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

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 ρ and η, by means of a global CKM fit. The fit is dominated by the precision measurement of sin 2β by the B factories. A detailed numerical and graphical study of the impact of the results is presented. We propose to include sin 2α from the recent measurement of the time-dependent CP -violating asymmetries in B 0 → ρ + ρ − , using isospin relations to discriminate the penguin contribution. The constraint from ε ′ /ε is discussed. We study the impact from the branching fraction measurement of the rare kaon decay K + → π + νν, and give an outlook into the reach of a future measurement of K 0 L → π 0 νν. The B system is investigated in detail. We display the constraint on 2β + γ and γ from B 0 → D ( * )± π ∓ and B + → D ( * )0 K + decays, respectively. A significant part of this paper is dedicated to the understanding of the dynamics of B decays into ππ, Kπ, ρπ, ρρ and modes related to these by flavor symmetry. Various phenomenological approaches and theoretical frameworks are discussed. We find a remarkable agreement of the ππ and Kπ 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 ππ and Kπ 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 → Kπ 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 B 0 mixing and B decays, namely in the b → d and b → 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 ∆m s from the experimental information on B 0 s B 0 s 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.

Direct and indirect constraints on CP-violating Higgs-quark and Higgs-gluon interactions

“…(b) Assuming that the matrix elements have a flat distribution in a certain range corresponding to existing calculations: this is the range-fit method used in ref. [87] in the context of fits to the elements of the Cabibbo-Kobayashi-Maskawa matrix. The resulting bounds account for the theoretical uncertainties in the safest possible way (perhaps over-conservative, but realistic).…”

“…This method corresponds to the Range-fit (Rfit) procedure defined in ref. [87]. It always gives the weakest constraint of the three methods discussed in this work as it allows for cancellations between different contributions.…”

Framework for maximum likelihood analysis of neutronβdecay observables to resolve the limits of theV−Alaw

“…Inspired by the pioneering global fits of the CKM matrix developed by the CKMfitter Group [1,2] and the UTFit Collaboration [3][4][5][6][7] for the interpretation of flavorphysics results from the B factories and the Tevatron, we outline the prospects for the elucidation of physics beyond the standard model (BSM) via a global fit of neutron β decay observables, including the lifetime and the energy-dependence of the angular correlation coefficients. Our global fit, which we term nFitter, employs a maximum likelihood statistical framework which accounts for both experimental and theoretical uncertainties, with the latter arising primarily from the poorly known weak hadronic second-class currents.…”

“…To realize this we need only assume that new physics appears at an energy scale Λ in excess of the scale v, crudely that of the W and Z masses. This allows the construction of an effective Lagrangian in terms of operators of mass dimension d with d > 4 [36], where the nonobservation of non-SM invariant operators in flavor physics [2,7,37], allows us to impose SM electroweak gauge invariance in its construction. At leading power in v/Λ, there are then precisely ten dimension-six operators describing the semileptonic decay of the d quark.…”

“…We then describe the maximum likelihood approach to our global fit in Section IV, where we discuss the construction of our likelihood function, as well as the inclusion of experimental and theoretical uncertainties. We illustrate the prospects of our global fit with a few numerical examples employing the frequentist, or specifically RFit [1,2], statistical procedure, reserving the use of alternative statistical procedures for later work. We then show examples of the results from nFitter fits to Monte Carlo-generated pseudodata in Section V under various scenarios, and we quantify via these examples the statistical impact that future improvements in the precision of neutron β decay observables should have on the assessment of the validity of the SM.…”