CP violation and the CKM matrix: assessing the impact of the asymmetric B factories

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Abstract.

We present an up-to-date profile of the Cabibbo-Kobayashi-Maskawa matrix with emphasis on the interpretation of recent CP-violation results from the B factories. For this purpose, we review all relevant experimental and theoretical inputs from the contributing domains of electroweak interaction. We give the “standard” determination of the apex of the Unitarity Triangle, namely the Wolfenstein parameters \(\overline\rho\) and \(\overline\eta\) , by means of a global CKM fit. The fit is dominated by the precision measurement of \(\sin 2 \beta\) by the B factories. A detailed numerical and graphical study of the impact of the results is presented. We propose to include \(\sin 2\alpha\) from the recent measurement of the time-dependent CP-violating asymmetries in \(B^0\to\rho^ + \rho^-\) , using isospin relations to discriminate the penguin contribution. The constraint from \(\varepsilon^\prime/\varepsilon\) is discussed. We study the impact from the branching fraction measurement of the rare kaon decay \(K^ + \to\pi^ + \nu\overline\nu\) , and give an outlook into the reach of a future measurement of \(K^0_L\to\pi^0\nu\overline\nu\) . The B system is investigated in detail. We display the constraint on \(2\beta + \gamma\) and \(\gamma\) from \(B^0\to D^{(*)\pm}\pi^\mp\) and \(B^ + \to D^{(*)0}K^ + \) decays, respectively. A significant part of this paper is dedicated to the understanding of the dynamics of B decays into \(\pi\pi\) , \(K\pi\) , \(\rho\pi\) , \(\rho\rho\) and modes related to these by flavor symmetry. Various phenomenological approaches and theoretical frameworks are discussed. We find a remarkable agreement of the \(\pi\pi\) and \(K\pi\) data with the other constraints in the unitarity plane when the hadronic matrix elements are calculated within QCD Factorization, where we apply a conservative treatment of the theoretical uncertainties. A global fit of QCD Factorization to all \(\pi\pi\) and \(K\pi\) data leads to precise predictions of the related observables. However sizable phenomenological power corrections are preferred. Using an isospin-based phenomenological parameterization, we analyze separately the \(B\to K\pi\) decays, and the impact of electroweak penguins in response to recent discussions. We find that the present data are not sufficiently precise to constrain either electroweak parameters or hadronic amplitude ratios. We do not observe any unambiguous sign of New Physics, whereas there is some evidence for potentially large non-perturbative rescattering effects. Finally we use a model-independent description of a large class of New Physics effects in both \(B^0\overline B^0\) mixing and B decays, namely in the \(b\to d\) and \(b\to s\) gluonic penguin amplitudes, to perform a new numerical analysis. Significant non-standard corrections cannot be excluded yet, however Standard Model solutions are favored in most cases. In the appendix to this paper we propose a frequentist method to extract a confidence level on \(\Delta m_s\) from the experimental information on \(B^0_s \overline B_s^0\) oscillation. In addition we describe a novel approach to combine potentially inconsistent measurements. All results reported in this paper have been obtained with the numerical analysis package CKMfitter, featuring the frequentist statistical approach Rfit.

Received: 13 July 2004, Published online: 12 April 2005