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

A model for atomic and molecular interstellar gas: The Meudon PDR code

We present the revised ``Meudon'' model of Photon Dominated Region (PDR code), presently available on the web under the Gnu Public Licence at: http://aristote.obspm.fr/MIS. General organisation of the code is described down to a level that should allow most observers to use it as an interpretation tool with minimal help from our part. Two grids of models, one for low excitation diffuse clouds and one for dense highly illuminated clouds, are discussed, and some new results on PDR modelisation highlighted.Comment: accepted in ApJ sup

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

The effect of an imaginary part of the Schwinger-Dyson equation at finite temperature and density

We examined the effect of an imaginary part of the ladder approximation Schwinger-Dyson equation. We show the imaginary part enhances the effect of the first order transition, and affects a tricritical point. In particular, a chemical potential at a tricritical point is moved about 200(MeV). Thus, one should not ignore the imaginary part. On the other hand, since an imaginary part is small away from a tricritical point, one should be able to ignore an imaginary part. In addition, we also examined the contribution of the wave function renormalization constant.Comment: 12 pages, 14 figure

Galaxy Selection and Clustering and Lyman alpha Absorber Identification

The effects of galaxy selection on our ability to constrain the nature of weak Ly\alpha absorbers at low redshift are explored. Current observations indicate the existence of a population of gas-rich, low surface brightness (LSB) galaxies, and these galaxies may have large cross sections for Ly\alpha absorption. Absorption arising in LSB galaxies may be attributed to HSB galaxies at larger impact parameters from quasar lines of sight, so that the observed absorption cross sections of galaxies may seem unreasonably large. Thus it is not possible to rule out scenarios where LSB galaxies make substantial contributions to Ly\alpha absorption using direct observations. Less direct tests, where observational selection effects are taken into account using simulations, should make it possible to determine the nature of Ly\alpha absorbers by observing a sample of ~100 galaxies around quasar lines of sight with well-defined selection criteria. Such tests, which involve comparing simulated and observed plots of the unidentified absorber fractions and absorbing galaxy fractions versus impact parameter, can distinguish between scenarios where absorbers arise in particular galaxies and those where absorbers arise in gas tracing the large scale galaxy distribution. Care must be taken to minimize selection effects even when using these tests. Results from such tests are likely to depend upon the limiting neutral hydrogen column density. While not enough data are currently available to make a strong conclusion about the nature of moderately weak absorbers, evidence is seen that such absorbers arise in gas that is around or between galaxies that are often not detected in surveys.Comment: 15 pages, 10 figures, accepted to the Astrophysical Journa