Inclusive Pion Spectra Research Articles

The Yield Ratio of Anti-Nuclei and Nuclei in Relativistic Nuclear Collisions in the Central Rapidity Region

This article describes calculations of the yield ratio of anti-particles to the yield of particles ($\bar{p}/p$, $\bar{d}/d$,$\overline{^{3}\mathrm{He}}$/$^{3}$He) in proton-proton and nuclear-nuclear interactions using the self-similarity parameter in the central rapidity region. The used approach is based on the study of relativistic nuclear interactions in the four-velocity space. The results of the calculations are compared with the existing experimental data in a wide center-of-mass energy range ($SPS$, $RHIC$, $LHC$). Within this approach the inclusive spectra of pions and kaons and ratios of their yields in $pp$ collisions have been successfully described earlier.

Ratio of kaon-to-pion production cross-sections in BeBe collisions as a function of $$\sqrt{s}$$

The inclusive spectra of pions and kaons produced in $Be Be$ collisions as functions of their transverse momentum $p_t$ at mid-rapidity are calculated within the self-similarity approach. A satisfactory description of NA61/SHINE data on these spectra and the ratio of $K^\pm$ to $\pi^\pm$ meson production cross sections in $Be Be$ collisions as a function of $\sqrt{s}$ are presented. The similarity of these observables to the ones for $pp$ collisions at mid-rapidity and in the wide range of initial energies is illustrated.

Ratio of cross-sections of kaons to pions produced in pp collisions as a function of $$\sqrt{s}$$

A calculation of the inclusive spectra of pions and kaons produced in $pp$ collisions as functions of their transverse momentum $p_t$ at mid-rapidity is presented within the self-similarity approach. A satisfactory description of the data within a wide range of initial energies is presented. We focus mainly on the ratio of cross-sections of $K^\pm$ to $\pi^\pm$ mesons produced in $pp$ collisions as a function of $\sqrt{s}$. A fast rise of this ratio, when the initial energy increases starting from the kaon production threshold up to $\sqrt{s}\simeq$ 20-30 Gev, is revealed together with its very slow increase up to LHC energies. The energy dependence of this ratio is due to the conservation laws of four-momenta and quantum numbers of the initial and produced hadrons, and to the Regge behavior of cross-sections at large energies. The more or less satisfactory agreement of these ratios with NA61-SHINE, RHIC and LHC data is demonstrated.

Mid-rapidity dependence of pion production in $$p-p$$ and $$A-A$$ collisions.

The calculation of inclusive spectra of pions produced in $pp$ and $AA$ collisions as a function of rapidity $y$ is presented within the self-similarity approach. It is shown that at not large rapidities $y$ one can obtain the analytical form of the self-similarity function $\Pi(y,p_t)$ dependent of $y$ and hadron transverse momentum $p_t$. A satisfactory description of data on the rapidity spectra at $|y|\leq$ 0.3 is illustrated within a good agreement. The universal energy dependence of these spectra is also shown.

Ultraforward particle production from color glass condensate and Lund fragmentation

We present an analysis of data on single inclusive pion production measured by the LHCf collaboration in high-energy proton-proton and proton-nucleus at ultra-forward rapidities, $8.8 \leq\! y\leq \!10.8$. We also analyse forward RHIC data for calibration purposes. Our analysis relies on the use of a Monte Carlo event generator that combines a perturbative description of the elementary scattering process at partonic level based on the hybrid formalism of the Color Glass Condensate with an implementation of hadronization in the framework of the Lund string fragmentation model. This procedure allows us to reach values of the momenta of the produced particles as low as detected experimentally $p_t\sim0.1$ GeV. We achieve a good description of single inclusive spectra of charged particles and neutral pions at RHIC and the LHC respectively, and nuclear modification factors for proton-lead collisions at the LHC. Our results add evidence to the idea that particle production in the domain of very small Bjorken-$x$ is dominated by the saturation effects encoded in the unintegrated gluon distribution of the target. Being forward particle production of key importance in the development of air showers, we stress that this approach allows for a theoretically controlled extrapolation of our results to the scale of ultra-high energy cosmic rays, thus serving as starting point for future works on this topic.

Simulated nucleon–nucleon and nucleon–nucleus reactions in the frame of the cascade exciton model at high and intermediate energies

In this study, we have used the cascade exciton model (CEM) to investigate different characteristics of nuclear reactions. Number of nucleon–nucleon collisions in Pb+Pb collisions as a function of impact parameter and rapidity distributions of negative particles from p+Ar and p+Xe interactions at p lab = 200 GeV/c have been studied. We could create inclusive spectra of pions for separate charged states from reactions and total neutron multiplicities per primary reaction at 1000 MeV for different thin targets. Also, the cross-sections for the reactions 209Bi(p, f) and 209Bi(n, f) were studied. Interactions of 1.0 GeV protons with C, Al, Cu, Sn, and Pb are presented in this study. All the calculated characteristics are compared with other theoretical calculations and compared with the experimental data. CEM shows good agreement with both theoretical and experimental results. In this study, we have used quantum molecular dynamic (QMD) as a theoretical model to compare our results.

FRAGMENTATION FUNCTIONS AT BABAR

Inclusive hadron production cross section in e+e- annihilation shed light on fundamental questions of hadronization and fragmentation processes. We present measurements of inclusive spectra of charged pions, kaons, and protons (antiprotons) produced in e+e- collisions at the center-of-mass energy of 10.54 GeV, and tests of QCD predictions and hadronization models. We also report the results on the measurement of the azimuthal modulation induced by the Collins effect in inclusive production of charged pion pairs e+e- → ππX, where the two pions are produced in opposite hemispheres. These data allows the determination of the polarized Collins fragmentation functions.

Self-similarity of pion production in AA collisions at RHIC

Experimental data on inclusive spectra of pions produced in heavy-ion collisions at RHIC are analyzed in the framework of z-scaling. The data indicate similarity as a characteristic feature of the mechanism of pion production at high energies. It is argued that this property includes structure of the colliding objects, interaction of their constituents, and character of the fragmentation process. A microscopic scenario of nucleus interactions at a constituent level in terms of momentum fractions is developed. The centrality dependence of the shape of the scaling function Ψ(z) and the fractal dimention ɛ AA of the fragmentation process is studied. Energy losses of particles in the final state as a function of the collision energy, transverse momentum, and centrality are estimated. The scale dependence of the energy losses is discussed. A decreasing tendency of specific heat of the produced medium with the system size is established. The obtained results may be exploited to search for and study new physics phenomena in pion production in pp and AA collisions at high multiplicities.

Comparison of Geant4 hadron generation with data from the interactions with beryllium nuclei of +8.9 GeV/c protons and pions and −8.0 GeV/c pions

Hadron generation in the Geant4 simulation tool kit is compared with inclusive spectra of secondary protons and pions from the interactions with beryllium nuclei of +8.9 GeV/c protons and pions, and of −8.0 GeV/c pions. The data were taken in 2002 at the CERN Proton Synchrotron with the HARP spectrometer. We report on significant disagreements between data and Monte Carlo simulation especially in the polar-angle distributions of secondary protons and pions.

The analysis of π −-meson spectra in semicentral CC and CTa collisions at a momentum of 4.2 GeV/c per nucleon in terms of light-front variables

The inclusive spectra of pions produced in CC and CTa collisions at a momentum of 4.2 GeV/c per nucleon are analyzed in terms of light-front variables ξ and ζ. The phase space of the secondary pions is divided into two parts with very different angular and momentum distributions. In one of these parts, the thermal equilibrium assumption seems to be in good agreement with the data. Corresponding temperatures T are extracted, and their dependence on (APAT)1/2 is studied: T decreases linearly with increasing (APAT)1/2. The results are compared with the predictions of the quark-gluon string model (QGSM). The QGSM satisfactorily reproduces the experimental data.

Probing the deuteron structure at small N-N distances by cumulative pion production

The fragmentation of deuterons into pions emitted forward in the kinematic region forbidden for free nucleon-nucleon collisions is analyzed. It is shown that the inclusion of the non-nucleonic degrees of freedom in a deuteron results in a satisfactory description of the data for the inclusive pion spectrum and improves the description of the data about $T_{20}$. According to the data, $T_{20}$ has very small positive values, less than 0.2, which contradicts the theoretical calculations ignoring these degrees of freedom.

ON THE SCALING OF INCLUSIVE SPECTRA OF SECONDARY PIONS IN THE FORWARD REGION

Using available collider data the Feynman scaling on inclusive spectra of secondary pions is critically examined in the forward and very forward region incorporating the seagull effect. It is found that scaling holds to 10–15% in the forward region at least up to the center-of-mass energy 900 GeV. It is further observed that the Wdowczyk–Wolfendale scale breaking model is satisfied in the forward region only when inelasticity into pions decreases with energy.

Investigation of the inclusive spectra of secondary protons and pions of low kinetic energies and of their wide pair correlations in π − A interactions at 43 GeV/c

The inclusive invariant cross sections for protons produced at angles of θ=90° and 60° and for positively and negatively charged pions produced at an angle of θ=90° are presented for π−Be, π−Al, and π−Cu interactions induced by 43-GeV/c incident π− mesons. The shape of the inclusive spectra of secondary hadrons, the A dependence of their cross sections, and the correlation functions for pairs of likely charged secondary hadrons at large angles of their divergence are studied. The kinematical region explored in the present article corresponded to kinetic energies of T≈0.16–0.70 GeV and T≈0.20–0.76 GeV for secondary protons and secondary pions, respectively. The angles of divergence of hadrons forming a pair, ψ, satisfied the condition cos ψ<−0.5.

Polarization phenomena by deuteron fragmentation into pions

The fragmentation of deuterons into pions emitted forward in the kinematic region forbidden for free nucleon-nucleon collisions is analyzed. The inclusive relativistic invariant spectrum of pions and the tensor analyzing power T20 are investigated within the framework of an impulse approximation using various deuteron wave functions. The influence of -wave inclusion in the deuteron wave function is also studied. The invariant spectrum is shown to be more sensitive to the amplitude of the NN↦πX process than the tensor analyzing power T20. It is shown that the inclusion of the non-nucleonic degrees of freedom in a deuteron results in a satisfactory description of the data for the inclusive pion spectrum and improves the description of the data about T20. According to the data, T20 has very small positive values, less than 0.2, which contradicts the theoretical calculations ignoring these degrees of freedom.

Formation of two pions on nuclei in A(γ, ππN)B reactions

A model is proposed for double pion photoproduction on nuclei that is accompanied by nucleon emission. Simple models that faithfully reproduce single-particle differential cross sections are used to describe photon interactions with intranuclear nucleons. The calculated cross sections for pion photoproduction on 12C nuclei are compared with inclusive pion spectra measured in the second resonance region of photon energies.

Event-by-event fluctuations in heavy ion collisions and the QCD critical point

The event-by-event fluctuations of suitably chosen observables in heavy ion collisions at SPS, RHIC and LHC can tell us about the thermodynamic properties of the hadronic system at freeze-out. By studying these fluctuations as a function of varying control parameters, it is possible to learn much about the phase diagram of QCD. As a timely example, we stress the methods by which present experiments at the CERN SPS can locate the second-order critical endpoint of the first-order transition between quark-gluon plasma and hadron matter. Those event-by-event signatures which are characteristic of freeze-out in the vicinity of the critical point will exhibit nonmonotonic dependence on control parameters. We focus on observables constructed from the multiplicity and transverse momenta of charged pions. We first consider how the event-by-event fluctuations of such observables are affected by Bose-Einstein correlations, by resonances which decay after freeze-out and by fluctuations in the transverse flow velocity. We compare our thermodynamic predictions for such noncritical event-by-event fluctuations with NA49 data, finding broad agreement. We then focus on effects due to thermal contact between the observed pions and a heat bath with a given (possibly singular) specific heat, and due to the direct coupling between the critical fluctuations of the sigma field and the observed pions. We also discuss the effect of the pions produced in the decay of sigma particles just above threshold after freeze-out on the inclusive pion spectrum and on multiplicity fluctuations. We estimate the size of these nonmonotonic effects which appear near the critical point, including restrictions imposed by finite size and finite time, and conclude that they should be easily observable.

Pion-pair formation and the pion dispersion relation in a hot pion gas

The possibility of pion-pair formation in a hot pion gas, based on the bosonic gap equation, is pointed out and discussed in detail. The critical temperature for condensation of pion pairs (Evans-Rashid transition) is determined as a function of the pion density. As for fermions, this phase transition is signated by the appearance of a pole in the two-particle propagator. In Bose systems there exists a second, lower critical temperature, associated with the appearance of the single-particle condensate. Between the two critical temperatures the pion dispersion relation changes from the usual quasiparticle dispersion to a Bogoliubov-like dispersion relation at low momenta. This generalizes the non-relativistic result for an attractive Bose gas by Evans et al. Possible consequences for the inclusive pion spectra measured in heavy-ion collisions at ultra-relativistic energies are discussed.

Inclusive production of charged pions, kaons and protons in υ(4S) decays

Using the detector ARGUS at thee + e − storage ring DORIS II, we have investigated inclusive momentum spectra of charged pions, kaons, and protons from decays of the υ(4S) meson. The kaon spectra have been measured in two independent ways, by coherently exploiting the detector's particle identification capabilities, and by detecting decays in-flight. The extracted mean multiplicities for charged hadrons are 7.17±0.05±0.14 pions, 1.56±0.03±0.05 kaons and 0.110±0.010±0.007 protons per υ(4S) decay, where pions and protons fromK and Δ decays have been subtracted.

Inclusive pion production at the angles 0 degrees and 57.8 degrees in 1 GeV proton-nucleus collisions

Differential cross sections for charge pion production in the pA to pi X reaction have been measured at a proton kinetic energy of 1 GeV with a relative accuracy of 2-5% for the following targets: 1H, 2D, 10B, 11B, 12C, 16O, 24Mg, 25Mg, 26Mg, 27Al, 64Cu, 116Sn, 124Sn, 181Ta, 184W and 208Pb. The measurements were performed with the help of two independent magnetic spectrometers with an angular acceptance of Delta Omega approximately=0.01 sr. The momentum resolution was equal to Delta P/P=1.4% in the range P=200-950 MeV/c at theta =0 degrees and Delta P/P=3% in the range P=75-600 MeV/sc at theta =57.8 degrees . The absolute normalisation of the cross sections was carried out using recent LNPI data on d sigma /d Omega for the pi +d to pp reaction. The contribution of various mechanisms to the inclusive pion spectra is discussed.

The effect of resonance production and diffraction on the inclusive spectra of pions and protons in 19 GeV/c pn interactions

Bubble chamber data on pn interactions at 19 GeV/c are used to investigate the effects of nucleon diffraction and resonance production on the inclusivex- andpT2-distributions of protons and pions. We determine the differential distributions of p, π− and π+ due to neutron and proton diffraction and similarly the distributions from the decay of the strong resonances Δ++(1232) and Δ−(1232) and from ρ0(770). Thex-distributions of the protons in the two c.m. hemispheres become quite similar when the effect of diffraction and Δ++ is subtracted. ThepT2-distributions can then be described by a single exponential in the whole kinematic region. The net effect on the shapes of thex-distributions of the pions due to diffraction, Δ++/Δ− and ρ0 production is rather small. The separate effects of these processes on the particle ratio π−/π+ is investigated. By excluding the diffraction and Δ++/Δ− production, the strength of the low-pT2 component of thepT2-distributions of the pions is reduced, but it seems that diffraction and resonance production cannot account for all oft hislow-pT2 enhancement.