Introduction

The ``2000 CKM-triangle analysis'' by Ciuchini et al. [1] is in my opinion the most accurate way to use consistently all pieces of experimental and theoretical information relevant to infer, within the framework of the Standard Model (SM), the parameters of the unitarity triangle. The basic idea is that beliefs (i.e. probabilities) on the value of each input quantity are propagated into beliefs about the output quantities, namely $\bar {\rho}$ and $\bar{\eta}$, and SM related quantities. The propagation is performed using the rules of logic applied to uncertain events, i.e. probability theory, without arbitrariness or ``prescriptions''. All hypotheses are clearly stated and the influence on the results of reasonable variations of models and model parameters have been checked and found irrelevant (see Ref. [1] for details). Such a propagation of uncertainty, done by responsible people on physics quantities they feel knowledgeable about should not be confused with the kind of mathematical games described in Appendix A of Ref. [2]. In other words, when we say that the value of a quantity has 50% probability to lie in a certain region, given well defined hypotheses and with reasonably large flexibility of them, means that we are equally confident that it could be there or elsewhere. This is in contrast to ``95% C.L. results'' which should not be interpreted as 95% confidence on a certain statement (see e.g. Section 5.2 of Ref. [3], and the Conclusion of Ref. [4] for an independent account).

The motivation of this note is to illustrate a simplified way to perform the analysis of Ref. [1]. In fact, the Monte Carlo integration used there could seem a bit mysterious. As well known, approximations usually loose accuracy, but often help in gaining awareness. And this is exactly the spirit of this note. Therefore, I have little to add here to phenomenology, experimental data and inferential framework of the analysis, and I point to Ref. [1] and references therein.

The note is organized in the following way. In Section 2 the relations between CKM parameters are schematically recalled. In the following sections the reweighting effect on the points of the $\bar {\rho}$-$\bar{\eta}$ plane due to all pieces of information, is shown in detail. The final result is then compared to that of Ref. [1].