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

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

Analysing powers for the reaction n⃗p→ppπ−\vec{\rm n} {\rm p} \to {\rm p} {\rm p} \pi^{-} and for np elastic scattering from 270 to 570 MeV

The analysing power of the reaction ${\rm n}{\rm p} \to {\rm p}{\rm p} \pi^{-}$ for neutron energies between threshold and 570 MeV has been determined using a transversely polarised neutron beam at PSI. The reaction has been studied in a kinematically complete measurement using a time-of-flight spectrometer with large acceptance. Analysing powers have been determined as a function of the c.m. pion angle in different regions of the proton-proton invariant mass. They are compared to other data from the reactions ${\rm n}{\rm p} \to {\rm p}{\rm p} \pi^{-}$ and ${{\rm p}{\rm p} \to {\rm p}{\rm p} \pi^{0}}$. The np elastic scattering analysing power was determined as a by-product of the measurements.Comment: 12 pages, 6 figures, subitted to EPJ-

The reaction np→ppπ−{n} {p} \to {p} {p} \pi^{-} from threshold up to 570 MeV

The reaction ${n} {p} \to {p} {p} \pi^{-}$ has been studied in a kinematically complete measurement with a large acceptance time-of-flight spectrometer for incident neutron energies between threshold and 570 MeV. The proton-proton invariant mass distributions show a strong enhancement due to the pp($^{1}{S}_{0}$) final state interaction. A large anisotropy was found in the pion angular distributions in contrast to the reaction ${p}{p} \to {p}{p} \pi^{0}$. At small energies, a large forward/backward asymmetry has been observed. From the measured integrated cross section $\sigma({n}{p} \to {\rm p}{p} \pi^{-})$, the isoscalar cross section $\sigma_{01}$ has been extracted. Its energy dependence indicates that mainly partial waves with Sp final states contribute. Note: Due to a coding error, the differential cross sections ${d \sigma}/{d M_{pp}}$ as shown in Fig. 9 are too small by a factor of two, and inn Table 3 the differential cross sections ${d \sigma}/{d \Omega_{\pi}^{*}}$ are too large by a factor of $10/2\pi$. The integrated cross sections and all conclusions remain unchanged. A corresponding erratum has been submitted and accepted by European Physics Journal.Comment: 18 pages, 16 figure

Measurement of sin2beta in tree-dominated B0-decays and ambiguity removal

The most recent results from the B-factories on the time-dependent CP asymmetries measured in B0-decays mediated by b --> c c(bar) s quark-transitions are reviewed. The Standard Model interpretation of the results in terms of the parameter sin2beta leads to a four-fold ambiguity on the unitarity triangle beta which can be reduced to a two-fold ambiguity by measuring the sign of the parameter cos2beta. The results on cos2beta obtained so far are reviewed.Comment: 6 pages, 3 postscript figues, contributed to the Proceedings of Beauty200

Predictions of selected flavour observables within the Standard Model

This letter gathers a selection of Standard Model predictions issued from the metrology of the CKM parameters performed by the CKMfitter group. The selection includes purely leptonic decays of neutral and charged B, D and K mesons. In the light of the expected measurements from the LHCb experiment, a special attention is given to the radiative decay modes of B mesons as well as to the B-meson mixing observables, in particular the semileptonic charge asymmetries a^d,s_SL which have been recently investigated by the D0 experiment at Tevatron. Constraints arising from rare kaon decays are addressed, in light of both current results and expected performances of future rare kaon experiments. All results have been obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using Rfit to handle theoretical uncertainties.Comment: 8 pages, 1 figure, 2 tables. Typos corrected and discussion of agreement between SM and data update

Master equation approach to friction at the mesoscale

At the mesoscale friction occurs through the breaking and formation of local contacts. This is often described by the earthquake-like model which requires numerical studies. We show that this phenomenon can also be described by a master equation, which can be solved analytically in some cases and provides an efficient numerical solution for more general cases. We examine the effect of temperature and aging of the contacts and discuss the statistical properties of the contacts for different situations of friction and their implications, particularly regarding the existence of stick-slip.Comment: To be published in Physical Review