ATLAS sensitivity to Wtb anomalous couplings in top quark decays

We study the sensitivity of the ATLAS experiment to Wtb anomalous couplings in top pair production with semileptonic decay, pp→tt̄→W⁺bW^-b̄ with one of the W bosons decaying leptonically and the other hadronically. Several observables are examined, including the W helicity fractions and new quantities recently introduced, such as the ratios of helicity fractions and some angular asymmetries defined in the W rest frame. The dependence on anomalous couplings of all these observables has been previously obtained. In this work we show that some of the new observables also have smaller systematic uncertainties than the helicity fractions, with a similar or stronger dependence on anomalous couplings. Consequently, their measurement can significantly improve the limits on anomalous couplings. Moreover, the most sensitive measurements can be combined. In this case, the precision achieved in the determination of Wtb anomalous couplings can be of a few percent in the semileptonic channel alone.     

How to solve the measurement problem of quantum mechanics

A solution to the measurement problem of quantum mechanics is proposed within the framework of an intepretation according to which only quantum systems with an infinite number of degrees of freedom have determinate properties, i.e., determinate values for (some) observables of the theory. The important feature of the infinite case is the existence of many inequivalent irreducible Hilbert space representations of the algebra of observables, which leads, in effect, to a restriction on the superposition principle, and hence the possibility of defining (macro-) observables which commute with every observable. Such observables have determinate values which are not subject to quantum interference effects. A measurement process is schematized as an interaction between a microsystem and a macrosystem, idealized as an infinite quantum system, and it is shown that there exists a unitary transformation which transforms the initial pure state of the composite system in a finite time (the duration of the interaction) into the required mixture of disjoint states.     

Completeness of observables and particle trajectories in quantum mechanics

The complete set of observables (bilinear Hermitian forms) is determined for the Schrödinger equation and their connection with the curvature and torsion of the curves, where conservation laws are fulfilled, is established. It is shown that these curves for a free particle, in the general case, are spiral lines with the radius and step length defined by the observables at the initial point (both parameters are proportional to the de Broglie wavelength). A spiral line turns to a straight line under some conditions. The trajectory variations are considered in the problem with a potential step and a rectangular barrier. It is shown that spiral lines can be transformed into straight lines and vice versa. All observables, which are changed along the potential barrier, can be restored under some constraints on the potential. The Hermitian transformations at the potential step are connected with the Lorentz transformations. A qualitative explanation of the double-slit experiment for extremely low intensity of the particles' source in the absence of the interference conditions is suggested.     

Computer simulation of particles with position-dependent mass

In the present work a dynamical system is investigated, in which the particles’ mass depends on their position in space. The first case study is that of a single point-like particle in one dimension, whose Hamiltonian is numerically integrated with a first-order, energy-conserving algorithm; subsequently, the model is extended to a Lennard-Jones fluid in three dimensions. The features of both setups are examined, and a simple, exact method is devised to obtain, from a system of particles with position-dependent mass, the same equilibrium observables that would be measured in a conventional simulation. The properties of these dynamical systems are explored, with possible applications in the development of efficient sampling strategies.     

The uncertainty relation expressed by means of a new entropic function

In this article we use a new entropic function, derived from an f-divergence between two probability distributions, for the construction of an alternative entropic uncertainty relation. After a brief review of some existing f-divergences, a new f-divergence and the corresponding entropic function, derived from it, is introduced and its useful characteristics are presented. This entropic function is then applied to construct an alternative uncertainty relation of two non-commuting observables in quantum physics. An explicit expression for such an uncertainty relation is found for the case of two observables which are the x- and z-components of the angular momentum of the spin-1/2 system.      

Theory of measurement of entangled states

Problem on reconstruction of state of finite-dimension quantum information transfer channel, pure or mixed, by results of measurements of needed number of observables, is considered. It is shown that in general case it is needed to measure incompatible observables in number exceeding by one dimension of space of vectors of state. Each of incompatible observables is measured in its statistically valuable series of measurements. In special case, when one of observables is a non-demolition observable, measurement of the other observables is needed for realization of control of property of non-demolition. In case of paired channel it is shown that results of measurements of observables that do not demolish states of sub-channels are characterized by mutual distribution of probabilities while results of measurement of over-classical observables are characterized by mutual correlation only. This correlation vanishes completely in case of pure unentangled states.     

The various facets of the deuteron

Models of the nucleon-nucleon interaction are based on both experimental data and theoretical assumptions. It is shown that some of the present models which exhibit differences with this last respect are to some extent equivalent up to a unitary transformation. Consequences for predictions of observables in the deuteron are examined.     

Pairwise correlations in a three-partite quantum system from a prequantum random field

Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility to represent the averages of quantum observables (including correlations of observables on subsystems of a composite system) as averages with respect to fluctuations of classical random fields. In view of the PCSFT terminology, quantum states are classical random fields. The aim of our approach is to represent all quantum probabilistic quantities by means of classical random fields. We obtain the classical-random-field representation for pairwise correlations in three-partite quantum systems. The three-partite case (surprisingly) differs substantially from the bipartite case. As an important first step, we generalized the theory developed for pure quantum states of bipartite systems to the states given by density operators.     

A Generalization of Entanglement to Convex Operational Theories: Entanglement Relative to a Subspace of Observables

We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This extends the notion of ordinary entanglement in quantum information theory to a much more general framework. Some important special cases are described, in which the distinguished observables are subspaces of the observables of a quantum system, leading to results like the identification of generalized unentangled states with Lie-group-theoretic coherent states when the special observables form an irreducibly represented Lie algebra. Some open problems, including that of generalizing the semigroup of local operations with classical communication to the convex cones case, are discussed. PACS: 03.65.Ud.     

Is soft physics entropy driven?

The soft physics, p_T<2 GeV/c, observables at both RHIC and the SPS have now been mapped out in quite specific detail. From these results there is mounting evidence that this regime is primarily driven by the multiplicity per unit rapidity, dN_ch/dη. This suggests that the entropy of the system alone is the underlying driving force for many of the global observables measured in heavy-ion collisions. That this is the case and there is an apparent independence on collision energy is surprising. I present the evidence for this multiplicity scaling and use it to make some extremely naive predictions for the soft sector results at the LHC.     

On the Stability of a Quantum Dynamics of a Bose-Einstein Condensate Trapped in a One-Dimensional Toroidal Geometry

We rigorously analyze the stability of the “quasi-classical” dynamics of a Bose-Einstein condensate with repulsive and attractive interactions, trapped in an effective 1D toroidal geometry. The “classical” dynamics, which corresponds to the Gross-Pitaevskii mean field theory, is stable in the case of repulsive interaction, and unstable (under some conditions) in the case of attractive interaction. The corresponding quantum dynamics for observables is described by using a closed system of linear partial differential equations. In both cases of stable and unstable quasi-classical dynamics the quantum effects represent a singular perturbation to the quasi-classical solutions, and are described by the terms in these equations which consist of a small quasi-classical parameter which multiplies high-order “spatial” derivatives. We demonstrate that as a result of the quantum singularity for observables a convergence of quantum solutions to the corresponding classical solutions exists only for limited times, and estimate the characteristic time-scales of the convergence.     

Twist-3 single-spin asymmetries in semi-inclusive deep-inelastic scattering

The single-spin asymmetries for a longitudinally polarized lepton beam or a longitudinally polarized nucleon target in semi-inclusive deep-inelastic scattering are twist-3 observables. We study these asymmetries in a simple diquark spectator model of the nucleon. Analogous to the case of transverse target polarization, non-vanishing asymmetries are generated by gluon exchange between the struck quark and the target system. It is pointed out that the coupling of the virtual photon to the diquark is needed in order to preserve electromagnetic gauge invariance at the twist-3 level. The calculation indicates that previous analyses of these observables are incomplete.     

Weak Observables in MV Algebras

A notion of a weak observable is defined and aconstruction of a weak observable is examined. With thehelp of the construction, the sum of weak observables isrealized as well as the upper and lower limits of a sequence of weak observables.     

Testing Nucleon–nucleon Potentials in Three- and Four-nucleon Scattering Observables

We present a theoretical study of three- and four-nucleon continuum within the hyperspherical harmonics method, using a representative variety of realistic nucleon–nucleon potential models, i.e. one of phenomenological type, the Argonne v ₁₈ (AV18), one obtained within chiral effective field theory up to next-to-next-to-next-leading order, the Idaho N3LO (I-N3LO), and a “low-k” model derived from the CD-Bonn potential. In particular, the convergence pattern for the four-nucleon system is found to be problematic for the P-waves phase-shifts in the case of the AV18 potential at higher energies. An extrapolation procedure is presented and discussed. Finally, we present the theoretical results for p?d and p?³ scattering observables at two selected energies, and we compare these with the available experimental data. In particular, some spread in the unpolarized cross section and in some polarization observables has been observed using the three potential models, in particular for A =  4. Furthermore the well known discrepancy in the vector polarization observables remains for the three potential models.     

Observables in 3d spinfoam quantum gravity with fermions

We study expectation values of observables in three-dimensional spinfoam quantum gravity coupled to Dirac fermions. We revisit the model introduced by one of the authors and extend it to the case of massless fermionic fields. We introduce observables, analyse their symmetries and the corresponding proper gauge fixing. The Berezin integral over the fermionic fields is performed and the fermionic observables are expanded in open paths and closed loops associated to pure quantum gravity observables. We obtain the vertex amplitudes for gauge-invariant observables, while the expectation values of gauge-variant observables, such as the fermion propagator, are given by the evaluation of particular spin networks.     

Ergodical time evolution of a Gaussian wave packet in quantum dots

The time evolution of a Gaussian wave packet (GWP) confined in a quantum dot is numerically studied. The quantum dots are modelled by a two-dimensional square box and by the potential x⁴ + y⁴. For the case of an incommensurate energy spectrum the time evolution of observables has no global period. As a result this leads to ergodic phase portraits with a finite phase volume. For the spatially wide GWP the distribution function of quantum observables may be approximated as a Gaussian one. For the case of commensurate transition frequencies in the quantum well the time evolution of observables is periodical and the phase portraits have a zero phase volume.     

Entanglement measures as physical observables

We discuss why regular observables cannot be proper entanglement measures, and how observables in a generalized setting can be used to make an entanglement monotone a directly observable quantity for the case of pure states. For the case of mixed states, these generalized observables can be used to find valid lower bounds on entanglement monotones that can be measured in laboratory experiments in the same fashion as it can also be done for pure states. PACS 03.67.-a; 03.67.Mn; 89.70.+c     

Optimal entropic uncertainty relation for successive measurements in quantum information theory

We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in the literature on the sum of entropie uncertainties of two observables which are measured on distinct but identically prepared ensembles of systems. In the case of a two-dimensional Hilbert space, the optimum bound for successive measurements of two-spin components, is seen to be strictly greater than the optimal bound for the case when they are measured on distinct ensembles, except when the spin components are mutually parallel or perpendicular