Abstract: We study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a one-dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definition of the Wigner function in this case and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system, which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states and to their superpositions.

Abstract: We study the weak decay of the Lambda(b) into J/psi K Xi. and J/psi eta Lambda states, and relate these processes to the Lambda(b) -> J/psi(K) over barN decay mode. The elementary weak transition at the quark level proceeds via the creation of a J/psi meson and an excited sud system with I = 0, which upon hadronization leads to (K) over barN or eta Lambda pairs. These states undergo final-state interaction in coupled channels and produce a final meson-baryon pair. The K. state only occurs via rescattering, hence making the Lambda(b) -> J/psi K Xi process very sensitive to the details of the meson-baryon interaction in strangeness S = -1 and isospin I = 0. We show that the corresponding invariant mass distribution is dominated by the next-to-leading-order terms of the chiral interaction. The I = 0 selectivity of this decay, and its large sensitivity to the higher-order terms, makes its measurement very useful and complementary to the K- p -> K Xi cross section data. The rates of the Lambda(b) -> J/psi K Xi and Lambda(b) -> J/psi eta Lambda invariant mass distributions are sizable compared to those of the Lambda(b) -> J/psi(K) over barN decay, which is measured experimentally, and thus, we provide arguments for an experimental determination of these decay modes that will help us understand better the chiral dynamics at higher energies.

Abstract: We study the Upsilon(1S) radiative decays to gamma pi(+)pi(-) and gamma K+K- using data recorded with the BABAR detector operating at the SLAC PEP-11 asymmetric-energy e(+)e(-) collider at center-of-mass energies at the Upsilon(2S) and Upsilon(3S) resonances. The Upsilon(1S) resonance is reconstructed from the decay Upsilon(nS) -> pi(+)pi(-) Upsilon(1S), n =2, 3. Branching fraction measurements and spin-parity analyses of Upsilon(1S) radiative decays are reported for the I = 0 S-wave and f(2) (1270) resonances in the pi(+)pi(-) mass spectrum, the f'(2) (1525) and f(0) (1500) in the K+K mass spectrum, and the f(0)(1710) in both.