Inclusive Spectra Research Articles

Spectra and mean multiplicities of pi ^{-}\xa0in central{}^{40}Ar+{}^{45}Sc collisions at 13A, 19A, 30A, 40A, 75A and 150A,text{ Ge }text{ V }!/!textit{c} beam momenta measured by the NA61/SHINE spectrometer at the CERN SPS

The physics goal of the strong interaction program of the NA61/SHINE experiment at the CERN Super Proton Synchrotron (SPS) is to study the phase diagram of hadronic matter by a scan of particle production in collisions of nuclei with various sizes at a set of energies covering the SPS energy range. This paper presents differential inclusive spectra of transverse momentum, transverse mass and rapidity of pi ^{-} mesons produced in central{}^{40}Ar+{}^{45}Sc collisions at beam momenta of 13A, 19A, 30A, 40A, 75A and 150A,text{ Ge }text{ V }!/!textit{c}. Energy and system size dependence of parameters of these distributions – mean transverse mass, the inverse slope parameter of transverse mass spectra, width of the rapidity distribution and mean multiplicity – are presented and discussed. Furthermore, the dependence of the ratio of the mean number of produced pions to the mean number of wounded nucleons on the collision energy was derived. The results are compared to predictions of several models.

Self-Similarity, Fractality and Entropy Principle in Collisions of Hadrons and Nuclei at Tevatron, RHIC and LHC

$$z$$ -Scaling of inclusive spectra as a manifestation of self-similarity and fractality of hadron interactions is illustrated. The scaling for negative particle production in $${\text{Au}} + {\text{Au}}$$ collisions from BES-I program at RHIC is demonstrated. The scaling variable $$z$$ depends on the momentum fractions of the colliding objects carried by the interacting constituents, and on the momentum fractions of the fragmenting objects in the scattered and recoil directions carried by the inclusive particle and its counterpart, respectively. Structures of the colliding objects and fragmentation processes in final state are expressed by fractal dimensions. Medium produced in the collisions is described by a specific heat. The scaling function $$\psi (z)$$ reveals energy, angular, multiplicity, and flavor independence. It has a power behavior at high $$z$$ (high $${{p}_{T}}$$ ). Based on the entropy principle and $$z$$ -scaling, energy loss as a function of the collision energy, centrality and transverse momentum of inclusive particle is estimated. New conservation law including fractal dimensions is found. Quantization of fractal dimensions is discussed.

The fragmentation spectrum from space-time reciprocity

Analyzing the single inclusive annihilation spectrum of charged hadrons in e+e− collisions, I confront the hadronization hypothesis of local parton-hadron duality with a systematic resummation of the dependence on the small energy fraction. This resummation is based on the reciprocity between time-like and space-like splitting processes in 4 − 2ϵ-dimensions, which I extend to resum all the soft terms of the cross-section for inclusive jet production. Under the local-parton-hadron duality hypothesis, the resulting distribution of jets essentially determines the spectrum of hadrons as the jet radius goes to zero. Thus I take the resummed perturbative jet function as the non-perturbative fragmentation function with an effective infra-red coupling. I find excellent agreement with data, and comment on the mixed leading log approximation previously used to justify local parton-hadron duality.

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.

The São Paulo Potential and the 3He Breakup Reaction at 130 MeV on 93Nb and 197Au

Nuclear reactions induced by weakly bound nuclei often result in the emission of light particles as products of the projectile breakup. The incident particle is expected to fragment before reaching the interior of the target nuclei, a characteristic that tends to favor forward angular emission. Although the first models developed for such reactions were proposed many decades ago by Udagawa and Tamura, Ichimura, Austern, Vincent, and Kasano, and Hussein and McVoy, to this date most of the attention has been dedicated to the breakup of the deuteron and other very weakly bound systems, while more strongly bound projectiles have not been fully explored. Here, we describe the production of protons and deuterons from the breakup of 3He. The breakup of 3He on two heavy targets, 93Nb and 197Au, is analyzed in this study. However, the incoming energy involved is much larger than that of the standard phenomenological optical potentials available in the literature for the 3He entrance channel. We have overcome this difficulty by using the São Paulo potential and adjusting the nuclear diffusivity. The deuteron inclusive spectra were calculated at several angles and compared well with the experimental data. Theoretical proton emission predictions are also given for future reference, since no inclusive measurements were performed for the targets under study. One of our goals is to verify the description of deuteron emission from fast projectiles, for which many partial waves contribute to the scattering process.

Application of Raman spectroscopy for identification of rinneite (K3NaFeCl6) in inclusions in minerals

AbstractSolid daughter phases in fluid and salt melt inclusions in minerals provide important clues to characterization of mineral‐forming processes. The analysis of the fluid inclusions often requires the exposure of the daughter minerals. Rinneite (K3NaFeCl6), which is a hygroscopic mineral, decomposes in air and cannot thus be identified by conventional methods. A combined approach has been applied for investigation of synthetic and natural rinneite to acquire its diagnostic Raman spectrum for a nondestructive identification. We used natural rinneite inclusions in halite, suitable for applying a complex of methods, to clear up the reference spectrum. Improved high‐resolution X‐ray diffraction (XRD) data obtained from natural rinneite inclusion are comparable with that of previously published, with similar unit cell dimensions. Polarized Raman spectra of natural inclusions were obtained using different geometries and polarization of the incident and scattered light. Interpretation of experimental Raman spectra was performed within the framework of lattice dynamics simulations and group analysis. Individual spectral bands are interpreted in terms of Raman‐active vibrational modes of K3NaFeCl6 structural units. Raman spectrum of synthetic rinneite with main peaks at 75, 91, 103, 143, 167, 171, 187, and 239 cm−1 agrees well with the spectra of rinneite inclusions in halite from the Nepa potash deposit and rinneite daughter minerals in salt melt inclusions hosted by quartz veinlets from the porphyry gold systems in the Central Slovakia Volcanic Field. This provides a firm basis for any future identification of this mineral worldwide, using nondestructive Raman spectroscopy.

Inclusive spectra and Bose-Einstein correlations in small thermal quantum systems

The spectra and correlation of identical particles emitted from small local-equilibrium sources are considered. The size of the system is defined by the negative part of the parabolic falling chemical potential. The analytical solution of the problem is found for the case of inclusive measurements. It is shown that in the case where the size of the system is comparable to the thermal wavelength of the particles, the spectra and correlation functions are far from the quasiclassical approximation expected for large systems, and observed femtoscopy scales (interferometry radii) will be essentially smaller than the Gaussian radii of the source. If the maximum value of the chemical potential approaches the critical one, specific for the system, one can consider the possibility of the Bose-Einstein condensation. In such a case the reduction of the intercept of the correlation function for inclusive measurements takes place. The results can be used for the searching of femtoscopy homogeneity lengths in proton-proton collisions at LHC energies.

Three-nucleon force effects in inclusive spectra of the neutron-deuteron breakup reaction

We investigate the sensitivity of the non-exclusive nucleon induced deuteron breakup reaction to the three-nucleon interaction and distributions of three-nucleon force effects in inclusive spectra. To this end we solve the three-nucleon Faddeev equation at a number of incoming nucleon laboratory energies using the CD Bonn nucleon-nucleon interaction alone or combined with the 2{\pi}-exchange Tucson-Melbourne three-nucleon force. Based on these solutions energy spectra of an outgoing nucleon, at a specified detection angle as well as spectra integrated over that angle, are calculated. By integrating the spectra at a given angle over the energy of the outgoing nucleon the angular distributions of three-nucleon force effects in the breakup process are additionally obtained. Contrary to elastic nucleon-deuteron scattering, where at higher energies significant three-nucleon force effects were encountered for scattering angles around the minimum of the cross section, for the breakup process only moderate effects are found and they are restricted to forward angles. Results of the present investigation show that the large three-nucleon force effects found for some specific complete breakup configurations are reduced substantially in the incomplete spectra when averaging over contributing complete geometries is performed.

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.

Double inclusive small- x gluon production and their azimuthal correlations in a biased ensemble

We consider double $gg\rightarrow g$ production in the presence of a bias on the unintegrated gluon distribution of the colliding hadron or nuclei. Such bias could be due to the selection of configurations with a greater number of gluons or higher mean transverse momentum squared or, more generally, due to a modified spectral shape of the gluon distribution in the hadrons. Hence, we consider reweighted functional averages over the stochastic ensemble of small-x gluons. We evaluate explicitly the double inclusive gluon transverse momentum spectrum in high-energy collisions, and their azimuthal correlations, for a few simple examples of biases.

Some properties of the pT regions observed at the LHC energies

The inclusive spectrum of the charged particles, [Formula: see text]0- and [Formula: see text]-mesons produced in the pp collisions at LHC energies were analyzed by fitting them with exponential functions. It was found the spectra were composed of several p[Formula: see text] regions, which could be characterized by the length of the regions [Formula: see text] and two free fitting parameters [Formula: see text] and [Formula: see text]. The study of the [Formula: see text] dependences of the parameters [Formula: see text] and [Formula: see text] and of the energy dependencies of the [Formula: see text], [Formula: see text] and [Formula: see text] showed that the regions can be classified into two groups depending on the values of the [Formula: see text], [Formula: see text] and [Formula: see text]. The values of the [Formula: see text] and [Formula: see text] for the first group don’t depend on colliding energy and the type of the particles (though the values of [Formula: see text] increase linearly with energy) whereas the characteristics in the second group of regions show strong dependencies. It was found that the ratio of the length for the [Formula: see text]-mesons to one for the [Formula: see text]0-mesons is approximately equal to the ratio of their mass: [Formula: see text]. Assuming that the values of the [Formula: see text] are directly proportional to the string tension the result could be considered as evidence in favor of parton string fragmentation dynamics. The increase in the lengths for the [Formula: see text]-mesons’ regions is accompanied by an increase of the values for the parameter [Formula: see text]. It can mean that the [Formula: see text]-mesons were produced at smaller values of [Formula: see text] compared with that for [Formula: see text]0-mesons. The results show that for the first group of regions the lengths of the regions are [Formula: see text]3–5 times greater than the lengths of neighboring, lower p[Formula: see text] regions. For the second group of regions the lengths of the regions are [Formula: see text]1–2 times greater than the lengths of neighboring lower p[Formula: see text] region. In the framework of the string fragmentation and hadronization dynamics, this could mean that the particles in the group [Formula: see text] of regions are produced through previous-generation strings decays into [Formula: see text]3–5 strings while those in group [Formula: see text] originate from previous-generation strings decays into [Formula: see text]2 strings.

Inclusive Spectra of Protons and α Particles from the Interaction between α Particles with an Energy of 29 MeV and 27Al and 59Co Nuclei

The energy spectra of protons and α particles are obtained for a wide range of angles in reactions between α particles with an energy of 29 MeV and 27Al and 59Co nuclei. The contributions from different mechanisms that shape the inclusive proton and α-particle spectra of the studied reactions are determined by analyzing the experimental data with the PRECO-2006 code. The experimental results are added to the bank of data needed for the development of advanced nuclear technologies.

Carbonate-silicate inclusions in garnet as evidence for a carbonate-bearing source for fluids in leucocratic granitoids associated with granulites of the Southern Marginal Zone, Limpopo Complex, South Africa

We present a study of carbonate-bearing polyphase inclusions in garnets from leucocratic granitoids intruding metapelitic granulites of the Southern Marginal Zone (SMZ) of the Neoarchean Limpopo high-grade complex, South Africa, during the post-peak stage (2710–2650 Ma; U-Pb ages for zircons and monazites). Ternary feldspar thermometry suggests that the granitoid magma cooled from temperatures 800–900 °C at a pressure of ca. 6.5 kbar. Abundant CO2 fluid inclusions in quartz and T-XCO2 phase equilibria modeling via PERPLE_X imply action of an essentially carbonic fluid in the granitoids. Cores of almandine-rich garnet grains from the granitoids contain polyphase carbonate-bearing inclusions with a distinct negative crystal shape. The major carbonate in the inclusions is a strongly zoned magnesite-siderite variety, whereas pyrophyllite is the predominant silicate phase. Raman spectra of unexposed inclusions revealed a presence of CO2, as well as CH4 and H2O. The carbonate-bearing inclusions coexist with larger polyphase inclusions composed of biotite, quartz, K-feldspar, plagioclase, sillimanite, which are interpreted as relics of granitic melts. Modeling the mineral assemblage preserved within the carbonate-bearing inclusions shows that their present mineral and chemical compositions are a product of interaction of the trapped aqueous‑carbonic fluid with host garnet during cooling below 400 °C. Despite strong modifications, the inclusions bear evidence for initial saturation of the fluid with Mg‑carbonate. This is taken as an evidence for an origin of the fluids by devolatilization of the Mg-rich carbonate-bearing ultrabasic greenstone rocks of the Kaapvaal Craton that were buried under the SMZ. Being generated at temperatures between 650 and 700 °C, the fluid subsequently participated in anatexis and coexisted with the granite magma during exhumation and interaction of the SMZ granulites with cratonic rocks.

Gauge ambiguity of the quark spectrum in the Color Glass Condensate

In the Color Glass Condensate, the inclusive spectrum of produced quarks in a heavy ion collision is obtained as the Fourier transform of a 2-fermion correlation function. Due to its non-locality, the two points of this function must be linked by a Wilson line in order to have a gauge invariant result, but when the quark spectrum is evaluated in a background that has a non-zero chromo-magnetic field, this procedure suffers from an ambiguity related to the choice of the contour defining the Wilson line. In this paper, we use an analytically tractable toy model of the background field in order to study this contour dependence. We show that for a straight contour, unphysical contributions to the spectrum in p⊥−2 and p⊥−3 cancel, leading to a spectrum with a tail in p⊥−4. If the contour defining the Wilson line deviates from a straight line, the path dependence is at most of order p⊥−5 if its curvature is bounded, and of order p⊥−4 otherwise. When the contour is forced to go through a fixed point, the path dependence is even larger, of order p⊥−2.

Fractality in hadron interactions: a conservation law and quantization of fractal dimensions

A microscopic scenario of constituent interactions in high energy collisions of hadrons and nuclei is studied. The concept is based on the z-scaling of inclusive spectra observed in a wide range of collision energies, multiplicity densities, momenta, and angles of detected particles. We bring arguments that, due to the fractality and self-similarity of the hadron interactions assumed in the z-scaling scheme, there exists a conservation law of a new quantity named “fractal cumulativity.” The conserved quantity is proportional to the corresponding fractal dimensions and is a simple function of the respective momentum fractions. Based on statistical ideas and entropy considerations we demonstrate that the fractal dimensions possess quantum character.

Hadron production in pp and AA collisions at mid-rapidity within self-similarity approach

The self-consistent approach based on similarity of inclusive spectra of hadrons produced in pp and AA collisions is reviewed. We present its modification due to the quark-gluon dynamics to describe the inclusive spectra of hadrons produced in pp collision as a function of the transverse momentum pt at mid-rapidity. The extension of this approach to analyze the pion pt-spectra produced in AA collision at high and middle energies and mid-rapidity is given. A satisfactory description of experimental data on these spectra in pp and AA collisions within the offered approach is shown.

Analytical description of hadron production in hadron-hadron and nuclear-nuclear collisions in the mid-rapidity region

It is shown that the inclusive spectra of the produced hadrons in hadron-hadron and nuclear-nuclear collisions can be presented as the universal function dependent of the self-similarity parameter in the analytical form. The article gives a description of the self-similarity parameter depending on the rapidity in the mid-rapidity region. The experimental data are in good agreement with the results of our calculations in a wide energy range from a few GeV to a few TeV in the central rapidity region.

Self-consistent analysis of hadron production in pp and AA collisions at mid-rapidity

The self-consistent approach based on similarity of inclusive spectra of hadrons produced in $pp$ and $AA$ collisions is reviewed. This approach allows us to describe rather well the ratio of proton to anti-proton yields in $AA$ collisions as a function of the initial energy at a wide range from a few GeV to a few TeV. We suggest its modification due to the quark-gluon dynamics to describe the inclusive spectra of hadrons produced in $pp$ collision as a function of the transverse momentum $p_t$ at mid-rapidity. The extension of this approach to analyze the pion $p_t$-spectra produced in $AA$ collision at high and middle energies and mid-rapidity is given. The satisfactory description of experimental data on these spectra in $pp$ and $AA$ collisions within the offered approach is shown.

Rapid Identification of Calcium Aluminate Inclusions in Steels Using Cathodoluminescence Analysis

We propose a method to identify calcium aluminate inclusions in calcium-treated aluminum-killed steels (Ca12Al14O33, CaAl4O7, CaAl12O19, and Al2O3) using cathodoluminescence (CL) analysis. Such inclusions result in nozzle clogging and melting of the stopper rod during continuous casting. We obtain CL images and CL spectra of calcium aluminate inclusions in model samples of calcium-treated aluminum-killed steel. The model samples are prepared by heating mixtures of Fe powder, Al powder, and Ca shot at 1550 °C in an argon atmosphere. On the basis of the CL colors and CL spectra of the calcium aluminate inclusions, we demonstrate that it is possible to distinguish Ca12Al14O33, CaAl4O7, CaAl12O19, and Al2O3 inclusions from CaAl2O4 and Ca3Al10O18 inclusions, which do not cause nozzle clogging and melting of the stopper rod, by comparing CL images obtained using digital cameras with and without a built-in filter. The acquisition times for the CL images are less than 10 seconds. Thus, the method we present here can be applied for the rapid detection of harmful calcium aluminate inclusions during continuous casting. The CL spectra also provide basic information to specify compositions in agglomerated calcium aluminate inclusions.

On the Production of J/ψ-Mesons in Pion–Nucleus Collisions

The processes of J/ψ-mesons production in pion–nucleus collisions are considered. For the determination of the inclusive spectra πA → J/ψX, the model was used which takes into account the energy losses of hard gluons in the interactions of hadron states with the nucleus nucleons. The results of calculations are presented together with the experimental data of NA3 Collaboration on π–Pt195 → J/ψX spectra at the incident pions energies of 150 and 280 GeV.