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

Cranometric variability in brown bears of the Russian Far East

Morphometric analysis of 282 skulls of the brown bear Ursus arctos from the Far Eastern part of the range was carried out. The presence of two morphological clusters for both males and females is shown. Samples from two clusters were compared with their geographical location and subspecies. It was found that one cluster or another had no specific reference to the particular region or subspecies of a particular cluster, only the superiority of one over the other in a cluster of different subspecies and regions was changed. A comparison with the spread of brown bear genetic lines in the Far East of Russia is made. It was noted that the precise distribution of a particular cluster to a specific genetic line of haplotypes was not found

Revisiting the 'LSND anomaly' II: critique of the data analysis

This paper, together with a preceding paper, questions the so-called 'LSND anomaly': a 3.8 sigma excess of antielectronneutrino interactions over standard backgrounds, observed by the LSND Collaboration in a beam dump experiment with 800 MeV protons. That excess has been interpreted as evidence for the antimuonneutrino to antielectronneutrino oscillation in the \Deltam2 range from 0.2 eV2 to 2 eV2. Such a \Deltam2 range is incompatible with the widely accepted model of oscillations between three light neutrino species and would require the existence of at least one light 'sterile' neutrino. In a preceding paper, it was concluded that the estimates of standard backgrounds must be significantly increased. In this paper, the LSND Collaboration's estimate of the number of antielectronneutrino interactions followed by neutron capture, and of its error, is questioned. The overall conclusion is that the significance of the 'LSND anomaly' is not larger than 2.3 sigma.Comment: 30 pages, 16 figures, 6 table

Why the paper CERN-PH-EP-2009-015 (arXiv:0903.4762) is scientifically unacceptable

The paper CERN-PH-EP-2009-015 (arXiv:0903.4762) by A. Bagulya et al. violates standards of quality of work and scientific ethics on several counts. The paper contains assertions that contradict established detector physics. The paper falls short of proving the correctness of the authors' concepts and results. The paper ignores or quotes misleadingly pertinent published work. The paper ignores the fact that the authors' concepts and results have already been shown wrong in the published literature. The authors seem unaware that cross-section results from the 'HARP Collaboration' that are based on the paper's concepts and algorithms are in gross disagreement with the results of a second analysis of the same data, and with the results of other experiments.Comment: 8 pages, 3 figure

Reply to 'Corrections to the HARP-CDP Analysis of the LSND Neutrino Oscillation Backgrounds'

The alleged mistakes in recent papers that reanalyze the backgrounds to the 'LSND anomaly' do not exist. We maintain our conclusion that the significance of the 'LSND anomaly' is not 3.8 sigma but not larger than 2.3 sigma.Comment: 3 page

TPC track distortions III: fiat lux

We present a comprehensive overview and final summary of all four types of static track distortions seen in the HARP TPC, in terms of physical origins, mathematical modelling, and correction algorithms. 'Static'Â distortions are defined as not depending on the event time within the 400 ms long accelerator spill. Calculated static distortions are compared with measurements from cosmic-muon tracks. We characterize track distortions by the r phi residuals of cluster positions with respect to the transverse projection of a helical trajectory constrained by hits in the RPC overlap regions. This method provides a fixed TPC-external reference system (by contrast to the co-moving coordinate system associated with a fit) which solely permits to identify individually, and measure quantitatively, the static TPC track distortions arising from (i) the inhomogeneity of the solenoidal magnetic field, (ii) the inhomogeneity of the electric field from the high-voltage mismatch between the inner and outer TPC field cages, (iii) the anode-wire durchgriff, and (iv) a homogenous ion-charge density in the drift volume. Five voltage levels are identified which were set incorrectly during data taking with the HARP TPC, and unfortunately conspired toward large static and dynamic track distortions. The observed time development of static distortions after a 83mKr calibration lends decisive support to our conclusions on static TPC distortions

Cross-sections of large-angle hadron production in proton- and pion-nucleus interactions VII: tin nuclei and beam momenta from \pm3 GeV/c to \pm15 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 tin 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 tin nuclei are compared with cross-sections on beryllium, carbon, copper, tantalum and lead nuclei.Comment: 68 pages, 13 figure