Rapidity Distributions Of Pions Research Articles

Comments on Rapidity Distributions of Pions in \(p+p\) and Pb+Pb Collisions at CERN SPS Energies

Comments on Rapidity Distributions of Pions in \(p+p\) and Pb+Pb Collisions at CERN SPS Energies

Rapidity distributions of pions in p+p and Pb+Pb collisions at energies available at the CERN Super Proton Synchrotron

The centrality dependence of rapidity distributions of pions in Pb+Pb reactions can be understood by imposing local energy-momentum conservation in the longitudinal "fire-streaks" of excited matter. With no tuning nor adjustment to the experimental data, the rapidity distribution of pions produced by the fire-streak which we obtained from Pb+Pb collisions reproduces the shape of the experimental pion rapidity distribution in p+p interactions, measured by the NA49 Collaboration at the same energy. The observed difference in the absolute normalization of this distribution can be explained by the difference in the overall energy balance, induced by baryon stopping and strangeness enhancement phenomena occurring in heavy ion collisions. We estimate the latter effects using a collection of SPS experimental data on $\pi^\pm$, $K^\pm$, net $p$, and $n$ production in p+p and Pb+Pb reactions. Implications of the above findings are discussed.

Rapidity distributions of hadrons in the HydHSD hybrid model

A multistage hybrid model intended for describing heavy-ion interactions in the energy region of the NICA collider under construction in Dubna is proposed. The model combines the initial, fast, interaction stage described by the model of hadron string dynamics (HSD) and the subsequent evolution that the expanding system formed at the first stage experiences at the second stage and which one treats on the basis of ideal hydrodynamics; after the completion of the second stage, the particles involved may still undergo rescattering (third interaction stage). The model admits three freeze-out scenarios: isochronous, isothermal, and isoenergetic. Generally, the HydHSD hybrid model developed in the present study provides fairly good agreement with available experimental data on proton rapidity spectra. It is shown that, within this hybrid model, the two-humped structure of proton rapidity distributions can be obtained either by increasing the freeze-out temperature and energy density or by more lately going over to the hydrodynamic stage. Although the proposed hybrid model reproduces rapidity spectra of protons, it is unable to describe rapidity distributions of pions, systematically underestimating their yield. It is necessary to refine the model by including viscosity effects at the hydrodynamic stage of evolution of the system and by considering in more detail the third interaction stage.

Implications of energy and momentum conservation for particle emission in A+A collisions at energies available at the CERN Super Proton Synchrotron

We construct a simple model of heavy ion collisions, local in the impact parameter plane, and appropriate for the SPS energy range. This model can be regarded as a new realization of the "fire-streak" approach, originally applied to studies of lower energy nucleus-nucleus reactions. Starting from local energy and momentum conservation, we nicely describe the broadening of the pion rapidity distribution when going from central to peripheral Pb+Pb collisions at $\sqrt{s_{NN}}$=17.3 GeV. The results of our calculations are compared with SPS experimental data. We discuss the resulting implications on the role of energy and momentum conservation for the dynamics of particle production in heavy ion collisions. A specific space-time picture emerges, where the longitudinal evolution of the system strongly depends on the position in the impact parameter (${b_x}$, ${b_y}$) plane. This picture is consistent with our earlier findings on the longitudinal evolution of the system as deduced from electromagnetic effects on charged pion directed flow, and can provide an explanation for specific low-$p_T$ phenomena seen in the fragmentation region of Pb+Pb collisions.

Hadron rapidity spectra within a hybrid model

A 2-stage hybrid model is proposed that joins the fast initial state of interaction, described by the hadron string dynamics (HSD) model, to subsequent evolution of the expanding system at the second stage, treated within ideal hydrodynamics. The developed hybrid model is assigned to describe heavy-ion collisions in the energy range of the NICA collider under construction in Dubna. Generally, the model is in reasonable agreement with the available data on proton rapidity spectra. However, reproducing proton rapidity spectra, our hybrid model cannot describe the rapidity distributions of pions. The model should be improved by taking into consideration viscosity effects at the hydrodynamical stage of system evolution.

Hadron rapidity spectra within a hybrid model

A 2-stage hybrid model is proposed that joins the fast initial state of interaction, described by the hadron string dynamics (HSD) model, to subsequent evolution of the expanding system at the second stage, treated within ideal hydrodynamics. The developed hybrid model is assigned to describe heavy-ion collisions in the energy range of the NICA collider under construction in Dubna. Generally, the model is in reasonable agreement with the available data on proton rapidity spectra. However, reproducing proton rapidity spectra, our hybrid model cannot describe the rapidity distributions of pions. The model should be improved by taking into consideration viscosity effects at the hydrodynamical stage of system evolution.

Viscous evolution of the rapidity distribution of matter created in relativistic heavy-ion collisions

The longitudinal hydrodynamic expansion of the fluid created in relativistic heavy-ion collisions is considered taking into account shear viscosity. We consider the dynamics of a non-boost-invariant energy density of the fluid in 1+1 dimensions, using the proper time and the space-time rapidity. Both a nonvanishing viscosity and a soft equation of state make the final particle distributions in rapidity narrower. The width of the initial Gaussian rapidity distribution and its central energy density are fitted to reproduce the rapidity distributions of pions and kaons as measured by the BRAHMS Collaboration. The presence of viscosity has dramatic consequences on the value of the initial energy density. Dissipative processes and the reduction of the longitudinal work due to the shear viscosity increase the total entropy and the particle multiplicity at central rapidities. Viscous corrections make the longitudinal velocity of the fluid stay close to the Bjorken scaling flow ${v}_{z}=z/t$ through the evolution.

Longitudinal fluid dynamics for ultrarelativistic heavy-ion collisions

We developed a $1+1$ dimensional hydrodynamical model for central heavy-ion collisions at ultrarelativistic energies. Deviations from Bjorken's scaling are taken into account by implementing finite-size profiles for the initial energy density. The calculated rapidity distributions of pions, kaons, and antiprotons in central Au+Au collisions at $\sqrt{{s}_{\mathit{NN}}}=200$ GeV are compared with experimental data of the BRAHMS Collaboration. The sensitivity of the results to the choice of the equation of state, the parameters of the initial state, and the freeze-out conditions were investigated. Experimental constraints on the total energy of produced particles were used to reduce the number of model parameters. The best fits of experimental data were obtained for soft equations of state and Gaussian-like initial profiles of the energy density. It was found that initial energy densities required for fitting the experimental data decrease with the increasing critical temperature of the phase transition.

(1 + 1) dimensional hydrodynamics for high-energy heavy-ion collisions

A (1 + 1)-dimensional hydrodynamical model in the light-cone coordinates is used to describe central heavy-ion collisions at ultrarelativistic bombarding energies. Deviations from Bjorken scaling are taken into account by choosing finite-size profiles for the initial energy density. The sensitivity of fluid-dynamical evolution to the equation of state and the parameters of initial state are investigated. Experimental constraints on the total energy of produced particles are used to reduce the number of model parameters. Spectra of secondary particles are calculated under the assumption that the transition from the hydrodynamical stage to the collisionless expansion of matter occurs at a certain freeze-out temperature. An important role of resonances in the formation of observed hadronic spectra is demonstrated. The calculated rapidity distributions of pions, kaons, and antiprotons in central Au + Au collisions at √s NN = 200 GeV are compared with experimental data of the BRAHMS Collaboration. Parameters of the initial state are reconstructed for different choices of the equation of state. The best fit of these data is obtained for a soft equation of state and Gaussian-like initial profiles of the energy density, intermediate between the Landau and Bjorken limits.

Relativistic heavy-ion collisions within three-fluid hydrodynamics: Hadronic scenario

A three-fluid hydrodynamic model for simulating relativistic heavy-ion collisions is introduced. Along with two baryon-rich fluids, the new model considers the time-delayed evolution of a third, baryon-free (i.e., with zero net baryonic charge) fluid of newly produced particles. Its evolution is delayed because of a formation time \ensuremath{\tau}, during which the baryon-free fluid neither thermalizes nor interacts with the baryon-rich fluids. After the formation it starts to interact with the baryon-rich fluids and quickly gets thermalized. Within this model with pure hadronic equation of state, a systematic analysis of various observables at incident energies between few and about 160A GeV has been done as well as a comparison with results of transport models. We have succeeded in reasonably reproducing a great body of experimental data in the incident energy range of ${E}_{\mathrm{lab}}\ensuremath{\simeq}$ (1--160)A GeV. The list includes proton and pion rapidity distributions, proton transverse-mass spectra, rapidity distributions of \ensuremath{\Lambda} and $\overline{\ensuremath{\Lambda}}$ hyperons, elliptic flow of protons and pions (with the exception of proton ${v}_{2}$ at 40A GeV), multiplicities of pions, positive kaons, \ensuremath{\phi} mesons, hyperons, and antihyperons, including multistrange particles. This agreement is achieved on the expense of substantial enhancement of the interflow friction as compared to that estimated proceeding from hadronic free cross sections. However, we have also found out certain problems. The calculated yield of ${K}^{\ensuremath{-}}$ is approximately higher than that in the experiment by a factor of 1.5. We have also failed to describe directed transverse flow of protons and pion at ${E}_{\mathrm{lab}}\ensuremath{\ge}40A$ GeV. This failure apparently indicates that the used EOS is too hard and thereby leaves room for a phase transition.

Results from the BRAHMS experiment at RHIC

Results from the BRAHMS collaboration for Au+Au collisions at √ S NN = 200 GeV are presented, focussing on the measurement of the net-proton rapidity distribution, the determination of the pseudorapidity distribution of charged particles and on the rapidity distributions of pions and kaons.

Hadronic observables at relativistic energies: Anything strange with strangeness?

We calculate p, ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},$ ${K}^{\ifmmode\pm\else\textpm\fi{}},$ and $\ensuremath{\Lambda}(+{\ensuremath{\Sigma}}^{0})$ rapidity distributions and compare to experimental data from SIS to SPS energies within the Ultrarelativistic-Quantum-Molecular Dynamics and Hadron-String Dynamics transport approaches that are both based on string, quark, diquark $(q,$ $\overline{q},$ $qq,$ $\overline{q}\overline{q}),$ and hadronic degrees of freedom. The two transport models do not include any explicit phase transition to a quark-gluon plasma. It is found that both approaches agree rather well with each other and with the experimental rapidity distributions for protons, \ensuremath{\Lambda}'s, ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},$ and ${K}^{\ifmmode\pm\else\textpm\fi{}}.$ In spite of this apparent agreement both transport models fail to reproduce the maximum in the excitation function for the ratio ${K}^{+}/{\ensuremath{\pi}}^{+}$ found experimentally between 11 and 40 A GeV. A comparison to the various experimental data shows that this ``failure'' is dominantly due to an insufficient description of pion rapidity distributions rather than missing ``strangeness.'' The modest differences in the transport model results\char22{}on the other hand\char22{}can be attributed to different implementations of string formation and fragmentation that are not sufficiently controlled by experimental data for the ``elementary'' reactions in vacuum.

Strangeness production in the HSD transport approach from SIS to SPS energies

We study systematically the production of strangeness in nuclear reactions from SIS to SPS energies within the covariant hadronic transport approach HSD. Whereas the proton and pion rapidity distributions as well as pion transverse momentum spectra are well described in the hadronic transport model from 2–200 A GeV, the K + and K − spectra are noticeably underestimated at AGS energies while the K + spectra match well at SIS and SPS energies with the experimental data. We conclude that the failure of the hadronic model at AGS energies points towards a non-hadronic phase during the collision of heavy systems around 10 A GeV.

Scaling of deuteron production in ultrarelativistic nucleus-nucleus collisions

Deuteron production in S- and Pb-induced collisions at ultrarelativistic energies is studied in a transport model, treating the deuteron production by phase space coalescence. The production rate of deuterons as a function of rapidity, dN d dy , is approximately found to satisfy a simple scaling behavior in terms of the proton and the pion rapidity distributions, dN p dy and dN π dy , namely dN d dy ∼ ( dN p dy ) 2/( dN π dy ) . The scaling is a consequence of the near equality of the freeze-out volumes the nucleons and mesons. Violation of the scaling is attributed to differences between these freeze-out volumes.

Centrality dependence of pion and proton spectra in C+C and C+Ta interactions at 4.2 GeV/c per nucleon.

Target and centrality dependence of pion and proton distributions is studied in C+C and C+Ta collisions at 4.2 GeV/c per nucleon using the 2-m propane bubble chamber. The experimental data are compared with the predictions of the Monte Carlo quark-gluon string model (QGSM). The pion and proton transverse momentum spectra at midrapidity are well described by the two-component thermal model. The shape of the proton rapidity distribution strongly depends on the collision centrality and reflects the stopping power of colliding nuclei. The pion rapidity distribution is Gaussian in shape regardless of the target mass number and collision centrality. The QGSM completely reproduces main features of pion and proton rapidity spectra as well as pion transverse momentum spectra. The model does not fully reproduce the features of the proton transverse momentum spectra.

Rapidity, Transverse Mass Distributions and Nuclear Stopping in (14.6 AGeV/c)Si+Au Reactions

The experimental data of proton and pion rapidity distributions and proton transverse mass distribution in reaction of (14.6 AGeV/c)Si + Au are compared with a simple relativistic hadronic cascade simulation. The theoretical results seem to prefer the statement of strong but incomplete nuclear stopping at AGS energy.

Interferometrical signature of mixed phase in A+A collisions

We have calculated the pion rapidity distribution, the transversal momentum spectrum and the pion correlator in outward, sideward and longitudinal directions for S+S collisions at high energy. We used a two-temperature model that allows us to explain the abundance of pions at smallp T and highp T . The first source, which is at high temperature, is in a quark-gluon-hadron mixed phase radiating pions due to a deflagration shock wave on the background of longitudinal expansion. The second source consists of the unburnt part of the matter in hadronic phase. The interferometrical analysis at differentp T gives a signature for two expanding sources separated in time and allows the measurement of the lifetime and other parameters of each of them.

Strangeness production by antiprotons

Specific features of strange-particle production in\(\bar p\)-nuclei annihilation are reviewed. The inclusive Λ/Ks0 production rate, sensitive to the relative weight of multinucleon annihilations, shows an enhancement in heavier nuclei with respect to the\(\bar p\)p and\(\bar p\)d annihilations. Rapidity distributions, obtained in the PS179 experiment at LEAR and in an experiment at KEK, seem to support the hypothesis of different effective targets for Λ’s and Ks0’s. The behaviour of the associated-to-strangeness pion rapidity distribution suggests the presence of a leading effect, bringing away a fraction of momentum not absorbed by any target system. The experimental signatures are analysed in the framework of theoretical models: the rescattering approach in the context of a conventional hadronic picture and a model of supercooled quark matter formation. Finally, the observed leading mesons can be included in a quark picture describing beam fragmentation.

Experimental manifestations of large kT double diffraction jets at collider energy range

The perceptible amount of large k T double diffraction jets at s ≳ 10 5GeV 2 is shown to lead to the prediction of certain experimental effects. They are: (a) an enormous increase of pion inclusive spectra at p T ≳ 4–5 GeV, (b) a positive correlation between transverse and longitudinal momenta of rapid secondaries, (c) a plato-like pion rapidity distribution in the jet direction, (d) the appearance of multicore extensive air showers (EAS) from cosmic rays, the number of cores slightly increasing with primary energy.

Rapidity distribution and charged multiplicity in high-energy pp interactions

The rapidity distributions of charged particles in high-energy hadron-hadron interactions are of great interest from the point of view of the Feynman scaling. Actually CERN-ISR data (L 2) of v's = (23-;-63) GeV have shown that the invariant cross-sections of 7t'± at Yc.m. = 0 increase as the c.m. energy increases. A similar rise of rapidity distribution is recently found in hadron production by e+eannihilation for c.m. energies between 5 and 31.6 GeV (3 ). The e+edata indicate that this rise is correlated with the faster growth of charged multiplicity at high energy than at low energy. In order to study this problem more clearly, we have studied the rapidity distributions of pions as a function of multiplicity, on the basis of our data of multiparticle production in pp interactions at 405 GeVfc, in comparison with other pp data in FNAL and CERN-ISR energies.