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

Nonlocal Scalar Quantum Field Theory: Functional Integration, Basis Functions Representation and Strong Coupling Expansion

Nonlocal QFT of one-component scalar field $\varphi$ in $D$-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions $\mathcal{Z}$ as a functional of external source $j$, coupling constant $g$, and spatial measure $d\mu$ is studied. An expression for GF $\mathcal{Z}$ in terms of the abstract integral over the primary field $\varphi$ is given. An expression for GF $\mathcal{Z}$ in terms of integrals over the primary field and separable Hilbert space (HS) is obtained by means of a separable expansion of the free theory inverse propagator $\hat{L}$ over the separable HS basis. The classification of functional integration measures $\mathcal{D}\left[\varphi\right]$ is formulated, according to which trivial and two nontrivial versions of GF $\mathcal{Z}$ are obtained. Nontrivial versions of GF $\mathcal{Z}$ are expressed in terms of $1$-norm and $0$-norm, respectively. The definition of the $0$-norm generator $\varPsi$ is suggested. Simple cases of sharp and smooth generators are considered. Expressions for GF $\mathcal{Z}$ in terms of integrals over the separable HS with new integrands are obtained. For polynomial theories $\varphi^{2n},\, n=2,3,4,\ldots,$ and for the nonpolynomial theory $\sinh^{4}\varphi$, integrals over the separable HS in terms of a power series over the inverse coupling constant $1/\sqrt{g}$ for both norms ($1$-norm and $0$-norm) are calculated. Critical values of model parameters when a phase transition occurs are found numerically. A generalization of the theory to the case of the uncountable integral over HS is formulated. A comparison of two GFs $\mathcal{Z}$, one in the case of uncountable HS integral and one obtained using the Parseval-Plancherel identity, is given.Comment: 26 pages, 2 figures; v2: significant additions in the text; prepared for the special issue "QCD and Hadron Structure" of the journal Particles; v3: minimal corrections; v4: paragraphs added related to Reviewer comment

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

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

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