Bounds on gamma from CP violation measurements in B -> pi+ pi- and B -> psi K_S

We study the determination of gamma from CP-violating observables in B -> pi+ pi- and B -> psi K_S. This determination requires theoretical input to one combination of hadronic parameters. We show that a mild assumption about this quantity may allow bounds to be placed on gamma, but we stress the pernicious effects that an eightfold discrete ambiguity has on such an analysis. The bounds are discussed as a function of the direct (C) and interference (S) CP-violating observables obtained from time-dependent B -> pi+ pi- decays, and their behavior in the presence of new physics effects in B-Bbar mixing is studied. (V2: Misprints corrected. Slightly improved discussion.)Comment: 11 pages, RevTex 4, 5 eps figures include

Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry

We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to be represented, the construction of the representation of the rotation group on this space, the deformation of the Leibnitz rule accompanying this representation and the implied necessity of deforming the co-product to restore the rotation symmetry automorphism. This also implies the breaking of rotational invariance on the level of the Schroedinger action and equation as well as the Hamiltonian, even for rotational invariant potentials. For rotational invariant potentials the symmetry breaking results purely from the deformation in the sense that the commutator of the Hamiltonian and angular momentum is proportional to the deformation.Comment: 21 page

Reparametrization invariance of B decay amplitudes and implications for new physics searches in B decays

When studying B decays within the Standard Model, it is customary to use the unitarity of the CKM matrix in order to write the decay amplitudes in terms of only two of the three weak phases which appear in the various diagrams. Occasionally, it is mentioned that those two weak phases can be used in order to describe any decay amplitude, even beyond the Standard Model. Here we point out that, when describing a generic decay amplitude, the two weak phases can be chosen completely at will, and we study the behavior of the decay amplitudes under changes in the two weak phases chosen as a basis. Of course, physical observables cannot depend on such reparametrizations. This has an impact in discussions of the SM and in attempts to parametrize new physics effects in the decay amplitudes. We illustrate these issues by looking at B --> psi K_S and the isospin analysis in B --> pi pi.Comment: 16 pages, RevTe

Nitrogen use of a mixed tree crop plantation with a leguminous cover crop.

Study on two associated frut tree crops take up their N in comparison to a leguminous cover crop in an agroforestry system. Preliminar results showed the pueraria had the highest foliar N content followed by pupunha; cupuacu having less than the other two. One year after application, cupuacu took up more of the applied N in comparison to the total N uptake than pueraria and pupunha as seen from the high &15N values. The amount of 15N taken up in relation to dry matter equaled between the three species, since pueraria had a lot higher N contents. The other sampling dates showed the same tendency.bitstream/item/181065/1/ID-2600-2-45-52.pd