Stopping In Collisions Research Articles

Search for baryon junctions in photonuclear processes and isobar collisions at RHIC

During the early development of quantum chromodynamics, it was proposed that baryon number could be carried by a non-perturbative Y-shaped topology of gluon fields, called the gluon junction, rather than by the valence quarks as in the QCD standard model. A puzzling feature of ultra-relativistic nucleus-nucleus collisions is the apparent substantial baryon excess in the mid-rapidity region that could not be adequately accounted for in most conventional models of quark and diquark transport. The transport of baryonic gluon junctions is predicted to lead to a characteristic exponential distribution of net-baryon density with rapidity and could resolve the puzzle. In this context we point out that the rapidity density of net-baryons near mid-rapidity indeed follows an exponential distribution with a slope of -0.61±0.03\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-0.61\\pm 0.03$$\\end{document} as a function of beam rapidity in the existing global data from A+A collisions at AGS, SPS and RHIC energies. To further test if quarks or gluon junctions carry the baryon quantum number, we propose to study the absolute magnitude of the baryon vs. charge stopping in isobar collisions at RHIC. We also argue that semi-inclusive photon-induced processes (γ+p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma +p$$\\end{document}/A) at RHIC kinematics provide an opportunity to search for the signatures of the baryon junction and to shed light onto the mechanisms of observed baryon excess in the mid-rapidity region in ultra-relativistic nucleus-nucleus collisions. Such measurements can be further validated in A+A collisions at the LHC and e+p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e+p$$\\end{document}/A collisions at the EIC.

Diquark break-up jet effects on particle production in central Ar+Sc and Pb+Pb collisions at CERN SPS energies

We investigate the rapidity spectra of protons in central Ar+Sc and Pb+Pb collisions at Conseil Européen pour la Recherche Nucléaire (CERN) super proton synchrotron (SPS) energies, utilizing the HIJING code integrated with the advanced popcorn (AP) mechanism from PYTHIA6.4. We find that the standard HIJING/AP model is inadequate for fully capturing the proton rapidity distributions observed in these collisions. To overcome this, we focus on the leading diquark (LD) break-up component, distinguishing between diquark preserving and diquark breaking (DB) behaviors. Our analysis reveals that the suppressed DB component is essential for accurately describing the proton and neutron x F spectra, particularly noting an excess of baryon number at lower x F values consistent with experimental observations. By integrating the suppressed LD break-up mechanism, informed by pp and Be+Be collision data, we successfully replicate the proton rapidity spectra and also effectively capture the rapidity spectra of negative pions and charged kaons for the studied reactions. These outcomes underscore the critical role of the suppressed LD break-up component in elucidating the mechanisms of baryon production and stopping in heavy-ion collisions at CERN SPS energies.

Baryon transport in color flux tubes

Color flux tubes are a standard perspective from which to understand stopping in high-energy collisions. Mechanisms for baryon transport and polarization within a tube are considered here, both in regards to the transport of baryons from the target and projectile toward midrapidity and in regards to the correlations of baryon-antibaryon pairs created in the tube. The roles of tube merging and gluon radiation within a tube are emphasized. Published by the American Physical Society 2024

Correlations of baryon and charge stopping in heavy ion collisions* *Supported in part by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB34030000) and the National Key Research and Development Program of China (2022YFA1604900), the U.S. DOE Office of Science365 under contract (DE-SC0012704, DE-FG02-10ER41666, DE-AC02-98CH10886)

Baryon numbers are theorized to be carried by valence quarks in the standard QCD picture of the baryon structure. Another theory proposed an alternative baryon number carrier, a non-perturbative Y-shaped configuration of the gluon field, called the baryon junction in the 1970s. However, neither of these theories has been verified experimentally. Recently, searching for the baryon junction by investigating the correlation of net-charge and net-baryon yields at midrapidity in heavy-ion collisions has been suggested. This paper presents studies of such correlations in collisions of various heavy ions from oxygen to uranium with the UrQMD Monte Carlo model. The UrQMD model implements valence quark transport as the primary means of charge and baryon stopping at midrapidity. Detailed studies are also conducted for isobaric + and + collisions. We found a universal trend of charge stopping with respect to baryon stopping and discovered that the charge stopping is always greater than the baryon stopping. This study provides a model baseline in valence quark transport for what is expected in net-charge and net-baryon yields at the midrapidity of relativistic heavy-ion collisions.

Limiting fragmentation in heavy-ion stopping?

Based on a nonequilibrium–statistical relativistic diffusion model that is consistent with quantum chromodynamics (QCD), we investigate baryon stopping in relativistic heavy-ion collisions at SPS, RHIC, and LHC energies. The net-proton rapidity distributions of the individual fragments exhibit a scaling behaviour similar to limiting fragmentation (LF) that is related to geometric scaling in the colour-glass condensate (CGC) and depends upon the gluon saturation scale. Forward-angle net-proton data at energies reached at the LHC are required to verify the prediction.

Bremsstrahlung as a probe of baryon stopping in heavy-ion collisions

In collisions between heavy ions at ultra-relativistic energies the participating protons lose energy, which is converted into new particles. As the protons slow down, they emit bremsstrahlung radiation. The yield and angular distribution of the emitted radiation are sensitive probes of how much energy the incoming protons have lost. In this paper, the spectrum of bremsstrahlung radiation is calculated for different stopping scenarios, and the results are compared with the expected yield of photons from hadronic interactions.

Bremsstrahlung photons from stopping in heavy-ion collisions

We examine the spectrum of bremsstrahlung photons that results from the stopping of the initial net charge distributions in ultrarelativistic nucleus-nucleus collisions at the CERN Large Hadron Collier (LHC). This effect has escaped detection so far since it becomes sizable only at very low transverse momentum and at sufficiently forward rapidity. We argue that it may be within reach of the next-generation LHC heavy-ion detector ALICE-3 that is currently under study, and we comment on the physics motivation for measuring it.

Baryon stopping as a relativistic Markov process in phase space

We reconsider baryon stopping in relativistic heavy-ion collisions in a nonequilibrium-statistical framework. The approach combines earlier formulations based on quantum chromodynamics with a relativistic diffusion model through a suitably derived fluctuation-dissipation relation, thus allowing for a fully time-dependent theory that is consistent with QCD. We use an existing framework for relativistic stochastic processes in spacetime that are Markovian in phase space, and adapt it to derive a Fokker-Planck equation in rapidity space, which is solved numerically. The time evolution of the net-proton distribution function in rapidity space agrees with stopping data from the CERN Super Proton Synchrotron and the BNL Relativistic Heavy Ion Collider.

Probing neutron–proton effective mass splitting using nuclear stopping and isospin mix in heavy-ion collisions in GeV energy region

The ramifications of the effective mass splitting on the nuclear stopping and isospin tracer during heavy-ion collisions within the gigaelectron volt energy region are studied using an isospin-dependent quantum molecular dynamics model. Three isotope probes, i.e., a proton, deuteron, and triton, are used to calculate the nuclear stopping. Compared to the $$m_\text {n}^{*} > m_\text {p}^{*}$$ case, the $$m_\text {n}^{*} < m_\text {p}^{*}$$ parameter results in a stronger stopping for protons but a weaker stopping for tritons. The calculations of the isospin tracer show that the $$m_\text {n}^{*} > m_\text {p}^{*}$$ parameter results in a higher isospin mix than the $$m_\text {n}^{*} < m_\text {p}^{*}$$ parameter. The rapidity and impact parameter dependences of the isospin tracer are also studied. A constraining of the effective mass splitting using the free nucleons with high rapidity and in a central rather than peripheral collision is suggested.

Radiative Parton Energy Loss and Baryon Stopping in AA Collisions

We study the radiative energy loss contribution to proton stopping in $AA$ collisions. The analyses is performed within the light-cone path integral approach to induced gluon emission. We have found that the radiative correction can fill in partly the midrapidity dip in the net proton rapidity distribution in $AA$ collisions at $\sqrt{s}\sim 10$ GeV. We argue that at $\sqrt{s}\sim 10$ GeV the net proton fluctuations at midrapidity may be dominated by the initial fluctuations of the proton flow, which, to a good accuracy, should be binomial.

Testing nonextensive statistics in relativistic heavy-ion collisions

Numerical solutions of the nonlinear Fokker-Planck equation (FPE) which has been associated with nonextensive q-statistics show that the available data on rapidity distributions for stopping in relativistic heavy-ion collisions cannot be reproduced with any permitted value of the nonextensivity parameter (1 &lt; q &lt; 1.5). This casts doubt on the nonextensivity concept that is widely used in relativistic heavy-ion physics.

Collective flow and nuclear stopping in heavy ion collisions in Fermi energy domain

The effects of the in-medium nucleon–nucleon (NN) elastic cross section on the observables in heavy ion collisions in the Fermi energy domain are investigated within the framework of the ultrarelativistic quantum molecular dynamics model. The results simulated using medium correction factors of $${\mathcal{F}}=\sigma ^{\mathrm{in-medium}}_\mathrm{NN}/ \sigma ^{\mathrm{free}}_\mathrm{NN}=0.2,~0.3,~0.5,$$ and the density- and momentum-dependent factor obtained from the FU3FP1 parametrization are compared with the FOPI and INDRA experimental data. It is found that the calculations using the correction factors $${\mathcal{F}} =$$ 0.2 and 0.5 reproduce the experimental data (i.e., collective flow and nuclear stopping) at 40 and 150 MeV/nucleon, respectively. Calculations with the FU3FP1 parametrization can best fit these experimental data. These conclusions can be confirmed in both $$^{197}\text{Au}+^{197}\text{Au}$$ and $$^{129}\text{Xe}+^{120}\text{Sn}$$ .

Effects of the in-medium nucleon-nucleon cross section on collective flow and nuclear stopping in heavy-ion collisions in the Fermi-energy domain

With the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, a systematic investigation of the effects of in-medium nucleon-nucleon ($\mathit{NN}$) elastic cross section on the collective flow and the stopping observables in $^{197}\mathrm{Au}+^{197}\mathrm{Au}$ collisions at beam energies from 40 to 150 MeV/nucleon is performed. Simulations with the medium correction factors $\mathcal{F}={\ensuremath{\sigma}}_{NN}^{\mathrm{in}\text{\ensuremath{-}}\mathrm{medium}}/{\ensuremath{\sigma}}_{NN}^{\mathrm{free}}=0.2,0.3,0.5$ and the one obtained with the FU3FP1 parametrization which depends on both the density and the momentum are compared to the FOPI and INDRA experimental data. It is found that, to best fit the experimental data of the slope of the directed flow and the elliptic flow at midrapidity as well as the nuclear stopping, the correction factors of $\mathcal{F}=0.2$ and 0.5 are required for reactions at beam energies of 40 and 150 MeV/nucleon, respectively. Whereas calculations with the FU3FP1 parametrization can simultaneously reproduce these experimental data reasonably well. And, the observed increasing nuclear stopping with increasing beam energy in experimental data can also be reproduced by using the FU3FP1 parametrization, whereas the calculated stopping power in Au + Au collisions with beam energies from 40 to $150\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$ almost remains constant when taking $\mathcal{F}$ equal to a fixed value.

Examining nonextensive statistics in relativistic heavy-ion collisions

We show in detailed numerical solutions of the nonlinear Fokker-Planck equation (FPE), which has been associated with nonextensive $q$ statistics, that the available data on rapidity distributions for stopping in relativistic heavy-ion collisions cannot be reproduced with any permitted value of the nonextensivity parameter ($1&lt;q&lt;1.5$). This casts doubt on the nonextensivity concept that is widely used in relativistic heavy-ion physics.

Effect of the nuclear charge of a fast structural ion on its internal effective stopping in collisions with atoms

The energy losses of fast structural ions in collisions with atoms have been considered in the eikonal approximation. The structural ions are ions consisting of a nucleus and a certain number of electrons bound to it. The effect of nuclear charge Z of the ion on its effective deceleration κ(p) (energy losses associated with excitation of only intrinsic ion shells) has been analyzed. It is shown that the allowance for the interaction of an atom with the ion nucleus for Z a Z/v > 1, where Z a is the charge of the atomic nucleus and v is the velocity of collisions in atomic units, considerably affects the value of κ(p), which generally necessitates taking into account nonperturbatively the effect of both charges Z a and Z on κ(p).

Influence of differential elastic nucleon-nucleon cross section on stopping and collective flow in heavy-ion collisions at intermediate energies

By considering three different Nucleon-Nucleon (NN) elastic differential cross sections: the Cugnon \emph{et al.} parameterized differential cross section [Nucl. Instrum. Methods Phys. Res., Sect. \textbf{B111}, 215 (1996)], and the differential cross section derived from the collision term of the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation proposed by Mao \emph{et al.} [Z.\ Phys.\ A {\bf 347}, 173 (1994)], as well as the isotropic differential cross section, within the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, the influence of the differential elastic NN cross section on various observables (e.g., nuclear stopping, both the rapidity and transverse-velocity dependence of the directed and elliptic flows) in Au+Au collisions at beam energies 150, 250, 400, and 800 MeV$/$nucleon is investigated. By comparing calculations with those three differential cross sections, it is found that the nuclear stopping power, the directed and elliptic flows are affected to some extent by the differential cross sections, and the impact of differential cross section on those observables becomes more visible as the beam energy increases. The effect on the elliptic flow difference $v_{2}^{n}$-$v_{2}^{H}$ and ratio $v_{2}^{n}$/$v_{2}^{H}$ of neutrons versus hydrogen isotopes ($Z=1$), which have been used as sensitive observables for probing nuclear symmetry energy at high densities, is weak.

Baryon stopping in heavy-ion collisions at Elab = 2A-200A GeV

It is argued that an irregularity in the baryon stopping is a natural consequence of the onset of deconfinement occurring in the compression stage of a nuclear collision. It is an effect of the softest point inherent in an equation of state (EoS) with a deconfinement transition. In order to illustrate this effect, calculations within the three-fluid model were performed with three different EoSs: a purely hadronic EoS, an EoS with a first-order phase transition and a third one with a smooth crossover transition. It is demonstrated that this irregularity is a very robust signal of the first-order phase transition that survives under acceptance conditions of the NICA MPD experiment.

Contribution of different components of interaction potential towards global nuclear stopping

We present our analysis of the effect of isospin content as well as the contributions of various components of nucleon–nucleon interaction potential on stopping ratio of protons and neutrons for the reaction \(^{120}_{50}\hbox {Sn}+{}^{120}_{50}\hbox {Sn}\). This study is performed within the framework of isospin-dependent quantum molecular dynamics model. We show that the momentum-dependent interactions affect the nuclear stopping to a larger extent compared to the other components of the nucleon–nucleon interaction potential. The isospin-dependent nucleon–nucleon cross section is also found to affect the stopping in central collisions only.

In-medium effects around the Fermi energy

We study nuclear stopping in central collisions for heavy-ion induced reactions in the Fermi energy domain (15-100 AMeV). Using the large dataset provided by the 4π array INDRA, we determine that stopping can be directly related to the transport properties in the nuclear medium. By looking specifically at protons, we present a comprehensive body of experimental results concerning the mean free path, the nucleon-nucleon cross-section and in-medium effects in nuclear matter.

In-medium effects for nuclear matter in the Fermi-energy domain

We study nuclear stopping in central collisions for heavy-ion induced reactions in the Fermi energy domain, between $15$ and $100$ A\,\textrm{MeV}. Using the large dataset of exclusive measurements provided by the $4\pi$ array \emph{INDRA}, we determine the relative degree of stopping as a function of system mass and bombarding energy. We show that the stopping can be directly related to the transport properties in the nuclear medium. By looking specifically at free nucleons (here protons), we present for the first time a comprehensive body of experimental results concerning the mean free path, the nucleon-nucleon cross-section and in-medium effects in nuclear matter. It is shown that the mean free path exhibits a maximum at $\lambda_{NN}=9.5 \pm 2$ \textrm{fm}, around $E_{inc}=35-40$ A\,\textrm{MeV} incident energy and decreases toward an asymptotic value $\lambda_{NN}= 4.5 \pm 1$ \textrm{fm} at $E_{inc} = 100$ A\,\textrm{MeV}. After accounting for Pauli blocking of elastic nucleon-nucleon collisions, it is shown that the effective in-medium \emph{NN} cross section is further reduced compared to the free value in this energy range. Therefore, in-medium effects cannot be neglected in the Fermi energy range. These results bring new fundamental inputs for microscopic descriptions of nuclear reactions in the Fermi energy domain.