color dipoles, the total inelastic cross section and the multiplicity of the charged particles are estimated and used for the parameters fixing. The special attention is given to the modelling of exclusive parton distributions taking into account the energy conservation and fixing the mass center that is necessary for the description of correlations, corresponding Monte Carlo procedures are developed for an arbitrary number of partons in a hadron. The string fusion algorithm in a cross-section plane is developed taking into account the finite rapidity width of strings. In this framework the influence of string fusion effects on long-range correlations of charged particles are estimated. The proposed algorithms are planned to be used for studying of heavy ion collisions.

Color Reconnection and Flowlike Patterns inppCollisions

Increasingly, with the data collected at the LHC we are confronted with the possible existence of flow in pp collisions. In this work, we show that PYTHIA8 produces flowlike effects in events with multiple hard subcollisions due to color string formations between final partons from independent hard scatterings, the so-called color reconnection. We present studies of different identified hadron observables in pp collisions at 7TeV. Studies have been done both for minimum bias and multiplicity intervals in events with and without color reconnection to isolate the flowlike effect.

Anisotropic flows from colour strings: Monte Carlo simulations

By direct Monte-Carlo simulations it is shown that the anisotropic flows can be successfully described in the colour string picture with fusion and percolation provided anisotropy of particle emission from the fused string is taken into account. Quenching of produced particles in the strong colour field of the string is the basic mechanism for this anisotropy. The concrete realization of this mechanism is borrowed from the QED. Due to dependence of this mechanism on the external field strength the found flows grow with energy, with values for $v_2$ at LHC energies greater by ~15% than at RHIC energies.

Clustering of Color sources and the Equation of State in Heavy Ion Collisions at RHIC and LHC Energies

The initial temperature Ti, energy density εi, and formation time τi of the initial state of the QGP formed in the heavy ion collisions at RHIC and LHC energies are determined using the data driven Color String Percolation Model (CSPM). Multiparticle production by interacting strings stretched between projectile and target form a spanning cluster at the percolation threshold. The relativistic kinetic theory relation for η/s is evaluated as a function of T and the mean free path (λmfp) using data and CSPM. η/s(Ti, λmfp) describes the transition from a strongly interacting QGP at T/Tc ~ 1 to a weakly coupled QGP at T/Tc ≥ 6. We find that the reciprocal of η/s is equal to the trace anomaly Δ = ε − 3P/T4 which also describes the transition. We couple this initial state of the QGP to a ID Bjorken expansion to determine the sound velocity c2s of the QGP for 0.85 ≤ T/Tc ≤ 3. The bulk thermodynamic quantities and the equation of state are in excellent agreement with LQCD results.

The site of interference in the saccadic Stroop effect

In two experiments, the source of competition in the saccadic Stroop effect was investigated. Colored strings of letters were presented at fixation with colored patches in the surround. The task of the participants was to make an eye movement to the patch in the same color as the central string of letters. Three types of cues were compared: Either the string of letters composed a word indicating a direction (the saccadic Stroop condition), or it was a set of arrow signs, or a peripheral stimulus appeared. Whereas response times and saccade errors were similarly influenced by the different types of cues, saccade trajectory deviations away from the cue were found only for peripheral onsets. A second experiment demonstrated that the absence of the curvature effects for direction words was not due to insufficient time to process the words. The results raise doubts on whether the saccadic Stroop effect is effectively an oculomotor effect and could pose a challenge to models of saccade target selection.

Clustering of color sources and the shear viscosity of the QGP in heavy ion collisions at RHIC and LHC energies

The Color String Percolation Model (CSPM) is used to determine the shear viscosity to entropy ratio ($\eta/s$) of the Quark-Gluon Plasma (QGP) produced in Au-Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at RHIC and Pb-Pb at $\sqrt{s_{NN}}$ = 2.76 TeV at LHC. The relativistic kinetic theory relation for $\eta/s$ is evaluated using CSPM values for the temperature and the mean free path of the QGP constituents. The experimental charged hadron transverse momentum spectrum is used to determine the percolation density parameter $\xi$ in Au-Au collisions (STAR). For Pb-Pb at $\sqrt{s_{NN}}$ = 2.76 TeV $\xi$ values are obtained from the extrapolation at RHIC energy. The value of $\eta/s$ is 0.204$\pm$0.020 and 0.262$\pm$0.026 at the CSPM initial temperatures of 193.6$\pm$3 MeV (RHIC) and 262.2 $\pm$13 MeV (LHC) respectively. These values are 2.5 and 3.3 times the AdS/CFT conjectured lower bound $1/4\pi$. We compare the CSPM $\eta/s$ analytic expression with weak coupling (wQGP) and strong coupling (sQGP) calculations. This indicates that the QGP is a strongly coupled fluid in the phase transition region.

Percolation and Deconfinement

Possible phase transition of strongly interacting matter from hadron to a Quark-Gluon Plasma (QGP) state have in the p ast received considerable interest. It has been suggested that this problem might be treated by percolation theory. Th e Color String Percolation Model (CSPM) is used to determine the equation of state (EOS) of the QGP produced in central Au-Au collisions at RHIC energies. The bulk thermodynamic quantities- energy density, entropy density and t he sound velocity- are obtained in the framework of CSPM. It is shown that the results are in excellent agreement with the recent lattice QCD calculations(LQCD).

Elliptic flow from colour strings

It is shown that the elliptic flow can be successfully described in the color string picture with fusion and percolation provided anisotropy of particle emission from the fused string is taken into account. Two possible sources of this anisotropy are considered, propagation of the string in the transverse plane and quenching of produced particles in the strong color field of the string. Calculations show that the second source gives an overwhelming contribution to the flow at accessible energies.

Color transparency in hadronic attenuation ofρ0mesons

Ongoing experiments at JLAB investigate the nuclear transparency in exclusive rho0(770) electroproduction off nuclei. In this work we present transport model predictions for the attenuation of rho0s in nuclei and for color transparency (CT) effects as observable at CLAS with a 5 GeV electron beam energy. A full event simulation presented here permits to study the impact of actual experimental acceptance conditions and kinematical cuts. The exclusive (e,e'rho0) cross section off nucleons is described by diffractive and color string breaking mechanisms extended toward the onset of the deep inelastic regime. Different hadronization and CT scenarios are compared. We show that a detailed analysis of elementary cross section, nuclear effects and experimental cuts is needed to reveal the early onset of rho0-CT at present JLAB energies.