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We present an up-to-date profile of the Cabibbo-Kobayashi-Maskawa matrix with emphasis on the interpretation of recent CP -violation results from the B factories. For this purpose, we review all relevant experimental and theoretical inputs from the contributing domains of electroweak interaction. We give the "standard" determination of the apex of the Unitarity Triangle, namely the Wolfenstein parameters ρ and η, by means of a global CKM fit. The fit is dominated by the precision measurement of sin 2β by the B factories. A detailed numerical and graphical study of the impact of the results is presented. We propose to include sin 2α from the recent measurement of the time-dependent CP -violating asymmetries in B 0 → ρ + ρ − , using isospin relations to discriminate the penguin contribution. The constraint from ε ′ /ε is discussed. We study the impact from the branching fraction measurement of the rare kaon decay K + → π + νν, and give an outlook into the reach of a future measurement of K 0 L → π 0 νν. The B system is investigated in detail. We display the constraint on 2β + γ and γ from B 0 → D ( * )± π ∓ and B + → D ( * )0 K + decays, respectively. A significant part of this paper is dedicated to the understanding of the dynamics of B decays into ππ, Kπ, ρπ, ρρ and modes related to these by flavor symmetry. Various phenomenological approaches and theoretical frameworks are discussed. We find a remarkable agreement of the ππ and Kπ data with the other constraints in the unitarity plane when the hadronic matrix elements are calculated within QCD Factorization, where we apply a conservative treatment of the theoretical uncertainties. A global fit of QCD Factorization to all ππ and Kπ data leads to precise predictions of the related observables. However sizable phenomenological power corrections are preferred. Using an isospin-based phenomenological parameterization, we analyze separately the B → Kπ decays, and the impact of electroweak penguins in response to recent discussions. We find that the present data are not sufficiently precise to constrain either electroweak parameters or hadronic amplitude ratios. We do not observe any unambiguous sign of New Physics, whereas there is some evidence for potentially large non-perturbative rescattering effects. Finally we use a model-independent description of a large class of New Physics effects in both B 0 B 0 mixing and B decays, namely in the b → d and b → s gluonic penguin amplitudes, to perform a new numerical analysis. Significant non-standard corrections cannot be excluded yet, however Standard Model solutions are favored in most cases. In the appendix to this paper we propose a frequentist method to extract a confidence level on ∆m s from the experimental information on B 0 s B 0 s oscillation. In addition we describe a novel approach to combine potentially inconsistent measurements. All results reported in this paper have been obtained with the numerical analysis package CKMfitter, featuring the frequentist statistical approach Rfit.

We argue that the Large Energy Effective Theory (LEET), originally proposed by Dugan and Grinstein, is applicable to exclusive semileptonic, radiative and rare heavy-to-light transitions in the region where the energy release E is large compared to the strong interaction scale and to the mass of the final hadron, i.e. for q 2 not close to the zero-recoil point. We derive the Effective Lagrangian from the QCD one, and show that in the limit of heavy mass M for the initial hadron and large energy E for the final one, the heavy and light quark fields behave as two-component spinors. Neglecting QCD short-distance corrections, this implies that there are only three form factors describing all the pseudoscalar to pseudoscalar or vector weak current matrix elements. We argue that the dependence of these form factors with respect to M and E should be factorizable, the M -dependence ( √ M ) being derived from the usual heavy quark expansion while the E-dependence is controlled by the behaviour of the light-cone distribution amplitude near the end-point u ∼ 1. The usual expectation of the ∼ (1 − u) behaviour leads to a 1/E 2 scaling law, that is a dipole form in q 2 . We also show explicitly that in the appropriate limit, the Light-Cone Sum Rule method satisfies our general relations as well as the scaling laws in M and E of the form factors, and obtain very compact and simple expressions for the latter. Finally we note that this formalism gives theoretical support to the quark model-inspired methods existing in the literature.