S\mathcal{S}-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant $g$ in the form of an infrared smooth function of argument $x$ for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter $l$. By representation of the $\mathcal{S}$-matrix in terms of abstract functional integral over primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. And, by expression of $\mathcal{S}$-matrix in terms of the partition function, the representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for discrete case where basis functions are Hermite functions, and for continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$-matrix are investigated within the framework of variational principle based on Jensen inequality. Equations with separable kernels satisfied by variational function $q$ are found and solved, yielding results for both the polynomial theory $\varphi^{4}$ and the nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$-matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are illustrated numerically. For simplicity of numerical calculation: the $D=1$ case is considered, and propagator for the free theory $G$ is in the form of Gaussian function typically in the Virton-Quark model. The formulation for nonlocal QFT in momentum $k$ space of extra dimensions with subsequent compactification into physical spacetime is discussed.Comment: 38 pages, 18 figures; v2: significant text editing; v3: text and plots edited, references and acknowledgments added; prepared for the special issue of the journal Particles in memory of G.V. Efimo

Flamelet Model Application for Non-Premixed Turbulent Combustion

The current Final Report contains results of the study which was performed in Scientific Research Center 'ECOLEN' (Moscow, Russia). The study concerns the development and verification of non-expensive approach for modeling of supersonic turbulent diffusion flames based on flamelet consideration of the chemistry/turbulence interaction (FL approach). Research work included: development of the approach and CFD tests of the flamelet model for supersonic jet flames; development of the simplified procedure for solution of the flamelet equations based on partial equilibrium chemistry assumption; study of the flame ignition/extinction predictions provided by flamelet model. The performed investigation demonstrated that FL approach allowed to describe satisfactory main features of supersonic H 2/air jet flames. Model demonstrated also high capabilities for reduction of the computational expenses in CFD modeling of the supersonic flames taking into account detailed oxidation chemistry. However, some disadvantages and restrictions of the existing version of approach were found in this study. They were: (1) inaccuracy in predictions of the passive scalar statistics by our turbulence model for one of the considered test cases; and (2) applicability of the available version of the flamelet model to flames without large ignition delay distance only. Based on the results of the performed investigation, we formulated and submitted to the National Aeronautics and Space Administration our Project Proposal for the next step research directed toward further improvement of the FL approach

Comparison of Geant4 hadron generation with data from the interactions with beryllium nuclei of +8.9 GeV/c protons and pions, and of -8 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 simulated data especially in the polar-angle distributions of secondary protons and pions.Comment: 15 pages, 13 figure

Cross-Sections of Large-Angle Hadron Production in Proton- and Pion-Nucleus Interactions III: Tantalum Nuclei and Beam Momenta from +/-3 Gev/c to +/-15 Gev/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% nuclear interaction length thick stationary tantalum target, of proton and pion beams with momentum from +/-3 GeV/c to +/-15 GeV/c. Results are given for secondary particles with production angles between 20 and 125 degrees. They are of particular relevance for the optimization of the design parameters of the proton driver of a neutrino factory.Comment: 68 pages, 12 figures, corrections in v2: added 'HARP -CDP group' to author name, corrected two typos in Table 4 (last two p values for 65-90 degrees were all 0.972

Cross-Sections of Large-Angle Hadron Production in Proton- and Pion-Nucleus Interactions V: Lead Nuclei and Beam Momenta from +/-3 Gev/c to +/-15 Gev/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% nuclear interaction length thick stationary lead target, of proton and pion beams with momentum from +/-3 GeV/c to +/-15 GeV/c. Results are given for secondary particles with production angles 20 to 125 degrees. Cross-sections on lead nuclei are compared with cross-sections on beryllium, copper, and tantalum nuclei.Comment: 67 pages, 13 figures, 47 table

Interferometry of Direct Photons in Central 280Pb+208Pb Collisions at 158A GeV

Two-particle correlations of direct photons were measured in central 208Pb+208Pb collisions at 158 AGeV. The invariant interferometric radii were extracted for 100<K_T<300 MeV/c and compared to radii extracted from charged pion correlations. The yield of soft direct photons, K_T<300 MeV/c, was extracted from the correlation strength and compared to theoretical calculations.Comment: 5 pages, 4 figure

Systematics of Inclusive Photon Production in 158 AGeV Pb Induced Reactions on Ni, Nb, and Pb Targets

The multiplicity of inclusive photons has been measured on an event-by-event basis for 158 AGeV Pb induced reactions on Ni, Nb, and Pb targets. The systematics of the pseudorapidity densities at midrapidity (rho_max) and the width of the pseudorapidity distributions have been studied for varying centralities for these collisions. A power law fit to the photon yield as a function of the number of participating nucleons gives a value of 1.13+-0.03 for the exponent. The mean transverse momentum, , of photons determined from the ratio of the measured electromagnetic transverse energy and photon multiplicity, remains almost constant with increasing rho_max. Results are compared with model predictions.Comment: 16 pages including 4 figure

Scaling of Particle and Transverse Energy Production in 208Pb+208Pb collisions at 158 A GeV

Transverse energy, charged particle pseudorapidity distributions and photon transverse momentum spectra have been studied as a function of the number of participants (N_{part}) and the number of binary nucleon-nucleon collisions (N_{coll}) in 158 A GeV Pb+Pb collisions over a wide impact parameter range. A scaling of the transverse energy pseudorapidity density at midrapidity as N_{part}^{1.08 \pm 0.06} and N_{coll}^{0.83 \pm 0.05} is observed. For the charged particle pseudorapidity density at midrapidity we find a scaling as N_{part}^{1.07 \pm 0.04} and N_{coll}^{0.82 \pm 0.03}. This faster than linear scaling with N_{part} indicates a violation of the naive Wounded Nucleon Model.Comment: 13 pages, 16 figures, submitted to European Physical Journal C (revised results for scaling exponents

Cross-sections of large-angle hadron production in proton- and pion-nucleus interactions VI: carbon nuclei and beam momenta from \pm 3 GeV/c to \pm 15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% nuclear interaction length thick stationary carbon target, of proton and pion beams with momentum from \pm 3 GeV/c to \pm 15 GeV/c. Results are given for secondary particles with production angles between 20 and 125 degrees. Cross-sections on carbon nuclei are compared with cross-sections on beryllium, copper, tantalum and lead nuclei.Comment: 67 pages, 13 figure

Cross-sections of large-angle hadron production in proton-- and pion--nucleus interactions VIII: aluminium nuclei and beam momenta from {\pm}3 GeV/c to {\pm}15 GeV/c

We report on double-differential inclusive cross-sections of the production of secondary protons, charged pions, and deuterons, in the interactions with a 5% {\lambda}int thick stationary aluminium target, of proton and pion beams with momentum from \pm3 GeV/c to \pm15 GeV/c. Results are given for secondary particles with production angles between 20 and 125 degrees. Cross-sections on aluminium nuclei are compared with cross-sections on beryllium, carbon, copper, tin, tantalum and lead nuclei.Comment: 71 pages, 16 figures, 47 table