B Decays

The following sections are included:

• Foreword

• Contents

This article is an introduction and overview of B-physics. It discusses the Kobayashi-Maskawa generalization of the Cabibbo-GIM matrix for flavour mixing in the standard model of electroweak interactions, postulating the existence of the b and t quarks, the discovery of the ϒ family of resonances by the Columbia-Fermilab-Stony Brook collaboration in 1977, and subsequent confirmation at DORIS II and later at CESR. The bulk of the article is, however, devoted to the physics of B-production and decays. Experimental evidence, demonstrating that B-physics is in accord with the standard model is summarized. Selective applications of QCD to the inclusive and exclusive B-decays are described. The role of B-decays in determining the CKM matrix elements involving the b- and t-quarks is discussed at length and quantified. The interest in pursuing precision B-physics at the ongoing and future experimental facilities is outlined, in particular in rare B-decays and CP-violation.

The present knowledge of b quark decay and spectroscopy is largely based on data accumulated at e⁺e⁻ colliders, in particular machines operating near threshold for open beauty production. The exciting goal of discovering CP violation in B meson decay is stirring a great deal of interest in several laboratories. Proposals for “asymmetric” e⁺e⁻ “b-factories” have been submitted. In addition, hadron machines which will be active in the next decade and beyond are starting a thorough investigation of their potential for beauty physics. Past achievements and potentials of different approaches will be presented and different strategies aiming at the measurement of CP asymmetry will be compared.

Our present understanding of nonleptonic B decays is reviewed with special emphasis on two questions: (i) What are the benchmarks that have to be reached before we can claim to “understand” nonleptonic B decays at least semiquantitatively? (ii) The ultimate prize in B physics is the discovery and interpretation of CP violation in B decays; what special knowledge do we need about the decay mechanisms to exploit the discovery potential in this field to the fullest? A definitive treatment of these b decays based solely on first principle considerations still appears many years away. Therefore I stress the fruitful role that will be played by a feedback between more phenomenological oriented descriptions and the data. In such an undertaking it will be crucial to treat different classes of nonleptonic decays separately rather than lump them all together.

B meson decays into hadrons reflect the underlying weak mechanisms coupled with hadronization effects. In this chapter both inclusive decays rates and exclusive rates into specific final states are presented and compared with theoretical predictions.

New symmetries of the strong interactions appear in heavy quark physics. They can be used to predict many properties of hadrons containing a single heavy quark. Some of these predictions are expected to play an important role in determining the values of elements of the Cabibbo–Kobayashi–Maskawa matrix.

Experimental measurements of inclusive and exclusive semileptonic decays of B mesons are summarized and compared with theoretical models. Branching ratios for and are found to be (4.4 ± 0.3 ± 0.6)% and (1.6 ± 0.3 ± 0.2)%, respectively. There are indications of a substantial (32%) D** (or D^(*)π) component in semileptonic decays. Using a model which includes this component to fit the lepton momentum spectrum, the average semileptonic branching ratio of charged and neutral B mesons is found to be (11.2 ± 0.3 ± 0.4)%. From separate analyses of exclusive branching ratios for B⁻ and mesons the lifetime ratio, is found to be consistent with unity within an error of ≅ ± 25%. Using various techniques involving both inclusive and exclusive decays, an average value of the CKM matrix element |V_cb| is determined as 0.041 ± 0.002 ± 0.004. The value for the ratio |V_ub|/|V_cb| is ≈0.1.

The theory and practice of measuring B-hadron lifetimes, and extracting the Cabibbo-Kobayshi-Maskawa (CKM) matrix element V_cb are reviewed. Experiments from CESR, DORIS, PEP, PETRA, LEP, and Fermilab are included to form an up-to-date compilation of the experimental results. The generic lifetime measurement techniques, the just-now-emerging meson-specific vertexing methods, as well as indirect methods for measuring lifetime ratios, are discussed.

The following sections are included:

• Phenomenology of BB̄ Oscillations

• Measurement of Mixing in the B_d and B_s systems
  • Observation of B⁰B̄⁰ Mixing at the ϒ(4S)
  • B⁰B̄⁰ and B_sB̄_s mixing measurements on the Z⁰ and in the continuum

• Implications from the Observed BB̄ Mixing

• Possible Determination of |V_ts| from B_sB̄_s Mixing

The quark mixing matrix of Cabibbo, Kobayashi, and Maskawa, and methods for determining its elements, are described.

Theory of CP violation in B decays is reviewed. For CP asymmetries in B⁰ decays, the general formalism is given; the relations with the angles of the unitarity triangle are derived; the sensitivity to new physics is discussed and effects of specific models are described. For CP asymmetries in B^± decays, the possible mechanisms are described and the difficulties of theoretical estimation are discussed.

The observation of CP violation and the clean extraction of the fundamental CKM phases form the subject of this chapter. After reviewing the classic CP eigenmodes, where CP asymmetries are straightforwardly related to the CKM phases, more detailed methods are discussed. They allow the extraction of the phases from many additional modes, which are no longer CP eigenstates. The methods covered in this review are angular correlations, time-dependent studies of non-CP eigenmodes, isospin analyses, and detailed studies of B modes with a D°.

The theory of loop induced rare B decays is reviewed. Both electromagnetic penguin processes and gluon mediated penguin processes are discussed. After considering b → sγ and b → se⁺e⁻ decays, purely hadronic modes like B → Kφ are estimated. CP violation in charged B Decays is reviewed. The asymmetries for pure penguin processes are estimated first. A larger asymmetry can result in those modes where a tree diagram and a penguin diagram interfere, however these estimates are necessarily model dependent.

We review recent studies of the properties of B-mesons which use the Lattice Formulation of Quantum Chromodynamics. We focus on attempts to compute the decay constant f_B, which is the quantity which has been studied in greatest detail, but we also present a brief discussion of the B-parameter needed for studies of mixing and of some topics in spectroscopy.

In this Chapter we analyze the impact of rare flavour changing neutral current B decays and B⁰ − B̄⁰ oscillations on low energy supersymmetric theories and on models with two Higgs doublets. In particular, it is shown that an improvement of the present experimental limit on BR(b → s + γ) by a factor 2–3 may probe a region of the supersymmetric parameter space complementary to that explorable at LEP I and comparable to the projected LEP II limits.

The left-handedness of the b quark weak couplings has not yet been tested experimentally. We present an SU(2)_L × SU(2)_R × U(1) model with purely righthanded b-decay couplings. We show that the model is consistent with the quite severe existing experimental constraints from B decays, from mixing and from the neutral K mass difference. We point out a difficulty in distinguishing our scheme from the standard model in semileptonic B decays. The difficulty of testing the V − A structure of b quark couplings, without assuming V − A for the corresponding lepton current, is of quite general nature.