The Lorentzian distance formula in noncommutative geometry

For almost twenty years, a search for a Lorentzian version of the well-known Connes' distance formula has been undertaken. Several authors have contributed to this search, providing important milestones, and the time has now come to put those elements together in order to get a valid and functional formula. This paper presents a historical review of the construction and the proof of a Lorentzian distance formula suitable for noncommutative geometry.Comment: 16 pages, final form, few references adde

A quantum theoretical explanation for probability judgment errors

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning

Heavy-heavy form factors and generalized factorization

We reanalyze B -> D pi and B -> K J/psi data to extract a set of parameters which give the relevant hadronic matrix elements in terms of factorized amplitudes. Various sources of theoretical uncertainties are studied, in particular those depending on the model adopted for the form factors. We find that the fit to the B -> D pi branching ratios substantially depends on the model describing the Isgur-Wise function and on the value of its slope. This dependence can be reduced by substituting the BR(B -> D pi) with suitable ratios of non-leptonic to differential semileptonic BRs. In this way, we obtain a model-independent determination of these parameters. Using these results, the B -> D form factors at q^2=M_pi^2 can be extracted from a fit of the BR(B -> D pi). The comparison between the form factors obtained in this way and the corresponding measurements in semileptonic decays can be used as a test of (generalized) factorization free from the uncertainties due to heavy-heavy form factor modeling. Finally, we present predictions for yet-unmeasured D pi and D K branching ratios and extract f_{D_s} and f_{D_s^*} from B -> DD_s decays. We find f_{D_s} = 270 +- 45 MeV and f_{D_s^*}=260 +- 40 MeV, in good agreement with recent measurements and lattice calculations.Comment: 20 pages, 16 ps/eps files, uses epsfig.sty; exp. numbers update

Penguin Contractions and Factorization in B -> K pi Decays

We study Lambda_{QCD}/m_B corrections to factorization in B -> K pi decays. First, we analyze these decay channels within factorization, showing that, irrespectively of the value of gamma, it is not possible to reproduce the experimental data. Then, we discuss Lambda_{QCD}/m_B corrections to these processes, and argue that there is a class of doubly Cabibbo enhanced non-factorizable contributions, usually called charming penguins, that cannot be neglected. Including these corrections, we obtain an excellent agreement with experimental data. Furthermore, contrary to what is obtained with factorization, we predict sizable rate asymmetries in B^\pm -> K^\pm \pi^0 and B -> K^\pm pi^\mp.Comment: 4 pages, 3 figures. Talk given by L. Silvestrini at BCP4, Ise-Shima, Japan, 18-23 Feb 200

Charming Penguins in B decays

Full expressions of the $B^0_d \to \pi^+ \pi^-$ and $B^0_d \to \pi^0 \pi^0$ amplitudes, given in terms of matrix elements of operators of the effective weak Hamiltonian, are used to study the dependence of the relevant branching ratios on the different contributions. The uncertainty in the extraction of the weak phase $\alpha$ from the measurement of the time-dependent asymmetry in $B^0_d \to \pi^+ \pi^-$ decays is also analyzed. We find that, among several effects which may enhance the $B^0_d \to \pi^0 \pi^0$ branching ratio, the most important is due to ``charming penguin" diagrams that have never been studied before. These diagrams easily increase $BR(B^0_d \to \pi^0 \pi^0)$ up to a value of $1-3 \times 10^{-6}$. The same effect produces, however, a large error in the extraction of $\alpha$ from the measurement of the $B^0_d \to \pi^+ \pi^-$ time-dependent asymmetry. We show that it is possible to determine charming-penguin amplitudes from the experimental measurement of many decay rates. Their effect is impressive in $B^+ \to \pi^+ K^0$ and $B^0_d \to K^+ \pi^-$ decays, where charming-penguin contributions easily give values of $BR(B^+ \to \pi^+ K^0)$ and $BR(B^0_d \to K^+ \pi^-)$ of about $1 \times 10^{-5}$. Among other possibilities, we also suggest to use $B^0_d \to K^0 \bar K^0$, the BR of which can be as large as $2-3 \times 10^{-6}$, to determine the size of charming-penguin amplitudes.Comment: LaTeX, 28 pages, 8 figure