CKM Matrix: Status and New Developments

An analysis of the CKM matrix parameters within the {\it R}fit approach is presented using updated input values with special emphasis on the recent $\sin{2\beta}$ measurements from BABAR and Belle. The QCD Factorisation Approach describing $B \to \pi\pi,K\pi$ decays has been implemented in the software package CKMfitter. Fits using branching ratios and CP asymmetries are discussed.Comment: 5 pages, 6 postscript figures, contribution to the proceedings of the 9th International Symposium on Heavy Flavour Physics, September 2001, Pasadena, US

A New Approach to a Global Fit of the CKM Matrix

We report on a global CKM matrix analysis taking into account most recent experimental and theoretical results. The statistical framework (Rfit) developed in this paper advocates formal frequentist statistics. Other approaches, such as Bayesian statistics or the 95% CL scan method are also discussed. We emphasize the distinction of a model testing and a model dependent, metrological phase in which the various parameters of the theory are determined. Measurements and theoretical parameters entering the global fit are thoroughly discussed, in particular with respect to their theoretical uncertainties. Graphical results for confidence levels are drawn in various one and two-dimensional parameter spaces. Numerical results are provided for all relevant CKM parameterizations, the CKM elements and theoretical input parameters. Predictions for branching ratios of rare K and B meson decays are obtained. A simple, predictive SUSY extension of the Standard Model is discussed.Comment: 66 pages, added figures, corrected typos, no quantitative change

Probing New Physics using top quark polarization in the e+e- -> t \bar{t} process at future Linear Colliders

We investigate the sensitivity to new physics of the process e+e- -> t bar{t} when the top polarization is analyzed using leptonic final states e+e- -> t \bar{t} -> l+l- b \bar{b} nu_l \bar{nu}_l. We first show that the kinematical reconstruction of the complete kinematics is experimentally tractable for this process. Then we apply the matrix element method to study the sensitivity to the Vt\bar{t} coupling (V being a vector gauge boson), at the tree level and in the narrow width approximation. Assuming the ILC baseline configuration, sqrt{S}=500 GeV, and a luminosity of 500 fb^{-1}, we conclude that this optimal analysis allows to determine simultaneously the ten form factors that parameterize the Vt\bar{t} coupling, below the percent level. We also discuss the effects of the next leading order (NLO) electroweak corrections using the GRACE program with polarized beams. It is found that the NLO corrections to different beam polarization lead to significantly different patterns of contributions.Comment: 14 pages, 4 figures, Proceedings for the TYL-FJPPL workshops on "Top Physics at ILC

Reply to: ''Improved Determination of the CKM Angle alpha from B -> pipi decays''

In reply to hep-ph/0701204 we demonstrate why the arguments made therein do not address the criticism exposed in hep-ph/0607246 on the fundamental shortcomings of the Bayesian approach when it comes to the extraction of parameters of Nature from experimental data. As for the isospin analysis and the CKM angle alpha it is shown that the use of uniform priors for the observed quantities in the Explicit Solution parametrization is equivalent to a frequentist construction resulting from a change of variables, and thus relies neither on prior PDFs nor on Bayes' theorem. This procedure provides in this particular case results that are similar to the Confidence Level approach, but the treatment of mirror solutions remains incorrect and it is far from being general. In a second part it is shown that important differences subsist between the Bayesian and frequentist approaches, when following the proposal of hep-ph/0701204 and inserting additional information on the hadronic amplitudes beyond isospin invariance. In particular the frequentist result preserves the exact degeneracy that is expected from the remaining symmetries of the problem while the Bayesian procedure does not. Moreover, in the Bayesian approach reducing inference to the 68% or 95% credible interval is a misconception of the meaning of the posterior PDF, which in turn implies that the significant dependence of the latter to the chosen parametrization cannot be viewed as a minor effect, contrary to the claim in hep-ph/0701204.Comment: 5 pages, 1 figure. Fig. 1 corrected (wrong file

Bayesian Statistics at Work: the Troublesome Extraction of the CKM Phase alpha

In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the isospin analysis of B-->PP (P = pi or rho) decays in heavy-flavor physics is chosen to illustrate the effect of the naive "objective" choice of flat priors in a multi-dimensional parameter space in presence of mirror solutions. It is demonstrated that the posterior distribution for the parameter of interest, the phase alpha, strongly depends on the choice of the parameterization in which the priors are uniform, and on the validity range in which the (un-normalizable) priors are truncated. We prove that the most probable values found by the Bayesian treatment do not coincide with the explicit analytical solution, in contrast to the frequentist approach. It is also shown in the appendix that the alpha-->0 limit cannot be consistently treated in the Bayesian paradigm, because the latter violates the physical symmetries of the problem.Comment: 17 pages, 10 figure

Isospin constraints from/on B->pipi

The Standard Model constraints on alpha which can be derived from the B-> pipi decays are revisited in some depth. As experimental inputs, the three branching ratios, the two CP parameters Spipi and Cpipi and/or the value of alpha as determined by the global CKM fit are used. The constraints discussed here are model independent in the sense that they rely only on Isospin symmetry, following the Gronau-London proposal. A new bound on B00 and the function C00(B00) are introduced. The Grossman-Quinn bound is rediscussed. A close form expression is given for alpha as a function of the measurements. Various scenarii for the future of the isospin analysis are explored. To probe the Standard Model the (B00,C00) plane is introduced.Comment: 25 pages, 8 figures, Submitted to Eur. Phys. J.

Mass Corrections to the Tau Decay Rate

In this note radiative corrections to the total hadronic decay rate of the $\tau$-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate ration $R_{\tau}$ to the order ${\cal O}(\alpha_s^2 m^2)$ and find that they contribute appreciably to the Cabbibo supressed decay modes of the $\tau$-lepton. We also discuss corrections of mass dimension D=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.Comment: 13 pages, LaTeX, no figures. This version fixes a typo in eq. (25) of the original paper (Z. Phys. C59 (1993) 525) and an errror in a numerical integration procedure which has resulted to a significant increase of the O(\alpha_s^2) coefficient in eq. (27). As a consequence also some tables in Section 4 have been modifie