abstract

There now exist several theoretical technologies for treating weak decays of heavy flavour hadrons that are genuinely based on QCD without having to invoke a deus ex machina. I focus on one of those, which employs an expansion in inverse powers of the heavy quark mass. It has developed into a rather mature framework incorporating many subtle aspects of quantum field theory. I describe its methodology for treating fully integrated decay rates as well as differential distributions, in particular energy spectra; the importance of a new type of sum rules, the SV sum rules, is emphasised. First practical benefits from this theoretical technology are listed, like predictions on lifetime ratios and extracting the KM parameter \(|V(cb)|\) from inclusive and from exclusive semileptonic \(B\) decays. An outlook is given onto future developments concerning the determination of the properly defined mass of the heavy quark and its kinetic energy and a reliable extraction of \(|V(ub)/V(cb)|\). A few comments on charm decays are added.

abstract

Recent progress in the theoretical description of exclusive heavy flavour decays is reviewed. After a general discussion of heavy quark symmetries some applications are studied.

abstract

Recent developments in the uses of QCD spectral sum rules (QSSR) for heavy flavours are summarized and updated. QSSR results are compared with the existing data and with the ones from alternative approaches.

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Recent theoretical results on the production and decay of top quarks are presented. The implications of the new experimental results from the TEVATRON are briefly discussed. Predictions for the top quark decay rate and distributions are described, including the influence of QCD and electroweak radiative corrections. Top production at an \(e^+e^-\) collider is discussed with emphasis towards the threshold region. The polarization of top quarks in the threshold region is calculated with techniques based on Green’s functions for \(S\) and \(P\) waves.

abstract

I review the non-perturbative method, developed with Martinelli, for defining the higher dimensional operators which appear in the Heavy Quark Effective Theory (HQET), such that their matrix elements are free of renormalon singularities, and diverge at most logarithmically with the ultra-violet cut-off. Matrix elements of these operators can be computed numerically in lattice simulations of the HQET. The procedures are illustrated by presenting physical definitions of the binding energy (\(\bar {\mit \Lambda }\)) and of the kinetic energy (\(-\lambda _1/2m_Q\)) of the heavy quark in a hadron. This allows for a definition of a “subtracted pole mass”, whose inverse can be used as the expansion parameter in applications of the HQET. I also present some numerical results for the binding energy (\(\bar {\mit \Lambda }=190 \pm 30\) MeV), and the kinetic energy (\(|\lambda _1|=|\langle B| \bar h \vec D^2h|B\rangle |/(2M_B) \lt 1.0\) GeV\(^2\)), obtained with Crisafulli, Gimenez and Martinelli.

abstract

We discuss several aspects of rare decays and CP violation in the standard model including the impact of the recent top quark discovery. In particular we review the present status of next-to-leading QCD calculations in this field stressing their importance in the determination of the parameters in the Cabibbo–Kobayashi–Maskawa matrix. We emphasise that the definitive tests of the standard model picture of rare decays and CP violation will come through a simultaneous study of CP asymmetries in \(B^0_{d,s}\) decays, the rare decays \(K^+ \to \pi ^+ \nu \bar \nu \) and \(K_L \to \pi ^0\nu \bar \nu \), and \((B^0_d - \bar B^0_d)/(B^0_s - \bar B^0_s)\).

abstract

Polarization studies for heavy quarks can lead to important tests of the Standard Model. Top quark pair production in \(e^+e^-\) annihilation is considered near energy threshold. It is shown that for longitudinally polarized electrons the produced top quarks and antiquarks are highly polarized. Dynamical effects originating from strong interactions in the \(t-\bar t\) system can be calculated using Green function method. Energy-angular distributions of leptons in semileptonic decays of polarized heavy quarks are sensitive to both the polarization of the decaying quark and V-A structure of the weak charged current. Some applications to \(b\) quark physics at the \(Z^0\) resonance are briefly reviewed.

abstract

Theoretical predictions and experimental aspects of the \({\mit \Lambda }^0_b\) baryon polarization measurement at LEP are briefly presented. In the typical LEP process \(e^+e^- \to Z^0 \to f \bar f\) down-type quarks are born with a high (\(\approx -0.94\)) longitudinal polarization. In case of a heavy \(b\) quark its almost full transfer to the ground baryonic state \({\mit \Lambda }^0_b\) makes an important prediction of the HQET (Heavy Quark Effective Theory). At LEP the \({\mit \Lambda }^0_b\) polarization is experimentally accessible in its semileptonic decay mode through the lepton energy spectra. Moreover, since neutrino is predicted to be the decay product most sensitive to polarization its energy reconstruction is essential for the described method. First result on \({\mit \Lambda }^0_b\) polarization coming from the ALEPH collaboration is presented.

abstract

A method to measure the structure of the weak charged-current in semileptonic \(b\)-hadron decays using the energy spectrum of the neutrinos is presented. This method allows to distinguish experimentally between the V\(-\)A\(\times \)V\(-\)A, V\(\times \)V\(-\)A and V\(+\)A\(\times \)V\(-\)A form of the charged current interaction. First result of such a measurement have now been obtained by the L3 collaboration, a brief summary of their results is also given. Their results allow to exclude the exotic V\(+\)A structure in \(b\)-decays.

abstract

We study the properties of nonrelativistic models of \(b \bar b\) quarkonia. We want to check if the present data can be reproduced by such a model within the experimental errors. A general formula including as special cases many existing models is introduced. The properties of a family of models are investigated. We find a new potential in the form of \(a \sqrt {r}-b+A\), which is agreed with data.

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Using the (modified) MIT bag model we have calculated formfactors and decay widths for pseudoscalar–pseudoscalar and pseudoscalar–vector semileptonic decays of heavy mesons. A comparison with the experimental results and predictions of other models is also given.

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A method of computing two-loop fermionic contributions to the width of a heavy quark is described. An analytical formula for this effect in the limit of mass of the quark much larger than the decay products is obtained for the first time. The result confirms previous numerical studies.

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Quark-level symmetry properties of the pole model of nonleptonic bar- yon decays are discussed. The obtained expressions generalize current algebra prescriptions to the flavour-symmetry-breaking case. This generalization permits a natural explanation of a several-decade-old puzzle in nonleptonic hyperon decays and provides an understanding of differences between various contemporary models of nonleptonic decays of charmed baryons.

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Decays of two heavy particles, produced in cosmic ray interactions, are presented. These particles decay into one charged particle and four photons each. The photons converted into electron pairs very close to the decay vertex. Attempts to explain this decay topology with known particle decays are presented. Unless both events represent a \(b \to u\) transition, which is statistically unlikely, then other known decay modes for charmed or bottom particles do not account satisfactorily for these observations. This could indicate, possibly, a new decay channel.