Statistics of weighted Poisson events and its applications

The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or relevance to a certain type of reaction. The sum is described by the compound Poisson distribution (CPD) which is shortly reviewed. It is shown that the CPD can be approximated by a scaled Poisson distribution (SPD). The SPD is applied to parameter estimation in situations where the data are distorted by resolution effects. It performs considerably better than the normal approximation that is usually used. A special Poisson bootstrap technique is presented which permits to derive confidence limits for observations following the CPD.Comment: 14 pages, 2 figure

Boundary reduction formula

An asymptotic theory is developed for general non-integrable boundary quantum field theory in 1+1 dimensions based on the Langrangean description. Reflection matrices are defined to connect asymptotic states and are shown to be related to the Green functions via the boundary reduction formula derived. The definition of the $R$-matrix for integrable theories due to Ghoshal and Zamolodchikov and the one used in the perturbative approaches are shown to be related.Comment: 12 pages, Latex2e file with 5 eps figures, two Appendices about the boundary Feynman rules and the structure of the two point functions are adde

Irreversible Quantum Mechanics in the Neutral K-System

The neutral Kaon system is used to test the quantum theory of resonance scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with complex Hamiltonian is obtained by truncating the complex basis vector expansion of the exact theory in Rigged Hilbert space. This can be done for K_1 and K_2 as well as for K_S and K_L, depending upon whether one chooses the (self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP. As an unexpected curiosity one can show that the exact theory (without truncation) predicts long-time 2 pion decays of the neutral Kaon system even if the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include

Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group

The velocity basis of the Poincare group is used in the direct product space of two irreducible unitary representations of the Poincare group. The velocity basis with total angular momentum j will be used for the definition of relativistic Gamow vectors.Comment: 14 pages; revte

Quantum mechanics with time-dependent parameters

Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.Comment: 7 pages, LaTe

On the p4p^4--corrections to K→3πK \to 3\pi decay amplitudes in nonlinear and linear chiral models

The calculations of isotopic amplitudes and their results for the direct $CP$--violating charge asymmetry in $K^\pm \to 3\pi$ decays within the nonlinear and linear ($\sigma$--model) chiral Lagrangian approach are compared with each other. It is shown, that the latter, taking into account intermediate scalar resonances, does not reproduce the $p^4$--corrections of the nonlinear approach introduced by Gasser and Leutwyler, being saturated mainly by vector resonance exchange. The resulting differences concerning the $CP$ violation effect are traced in some detail.Comment: 14 page

Quantum effective force in an expanding infinite square-well potential and Bohmian perspective

The Schr\"{o}dinger equation is solved for the case of a particle confined to a small region of a box with infinite walls. If walls of the well are moved, then, due to an effective quantum nonlocal interaction with the boundary, even though the particle is nowhere near the walls, it will be affected. It is shown that this force apart from a minus sign is equal to the expectation value of the gradient of the quantum potential for vanishing at the walls boundary condition. Variation of this force with time is studied. A selection of Bohmian trajectories of the confined particle is also computed.Comment: 7 figures, Accepted by Physica Script

The Higgs Boson Mass in Split Supersymmetry at Two-Loops

The mass of the Higgs boson in the Split Supersymmetric Standard Model is calculated, including all one-loop threshold effects and the renormalization group evolution of the Higgs quartic coupling through two-loops. The two-loop corrections are very small (<<1 GeV), while the one-loop threshold corrections generally push the Higgs mass down several GeV.Comment: 17 pages. 4 figures. Improved discussion and notation. Corrected typos. Added references. Added plots. Main results unchange