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The present contribution summarizes some results from the BaBar and Belle collaborations on the following categories of rare decays: Hadronic rare decays will not be treated in this contribution.

violation (), first detected in → decays in 1964 [], is accomodated in the Standard Model (SM) by a -violating phase in the CKM matrix, the matrix which describes the mixing of the quarks (under the weak interaction) []. From the unitarity constraints of the CKM matrix, we have + + = 0, the so-called Unitarity Triangle relation, represented in Fig. 1. is proportional to the area of the triangle and requires the angles and sides to be different from zero. The main goal of the BaBar experiment [] is to overconstrain the Unitarity Triangle parameters, measuring the sides and the angles directly from the data of and meson decays, in order to test the consistency of the SM.

Using our relativistic constituent quark model we present results on the exclusive nonleptonic and semileptonic decays of the -meson. The nonleptonic decays are studied in the framework of the factorization approximation. We calculate the branching ratios for a large set of exclusive nonleptonic and semileptonic decays of the meson and compare our results with the results of other models.

Non perturbative strong interaction effects make difficult a theoretical description of non leptonic weak decays of hadrons; so it is relevant the possibility to obtain predictive parametrizations of decay amplitudes. It is noticeable that the widths of a set of two-body transitions can be predicted using the symmetries of QCD and available information on decays [].

The first precise measurement of the oscillation frequency Δ with the CDFII experiment [] is summarized in this talk.

In the last decade, the flavor sector of the Standard Model, parametrized by the Cabibbo-Kobayashi-Maskawa (CKM) matrix [], has been studied and constrained with unprecedented precision thanks to the beautiful results obtained on Kaon CP violation experiments E731, KLOE and NA48, by the -factories KEKB and PEPII, by the charm factory CESR and by the experiments at Tevatron. The impact of these results on the experimental tests of the Standard Model is pictorially represented on the plane where the constraints on the Unitarity Triangle (UT) are displayed []. The Large Hadron Collider (LHC) in construction at CERN, is expected to deliver a large amount of events containing heavy flavors due to the high luminosity (10–10 cms) and high production cross sections (() ∼ 0.5mb).

We discuss the theoretical and experimental treatment of radiative corrections in hadronic decays. We present analytic expressions to describe the leading effects induced by both real and virtual (soft) photons in the generic process → (), where and are scalar or pseudoscalar particles. After discussing the procedures to be adopted in experimental analysis for a clear definition of the observables, we show how it is possible to explain the “ → π puzzle” in view of an (2) analysis taking into account QED corrections as a source of isospin breaking.

The analysis of the Unitarity Triangle (UT) and CP violation provides nowadays a unique opportunity to look for New Physics (NP) effects beyond the Standard Model (SM).

In the pursuit of improving our knowledge of short-distance physics from weak hadron decay (i. e. the CKM couplings in the Standard Model), reliable theoretical estimates of QCD non-perturbative effects are needed. For many decays from to physics (see Fig. 1), Lattice QCD remains the only tool to achieve this task. Once masses heavier than are integrated out, low-energy QCD effects are encoded into hadronic matrix elements of some local operator.

We introduce the supersymmetric flavour problem (Sect. 2) focusing on mixing processes in the quark sector (Sect. 3) and present updated plots of the bounds on squark mass matrices obtained in the mass insertion approximation (Sect. 4).