Charged Hadron Distributions Research Articles

Data-driven discovery of Tsallis-like distribution using symbolic regression in high-energy physics.

The application of atificial intelligence (AI) in fundamental physics has faced limitations due to its inherently uninterpretable nature, which is less conducive to solving physical problems where natural phenomena are expressed in human-understandable language, i.e. mathematical equations. Fortunately, there exists a form of interpretable AI that aligns seamlessly with this requirement, namely, symbolic regression (SR), which learns mathematical equations directly from data. We introduce a groundbreaking application of SR on actual experimental data with an unknown underlying model, representing a significant departure from previous applications, which are primarily limited to simulated data. This application aims to evaluate the reliability of SR as a bona fide scientific discovery tool. SR is applied on transverse-momentum-dependent distributions of charged hadrons measured in high-energy-physics experiments. The outcome underscores the capability of SR to derive an analytical expression closely resembling the Tsallis distribution. The latter is a well-established and widely employed functional form for fitting measured distributions across a broad spectrum of hadron transverse momentum. This achievement is among the first instances where SR demonstrates its potential as a scientific discovery tool. It holds promise for advancing and refining SR methods, paving the way for future applications on experimental data.

Multiplicity dependence of the pT -spectra for identified particles and its relationship with partonic entropy

We investigate the multiplicity dependence of the transverse momentum pT spectra of hadrons produced in high-energy collisions. We propose that the partonic distribution be parametrized by its nonextensive entropy and the parton saturation scale Qs(x). These two variables can be identified from the produced charged hadron distributions and provide important information on the gluon dynamics at the moment of interaction. From this perspective, we interpret data from different ALICE multiplicity classes at s=13 TeV and s=5.02 TeV. A multiplicity-dependent scaling function is presented and the dependence of the interaction area on multiplicity is also investigated. Published by the American Physical Society 2024

Dependence of thermodynamic quantities at freeze-out on pseudorapidity and collision energy in p-p collisions at LHC energies* *Supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R106), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. In addition, the authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA for funding this research

The transverse momentum distributions of charged hadrons produced in proton-proton collisions at center-of-mass energies ( ) of 0.9 TeV and 2.36 TeV, as measured by the CMS detector at the Large Hadron Collider (LHC), have been analyzed within various pseudorapidity classes utilizing the thermodynamically consistent Tsallis distribution. The fitting procedure resulted in the key parameters, namely, effective temperature (T), non-extensivity parameter (q), and kinetic freezeout volume (V). Additionally, the mean transverse momentum ( ) and initial temperature (Ti ) of the particle source are determined through the fit function and string percolation method, respectively. An alternative method is employed to calculate the kinetic freezeout temperature ( ) and transverse flow velocity ( ) from T. Furthermore, thermodynamic quantities at the freezeout, including energy density (ε), particle density (n), entropy density (s), pressure (P), and squared speed of sound ( ), are computed using the extracted T and q. It is also observed that, with a decrease in pseudorapidity, all thermodynamic quantities except V and q increase. This trend is attributed to greater energy transfer along the mid pseudorapidity. q increases towards higher values of pseudorapidity, indicating that particles close to the beam axis are far from equilibrium. Meanwhile, V remains nearly independent of pseudorapidity. The excitation function of these parameters (q) shows a direct (inverse) correlation with collision energy. The ε, n, s, and P show a strong dependence on collision energies at low pseudorapidities. Explicit verification of the thermodynamic inequality suggests the formation of a highly dense droplet-like Quark-Gluon Plasma (QGP). Additionally, the inequality is explicitly confirmed, aligning with the evolution of the produced fireball.

Two-particle azimuthal correlations in γp interactions using pPb collisions at [formula omitted

The first measurements of the Fourier coefficients (VnΔ) of the azimuthal distributions of charged hadrons emitted from photon-proton (γp) interactions are presented. The data are extracted from 68.8 nb−1 of ultra-peripheral proton-lead (pPb) collisions at sNN=8.16TeV using the CMS detector. The high energy lead ions produce a flux of photons that can interact with the oncoming proton. This γp system provides a set of unique initial conditions with multiplicity lower than in photon-lead collisions but comparable to recent electron-positron and electron-proton data. The VnΔ coefficients are presented in ranges of event multiplicity and transverse momentum (pT) and are compared to corresponding hadronic minimum bias pPb results. For a given multiplicity range, the mean pT of charged particles is smaller in γp than in pPb collisions. For both the γp and pPb samples, V1Δ is negative, V2Δ is positive, and V3Δ consistent with 0. For each multiplicity and pT range, V2Δ is larger for γp events. The γp data are consistent with model predictions that have no collective effects.

Charged Particles Transverse Momentum and Pseudorapidity Distribution in Hadronic Collisions at LHC Energies

We present an analysis of the pseudorapidity η and transverse momentum pT distributions of charged hadrons in pp collisions for the kinematic range of 0<pT<4 GeV/c and |η|<2.4 at 0.9, 2.36, and 7 TeV. Charged particles are produced in pp collision using several Monte Carlo event generators (Pythia Simple, Vincia, Dire showers, Sibyll2.3d, QGSJETII-04, EPOS-LHC) and compared with CMS data at LHC. It is observed that the Simple parton showers can explain the CMS data very well for pT>1 GeV/c at 0.9 and 2.36 TeV within the experimental errors, while Dire overshoots and Vicia undershoots the data by 50% each. At 7 TeV, the Dire module presents a good prediction, whereas the Simple and Vincia modules underestimate the data within 30% and 50%. Comparing the Simple module of the Pythia model and the predictions of the CRMC models with the experimental data shows that at 0.9 TeV, EPOS-LHC has better results than the others. At 2.36 GeV, the cosmic rays Monte Carlo (CRMC) models have better prediction than the Simple module of Pythia at low pT, while QGSJETII-04 predicts well at high pT. QGSJETII-04 and EPOS-LHC have closer results than the Pythia-Simple and Sibyll2.3d at 7 TeV. In the case of the pseudorapidity distributions, only the Pythia-Simple reproduced the experimental measurements at all energies. The Dire module overestimates, while Vincia underestimates the data in decreasing order of discrepancy (20%, 12%, 5%) with energy. All CRMC models underestimate the data over the entire η range at all energies by 20%. The angular ordering of partons and the parton fragmentation could be possible reasons for this deviation. Furthermore, we used the two-component standard distribution to fit the pT spectra to the experimental data and extracted the effective temperature (Teff) and the multiplicity parameter (N0). It is observed that Teff increases with the increase in the center of mass energy. The fit yielded 0.20368±0.01, 0.22348±0.011, and 0.24128±0.012 GeV for 0.9, 2.36, and 7 TeV, respectively. This shows that the system at higher energies freezes out earlier than lower ones because they quickly attain the equilibrium state.

Studying hadronization at LHCb

LHCb is a fully instrumented forward spectrometer with particle identification and muon reconstruction covering the pseudorapidity (\etaη) range from 2 to 5. Its full jet reconstruction capability makes the LHCb experiment a suitable venue to explore jet substructure observables, particularly formation of hadrons and heavy quarkonia resonances inside jets. This contribution presents a brief overview of ongoing research program and discusses recent results on non-identified charged hadron distributions in Z-tagged jets and charmonium distributions within jets. Future works towards furthering the knowledge of hadronizion are also discussed.

Using Z Boson Events to Study Parton-Medium Interactions in Pb-Pb Collisions.

The spectra measurements of charged hadrons produced in the shower of a parton originating in the same hard scattering with a leptonically decaying Z boson are reported in lead-lead nuclei (Pb-Pb) and proton-proton (pp) collisions at a nucleon-nucleon center-of-mass energy of 5.02TeV. Both Pb-Pb and pp data sets are recorded by the CMS experiment at the LHC and correspond to an integrated luminosity of 1.7 nb^{-1} and 320 pb^{-1}, respectively. Hadronic collision data with one reconstructed Z boson candidate with the transverse momentum p_{T}>30 GeV/c are analyzed. The Z boson constrains the initial energy and direction of the associated parton. In heavy ion events, azimuthal angular distributions of charged hadrons with respect to the direction of a Z boson are sensitive to modifications of the in-medium parton shower and medium response. compared to reference data from pp interactions, the results for central Pb-Pb collisions indicate a modification of the angular correlations. The measurements of the fragmentation functions and p_{T} spectra of charged particles in Z boson events, which are sensitive to medium modifications of the parton shower longitudinal structure, are also reported. Significant modifications in central Pb-Pb events compared to the pp reference data are also found for these observables.

Azimuthal asymmetries and transverse momentum distributions of charged hadrons in muon-proton deep inelastic scattering

In 2016 and 2017, the COMPASS Collaboration at CERN collected a large sample of DIS events with a longitudinally polarized 160 GeV/[Formula: see text] muon beam scattering off a liquid hydrogen target. Part of the collected data has been analyzed to extract preliminary results for the amplitudes of the modulations in the azimuthal angle of the charged hadrons and for their transverse momentum distributions. These observables give relevant information for the study of the transverse momentum and spin structure of the nucleon. The results, presented here for the first time, have been obtained from part of the data collected in 2016. In the analysis, a new method for the evaluation of the contribution of exclusive diffractive processes has been implemented. The azimuthal asymmetries exhibit strong kinematic dependencies, similar to those observed in COMPASS deuteron measurements. The transverse momentum distributions show smooth exponential trends and are compatible with the previous measurement on deuteron.

Measurement of Charged Hadron Distributions in Beauty and Charm Quark Tagged Jets at the Large Hadron Collider beauty Experiment

Measurement of Charged Hadron Distributions in Beauty and Charm Quark Tagged Jets at the Large Hadron Collider beauty Experiment

Measurement of b jet shapes in proton-proton collisions at sqrt{s} = 5.02 TeV

We present the first study of charged-hadron production associated with jets originating from b quarks in proton-proton collisions at a center-of-mass energy of 5.02 TeV. The data sample used in this study was collected with the CMS detector at the CERN LHC and corresponds to an integrated luminosity of 27.4 pb−1. To characterize the jet substructure, the differential jet shapes, defined as the normalized transverse momentum distribution of charged hadrons as a function of angular distance from the jet axis, are measured for b jets. In addition to the jet shapes, the per-jet yields of charged particles associated with b jets are also quantified, again as a function of the angular distance with respect to the jet axis. Extracted jet shape and particle yield distributions for b jets are compared with results for inclusive jets, as well as with the predictions from the pythia and herwig++ event generators.

Multiplicity and pseudo-rapidity density distributions of charged particles produced in pp, pA and AA collisions at RHIC & LHC energies

Multiplicity and pseudorapidity (η) density (dN ch/dη) distributions of charged hadrons provide key information towards understanding the particle production mechanisms and initial conditions of high-energy heavy-ion collisions. However, detector constraints limit the η-range across which charged particle measurements can be carried out. Extrapolating the measured distributions to large η-range by parameterizing measured distributions and by using calculations from event generators, we characterize the production of charged particles over the full kinematic range. In the present study, we use three different anstze to obtain quantitative descriptions of the shape of pseudorapidity distributions of charged hadrons produced in pp, p–A, and A–A collisions for beam energies () ranging from a few GeV to a few TeV corresponding to RHIC and LHC energies. We study the limiting fragmentation behavior in these collisions and report evidence for participant-scaling violations in high-energy collisions at the TeV scale. We additionally examine measured pseudorapidity distributions to constrain models describing initial conditions of particle production. We predict the centrality dependence of charged particle multiplicity distributions at FAIR and NICA energies and give an estimation of charged particle multiplicity at η = 0 for the proposed HE-LHC and FCC energies.

Energy density at kinetic freeze-out in Pb–Pb collisions at the LHC using the Tsallis distribution

The thermodynamic parameters like energy density, pressure, entropy density, temperature and particle density are determined from the transverse momentum distributions of charged hadrons in Pb–Pb collisions at the LHC. The results show a clear increase with the centrality and the beam energy in all parameters. It is determined that in the final freeze-out stage the energy density reaches a value of about 0.039 GeV fm−3 for the most central collisions at . This is less than that at chemical freeze-out where the energy density is about 0.36 GeV fm−3. This decrease approximately follows a T4 law. The results for the pressure and entropy density are also presented for each centrality class at and 5.02 TeV.

Transverse Momentum Distributions of Charged Hadrons Produced in He12C Collisions at 4.2A GeV/c

We study the trend of transverse momentum (pT) and maximum transverse momentum (pTmax) distributions of pions and protons in He12C-interactions at 4.2A GeV/c. A comparison between theoretical results, from Cascade model (Dubna version), and experimental results, provided by the 2-m propane bubble chamber of JINR, Dubna, is made. Different regions in terms of the trend of pT distributions of the particles are identified: a region where the pT is greater than 0.375 GeV/c is termed as region-III. This region has a maximum value of pT$$\sim $$ 1 and 1.5 GeV/c, respectively, for π -mesons and protons. Here, the protons affect the pT distribution one order more than the mesons and the experimental and Cascade results disagree with each other. In addition, the number of particles detected in the experiments is less than the model, in the region-III. This aimed to establish a correlation between the production of the maxim pT and high-pT region and to comprehend the dynamics of the production of particles with high momentum distribution.

Pseudorapidity distributions of charged hadrons in xenon-xenon collisions at [formula omitted

Measurements of the pseudorapidity distributions of charged hadrons produced in xenon-xenon collisions at a nucleon-nucleon centre-of-mass energy of sNN=5.44 TeV are presented. The measurements are based on data collected by the CMS experiment at the LHC. The yield of primary charged hadrons produced in xenon-xenon collisions in the pseudorapidity range |η|<3.2 is determined using the silicon pixel detector in the CMS tracking system. For the 5% most central collisions, the charged-hadron pseudorapidity density in the midrapidity region |η|<0.5 is found to be 1187±36 (syst), with a negligible statistical uncertainty. The rapidity distribution of charged hadrons is also presented in the range |y|<3.2 and is found to be independent of rapidity around y=0. Existing Monte-Carlo event generators are unable to simultaneously describe both results. Comparisons of charged-hadron multiplicities between xenon-xenon and lead-lead collisions at similar collision energies show that particle production at midrapidity is strongly dependent on the collision geometry in addition to the system size and collision energy.

Hadron production models\u2019 prediction for pT distribution of charged hadrons in pp interactions at 7 TeV

The yield of transverse momentum (pT) spectra of integrated hadrons and their ratios produced in pp collisions at 7 TeV are reported using DPMJET-III, EPOS1.99, EPOS-LHC, HIJING1.383, QGSJETII-04, and Sibyll2.3c models. The models’ predictions are compared with the ALICE measurements obtained at mid rapidity and in the pT range from 0.3–6 GeV/c, 0.2–6 GeV/c, and 0.1–3 GeV/c for protons, kaons and pions respectively. Compared to the experimental data, the EPOS1.99 and EPOS-LHC models predict the yield of pion very well while reproducing yields of kaon and proton at low pT only. The DPMJET-III model predicts the yield of pions, kaons and protons only at intermediate value of pT. The HIJING and Sibyll models describe the integrated yield of pion well at high pT only. The QGSJETII model predicts the yield of kaon for almost the whole pT range. EPOS1.99 and Sibyll models reproduce excellent prediction of the K/π ratio over the entire range of pT whereas the EPOS-LHC, HIJING and DPMJET models underpredict with increasing order of discrepancy respectively. The EPOS1.99, EPOS-LHC, and Sibyll models predict the p/π ratio for low values of pT, but overpredict at high values, while the DPMJET-III and HIJING models underpredict over the entire range of pT. Although the models’ predictions are mostly consistent with the ALICE measurements but none of the models completely describe the entire distribution for the integrated yield of hadron and their ratios.

Transverse momentum distribution of charged hadrons based on wounded quark model

In nucleus-nucleus collisions, new particles are produced mainly through strong interactions among the constituents of the QCD medium. The search of a unified phenomenological model to understand this production mechanism is one of the main motivation behind the heavy ion experiments. A vast variety of data coming from nucleus-nucleus collision experiments put a stringent constraint on the particle production models. A unified and proper model must satisfy the various data regarding pseudorapidity distributions, transverse energy density distributions, transverse momentum distributions with respect to control parameters in different types of collisions at various energies simultaneously. Recently we proposed a new version of wounded quark model (WQM) which actually satisfies many points of this criteria. However, these kind of static initial model conditions have problem in calculating the transverse momentum distributions of charged hadrons. In this article, we have used the important ingredients of WQM like number of wounded quarks and number of quark-quark collisions to fit the transverse momentum spectra of charged hadrons. Based on the assumption of different mechanisms at different regions, i.e. different mechanisms for soft $ p_{T}$ and hard momentum part, we have proposed a parameterization made of two functions to calculate the transverse momentum spectra in different collisions at different energies ranging from higher RHIC to LHC. We hope that this study along with our recent work on WQM will become a more suitable choice as unified model for particle production in strong interaction, instead of wounded nucleon model.

Transverse momentum distribution and elliptic flow of charged hadrons in U+U collisions at sqrt{s_{NN}}=193 GeV using HYDJET++

Recent experimental observations of the charged hadron properties in U+U collisions at 193 GeV contradict many of the theoretical models of particle production including two-component Monte Carlo Glauber model. The experimental results show a small correlation between the charged hadron properties and the initial geometrical configurations (e.g. body–body, tip–tip etc.) of U+U collisions. In this article, we have modified the Monte Carlo HYDJET++ model to study the charged hadron production in U+U collisions at 193 GeV center-of-mass energy in tip–tip and body–body initial configurations. We have modified the hard as well as soft production processes to make this model suitable for U+U collisions. We have calculated the pseudorapidity distribution, transverse momentum distribution and elliptic flow distribution of charged hadrons with different control parameters in various geometrical configurations possible for U+U collision. We find that HYDJET++ model supports a small correlation between the various properties of charged hadrons and the initial geometrical configurations of U+U collision. Further, the results obtained in modified HYDJET++ model regarding dn_{ch}/deta and elliptic flow (v_{2}) suitably matches with the experimental data of U+U collisions in minimum bias configuration.

PT spectra in pp and AA collisions at RHIC and LHC energies using the Tsallis-Weibull approach

The Tsallis q -statistics have been incorporated in the Weibull model of particle production, in the form of q-Weibull distribution, to describe the transverse momentum ( $p_{T}$ ) distribution of charged hadrons at mid-rapidity, measured at RHIC and LHC energies. The q-Weibull distribution is found to describe the observed $ p_{T}$ distributions over all ranges of measured $ p_{T}$ . Below 2.2 GeV/c, while going from peripheral to central collisions, the parameter q is found to decrease systematically towards unity, indicating an evolution from a non-equilibrated system in peripheral collisions, towards a more thermalized system in central collisions. However, the trend is reversed in the all inclusive $ p_{T}$ regime. This can be attributed to an increase in relative contribution of hard pQCD processes in central collisions. The $ \lambda$ -parameter is found to be associated with the mean $ p_{T}$ or the collective expansion velocity of the produced hadrons, which shows an expected increase with centrality of collisions. The k parameter is observed to increase with the onset of hard QCD scatterings, initial fluctuations, and other processes leading to non-equilibrium conditions.

Universal freezeout condition for charged hadrons in a hybrid approach

Hadronic freezeout during the evolution of the medium created in heavy-ion collisions is an important phenomena. It is quite useful to find a universal freezeout condition for each and every nuclear collisions. In this article, we have constructed a hybrid model to calculate the ratio of transverse energy to total mean multiplicity $E_{T} /N_{ch}$, since this ratio can possibly act as a freezeout condition in heavy-ion collision experiments. Present hybrid model blends two approaches : Tsallis statistics and wounded quark approach. Recently, Tsallis statistics has been reliably used to obtain the transverse momentum distribution of charged hadrons produced in relativistic ion collisions. On the other side it has been shown that the pseudorapidity distribution of charged hadrons can be calculated satisfactorily using the wounded quark model (WQM). We have used this hybrid model to calculate the transverse energy density distributions, $dE_{T}/d\eta$ at midrapidity using charged particle pseudorapidity distributions, $dN_{ch}/d\eta$ and mean transverse momentum $\langle p_{T} \rangle$ in various type of nuclear collisions. We found that present hybrid model satisfactorily explains the experimental data whether other models fail to reproduce the data at central and at peripheral collisions simultaneously. Finally, ratio of transverse energy to total mean multiplicity, $E_{T} /N_{ch}$ has been computed within hybrid model and compared with the available experimental data at RHIC and LHC energies. We observed no explicit dependence of $E_{T} /N_{ch}$ on energy as well as centrality and thus it can definitely act as a freezeout criteria.

Pseudorapidity distributions of charged hadrons in proton-lead collisions at sqrt{s_{mathrm{NN}}}=5.02 and 8.16 TeV

The pseudorapidity distributions of charged hadrons in proton-lead collisions at nucleon-nucleon center-of-mass energies sqrt{s_{mathrm{NN}}}=5.02 and 8.16 TeV are presented. The measurements are based on data samples collected by the CMS experiment at the LHC. The number of primary charged hadrons produced in non-single-diffractive proton-lead collisions is determined in the pseudorapidity range |ηlab| < 2.4. The charged-hadron multiplicity distributions are compared to the predictions from theoretical calculations and Monte Carlo event generators. In the center-of-mass pseudorapidity range |ηcm| < 0.5, the average charged-hadron multiplicity densities 〈dNch/dηcm〉|ηcm| < 0.5 are 17.31 ± 0.01 (stat) ± 0.59 (syst) and 20.10 ± 0.01 (stat) ± 0.85(syst) at sqrt{s_{mathrm{NN}}}=5.02 and 8.16 TeV, respectively. The particle densities per participant nucleon are compared to similar measurements in proton-proton, proton-nucleus, and nucleus-nucleus collisions.