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C. Pajares

Publications and source records attributed to C. Pajares.

At least 19 recordsLinked to original sources
arXiv2026

Percolation and de-confinement in relativistic nuclear collisions

In the present work we have analyzed the transverse momentum spectra of charged particles in high multiplicity $pp$ collisions at LHC energies $\sqrt s $ = 5.02 and 13 TeV using the Color String Percolation Model (CSPM). For heavy ions $Pb-Pb$ at $\sqrt {s_{NN}} $ = 2.76 and 5.02 TeV along with $Xe-Xe$ at $\sqrt {s_{NN}} $= 5.44 TeV have been analyzed. The initial temperature is extracted both in low and high multiplicity events in ${\it pp}$ collisions. For $A-A$ collisions the temperature is obtained as a function of centrality. From the measured energy density $ \varepsilon$ and the temperature T the dimensionless quantity $ \varepsilon/T^{4}$ is obtained. Our results for Pb-Pb and Xe-Xe collisions show a sharp increase in $\varepsilon/T^{4}$ above T $\sim$ 210 MeV and reaching the ideal gas of quarks and gluons value of $ \varepsilon/T^{4} \sim$ 16 at temperature $\sim $ 230 MeV. At this temperature there is a transition from the fluid behavior of QCD matter strongly interacting to a quasi free gas of quarks and gluons.

nucl-ex↗
arXiv2025

Thermal-nonthermal transition of the charged particle production in pp collisions

We determine the internal energy of charged particle production in minimum bias pp collisions using a thermostatistical approach by analyzing the $p_\text{T}$ spectrum reported by the ALICE Collaboration across LHC energies. To do this, we define temperature as the slope of the $p_\text{T}$ spectrum at low $p_\text{T}$ values and Shannon's entropy as the system's entropy, calculated considering the normalized $p_\text{T}$ spectrum. We found that the internal energy for the Hagedorn and Tricomi functions behaves linearly with temperature at low temperatures but becomes nonlinear at LHC energies, showing a thermal-nonthermal transition in the production of charged particles in pp collisions. Our estimation of the transition center of mass energy is $\sqrt{s^*}=27(11)\text{ keV}$ at baryon chemical potential $\mu_B=0$, which explains why the production of high $p_\text{T}$ hadrons has always been observed, even in earlier experiments, which may also encompass other experiments colliding e$^-$p or e$^+$e$^-$.

hep-ph↗
arXiv2024

Nonextensivity and temperature fluctuations of the Higgs boson production

We determine the temperature fluctuations associated with the Higgs boson $p_T$ spectrum through the derivation of the string tension distribution corresponding to the QCD-based Hagedorn function, frequently used to fit the transverse momentum distribution (TMD). The identified string tension fluctuations are heavy tailed, behaving similarly to the $q$-Gaussian distribution. After the convolution with the Schwinger mechanism, both approaches correctly describe the entire TMD. This approach is the onset for the nonthermal description of the particle production in ultrarelativistic pp collisions. By analyzing the data of pp collisions at $\sqrt{s} =13$ TeV, we found that the average temperature associated with the Higgs boson differential cross section is around 85 times greater than the estimated value for the charged particle TMD. Our results show that the Higgs boson production exhibits the largest deviation from the thermal description.

hep-ph↗
arXiv2024

Entropy and Heat Capacity of the transverse momentum distribution for pp collisions at RHIC and LHC energies

We investigate the transverse momentum distribution (TMD) statistics from three different theoretical approaches. In particular, we explore the framework used for string models, wherein the particle production is given by the Schwinger mechanism. The thermal distribution arises from the Gaussian fluctuations of the string tension. The hard part of the TMD can be reproduced by considering heavy tailed string tension fluctuations, for instance, the Tsallis $q$-Gaussian function, giving rise to a confluent hypergeometric function that fits the entire experimental TMD data. We also discuss the QCD-based Hagerdon function, another family of fitting functions frequently used to describe the spectrum. We analyze the experimental data of minimum bias pp collisions reported by the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) experiments (from $\sqrt{s}=0.2$ TeV to $\sqrt{s}=13$ TeV). We extracted the corresponding temperature by studying the behavior of the spectra at low transverse momentum values. For the three approaches, we compute all moments, highlighting the average, variance, and kurtosis. Finally, we compute the Shannon entropy and the heat capacity through the entropy derivative with respect to the temperature. We found that the $q$-Gaussian string tension fluctuations lead to a monotonically increasing heat capacity as a function of the center of mass energy, which is also observed for the Hagedorn fitting function. This behavior is consistent with the experimental observation that the temperature slowly rises with increments of the collision energy.

hep-ph↗
arXiv2023

Interacting color strings as the origin of the liquid behavior of the quark-gluon plasma

We study the radial distribution function of the color sources (strings) formed in hadronic collisions and the requirements to obtain a liquid. As a repulsive interaction is needed, we incorporate a concentric core in the strings as well as the probability that a string allows core-core overlaps. We find systems where the difference between the gas-liquid and confined-deconfined phase transition temperatures is small. This explains the experimentally observed liquid behavior of the quark-gluon plasma above the confined-deconfined transition temperature.

hep-ph↗
arXiv2022

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 $\sqrt{s}$, multiplicity or centrality increases. In this paper, we introduce the complete information of the TMD in the color string percolation model by means of the determination of 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 $\sqrt{s}$. We summarize these results in a phase diagram that indicates the $q$-Gaussian parameters region allowing the quark-gluon plasma formation.

hep-ph↗
arXiv2022

On the relation between the soft and hard parts of the transverse momentum distribution

Usually, the transverse momentum distribution is described by a sum of an exponential decay term plus a decreasing power like contribution representing the soft non-perturbative and hard perturbative QCD collisions, respectively. In this paper, we derive an analytical function that can describe the whole transverse momentum spectrum. This is obtained using a $q$-Gaussian distribution to describe the string tension fluctuations. The parameter $q$ determines the departure of the thermal distribution as well as the minimum length that can be explored at high transverse momentum. We also show that the ratio between both scales only depends on the $q$ parameter.

hep-ph↗
arXiv2022

Percolation leads to finite-size effects on the transition temperature and center of mass energy required for the 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 twenty 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.

hep-ph↗
arXiv2021

Deconfinement and degrees of freedom in $pp$ and $A-A$ collisions at LHC energies

We present the extraction of the temperature by analyzing the charged particle transverse momentum spectra in lead-lead (Pb-Pb) and proton-proton (${\bf pp}$) collisions at LHC energies from the ALICE Collaboration using the Color String Percolation Model (CSPM). From the measured energy density ${\bm \varepsilon}$ and the temperature T the dimensionless quantity ${\bm \varepsilon/}T^{4}$ is obtained to get the degrees of freedom (DOF), ${\bm \varepsilon}/T^{4}$ = DOF ${ π^{2}}$/30. We observe for the first time a two-step behavior in the increase of DOF, characteristic of deconfinement, above the hadronization temperature at temperature $\sim$ 210 MeV for both Pb-Pb and ${\bf pp}$ collisions and a sudden increase to the ideal gas value of $\sim $ 47 corresponding to three quark flavors in the case of Pb-Pb collisions.

hep-ph↗
arXiv2020

Area covered by disks in small-bounded continuum percolating systems: An application to the string percolation model

In string percolation model, the study of colliding systems at high energies is based on a continuum percolation theory in two dimensions where the number of strings distributed in the surface of interest is strongly determined by the size and the energy of the colliding particles. It is also expected that the surface where the disks are lying be finite, defining a system without periodic boundary conditions. In this work, we report modifications to the fraction of the area covered by disks in continuum percolating systems due to a finite number of disks and bounded by different geometries: circle, ellipse, triangle, square and pentagon, which correspond to the first Fourier modes of the shape fluctuation of the initial state after the particle collision. We find that the deviation of the fraction of area covered by disks from its corresponding value in the thermodynamic limit satisfies a universal behavior, where the free parameters depend on the density profile, number of disks and the shape of the boundary. Consequently, it is also found that the color suppression factor of the string percolation model is modified by a damping function related to the small-bounded effects. Corrections to the temperature and the speed of sound defined in string systems are also shown for small and elliptically bounded systems.

cond-mat.stat-mech↗
arXiv2020

Site-bond percolation solution to preventing the propagation of \textit{Phytophthora} zoospores on plantations

We propose a strategy based on the site-bond percolation to minimize the propagation of \textit{Phytophthora} zoospores on plantations, consisting in introducing physical barriers between neighboring plants. Two clustering processes are distinguished: i) one of cells with the presence of the pathogen, detected on soil analysis; and ii) that of diseased plants, revealed from a visual inspection of the plantation. The former is well described by the standard site-bond percolation. In the latter, the percolation threshold is fitted by a Tsallis distribution when no barriers are introduced. We provide, for both cases, the formulae for the minimal barrier density to prevent the emergence of the spanning cluster. Though this work is focused on a specific pathogen, the model presented here can also be applied to prevent the spreading of other pathogens that disseminate, by other means, from one plant to the neighboring ones. Finally, the application of this strategy to three types of commercialy important Mexican chili plants is also shown.

q-bio.PE↗
arXiv2019

De-Confinement in high multiplicity proton-proton collisions at LHC energies

Recently, the CMS Collaboration has published identified particle transverse momentum spectra in high multiplicity events at LHC energies $\sqrt s $ = 0.9-13 TeV. In the present work the transverse momentum spectra have been analyzed in the framework of the color fields inside the clusters of overlapping strings, which are produced in high energy hadronic collisions. The non-Abelian nature is reflected in the coherence sum of the color fields which as a consequence gives rise to an enhancement of the transverse momentum and a suppression of the multiplicities relative to the non overlapping strings. The initial temperature and shear viscosity to entropy density ratio $η/s$ are obtained. For the higher multiplicity events at $\sqrt s $ =7 and 13 TeV the initial temperature is above the universal hadronization temperature and is consistent with the creation of de-confined matter. In these small systems it can be argued that the thermalization is a consequence of the quantum tunneling through the event horizon introduced by the confining color fields, in analogy to the Hawking-Unruh effect. The small shear viscosity to entropy density ratio $η/s$ near the critical temperature suggests that the matter is a strongly coupled Quark Gluon Plasma.

hep-ph↗
arXiv2019

Elliptic and triangular flows in dAu collisions at 200 GeV in the fusing color string model

In the color string picture with fusion and percolation the elliptic and triangular flows are studied for p-Au and d-Au collisions at 200 GeV. The ordering $v_n(d-Au)>v_n(p-Au)$ observed experimentally for central collisions is reproduced.The calculated elliptic flow $v_2$ at central collisions agrees satisfactorily with thedata. The triangular flow $v_3$ is found to be greater than the experimental values, similar to the resultsobtained in the approach based on the Color Glass Condensate initial conditions with subsequenthydrodynamical evolution.

hep-ph↗
arXiv2019

String percolation in AA and p+p collisions

A brief review of the string percolation model and its results are presented together with the comparison to experimental data. First, it is done an introduction to the quark-gluon phase diagram and the lattice results concerning the confinement and the percolation of center domains. It is studied the interaction of the strings produced in nucleus-nucleus and proton-proton collisions showing how the string percolation arises. The main consequences of the string percolation, concerning the dependence on the energy and centrality, on the multiplicities and the mean transverse momentum are obtained comparing with experimental data. It is emphasized the non-abelian character of the color field of the strings forming the cluster to reproduce the rise of the transverse momentum with multiplicity and the relative suppression of multiplicities. It is also studied different observables like multiplicity and transverse momentum distributions, dependence with multiplicity and transverse momentum correlations, forward-backward correlations, the strength of the Bose-Einstein correlations, dependence on the multiplicity of $J/Ψ$ production and its possible suppression in pp collisions at high multiplicity, strangeness enhancement, elliptic flow, and ridge structure. The comparison with the data shows an overall agreement. The thermodynamical properties of the extended cluster formed in the collision are discussed computing its energy and entropy density, shear viscosity over entropy density ratio, bulk viscosity, sound speed and trace anomaly as a function of temperature, showing a remarkable agreement with lattice QCD evaluations. The string percolation can be regarded as the initial frame able to describe the collective behavior produced in AA and pp collisions.

hep-ph↗
arXiv2018

Thermal behavior, entanglement entropy and parton distributions

The apparent thermalization of the particles produced in hadronic collisions can be obtained by quantum entanglement of the partons of the initial state once a fast hard collision is produced. The scale of the hard collision is related to the thermal temperature. As the probability distribution of these events is of the form $np(n)$, as a consequence, the von Neumann entropy is larger than in the minimum bias case. The leading contribution to this entropy comes from the logarithm of the number of partons $n$, all with equal probability, making maximal the entropy. In addition there is another contribution related to the width of the parton multiplicity. Asymptotically, the entanglement entropy becomes the logarithm of $\sqrt{n}$, indicating that the number of microstates changes with energy from $n$ to $\sqrt{n}$.

hep-ph↗
arXiv2018

$p_t$- dependence of the flow coefficients for pp collisions in the color string scenario. Monte-Carlo simulations

In the color string picture with fusion and percolation the dependence of the flow coefficients $v_n$ on the transverse momentum is studied for pp collisions the LHC energy respectively. Monte-Carlo simulations are used to locate simple strings and their fused clusters. The results favorably agree with the CMS data in the region $0.2 \le p_t\le 3.$ GeV/c appropriate for the string scenario.

hep-ph↗
arXiv2018

Thermal behavior and entanglement in Pb-Pb and p-p collisions

The thermalization of the particles produced in collisions of small size objects can be achieved by quantum entanglement of the partons of the initial state as it was analyzed recently in proton-proton collisions. We extend such study to Pb-Pb collisions and to different multiplicities of proton-proton collisions. We observe that, in all cases, the effective temperature is approximately proportional to the hard scale of the collision. We show that such relation between the thermalization temperature and the hard scale can be explained as a consequence of the clustering of the color sources. The fluctuations on the number of parton states decreases with multiplicity in Pb-Pb collisions as far as the width of the transverse momentum distributions decreases, contrary to the p-p case. We relate these fluctuations to the temperature time fluctuations by means of a Langevin equation for the white noise due to the quench of a hard parton collision.

hep-ph↗