Abstract:
Using methods of effective field theory, a systematic analysis of the fragmentation functions D_{a/H}(x,m_Q) of a hadron H containing a heavy quark Q is performed (with a=Q,Q_bar,q,q_bar,g). By integrating out pair production of virtual and real heavy quarks, the fragmentation functions are matched onto a single nonperturbative function describing the fragmentation of the heavy quark Q into the hadron H in "partially quenched" QCD. All calculable, short-distance dependence on x is extracted in this step. For x->1, the remaining fragmentation function can be matched further onto a universal function defined in heavy-quark effective theory in order to factor off its residual dependence on the heavy-quark mass. By solving the evolution equation in the effective theory analytically, large logarithms of the ratio mu/m_Q are resummed to all orders in perturbation theory. Connections with existing approaches to heavy-quark fragmentation are discussed. In particular, it is shown that previous attempts to extract log^n(1-x) terms from the fragmentation function D_{Q/H}(x,m_Q) are incompatible with a proper separation of short- and long-distance effects.

Abstract:
Using methods of effective field theory, we show that after resummation of Sudakov logarithms the spectral densities of interacting quark and gluon fields in ordinary quantum field theories such as QCD are virtually indistinguishable from those of "unparticles" of a hypothetical conformal sector coupled to the Standard Model, recently studied by Georgi. Unparticles are therefore less exotic that originally thought. Models in which a hidden sector weakly coupled to the Standard Model contains a QCD-like theory, which confines at some scale much below the characteristic energy of a given process, can give rise to signatures closely resembling those from unparticles.

Abstract:
We present a QCD-based approach to the endpoint region of the lepton spectrum in $\bar B\to X_u\,\ell\,\bar\nu$ decays. We introduce a genuinely nonperturbative form factor, the shape function, which describes the fall-off of the spectrum close to the endpoint. The moments of this function are related to forward scattering matrix elements of local, higher-dimension operators. We find that nonperturbative effects are dominant over a finite region in the lepton energy spectrum, the width of which is related to the kinetic energy of the $b$-quark inside the $B$ meson. Applications of our method to the extraction of fundamental standard model parameters, among them $V_{ub}$, are discussed in detail.

Abstract:
Recently, we have developed a formalism to evaluate QCD loop diagrams with a single virtual gluon using a running coupling constant at the vertices. This corresponds to an all-order resummation of certain terms (the so-called renormalon chains) in a perturbative series and provides a generalization of the scale-setting prescription of Brodsky, Lepage and Mackenzie. In its original form, the method is applicable to Green functions without external gluons and to euclidean correlation functions. Here we generalize the approach to the case of cross sections and inclusive decay rates, which receive both virtual and real gluon corrections. We encounter nonperturbative ambiguities in the resummation of the perturbative series, which may hinder the construction of the operator product expansion in the physical region. The origin of these ambiguities and their relation to renormalon singularities in the Borel plane is investigated by introducing an explicit infrared cutoff. The ratios $R_{e^+ e^-}$ and $R_\tau$ are discussed in detail.

Abstract:
The formalism of the heavy quark effective theory is used to derive the field-theory analog of the virial theorem, which relates the matrix element of the kinetic energy of a heavy quark inside a hadron to a matrix element of the gluon field strength tensor. The existing QCD sum rule calculations of the kinetic energy are not consistent with this theorem.

Abstract:
Using a combination of the operator product and heavy quark expansions, we resum the leading nonperturbative contributions to the inclusive photon spectrum in $B\to X_s\,\gamma$ decays. The shape of the spectrum is determined by a universal structure function, which describes the distribution of the light-cone momentum of the $b$-quark inside the $B$-meson. The moments of this function are proportional to forward matrix elements of higher-dimension operators. As a by-product, we obtain the bound $\lambda_1<0$ for one of the parameters of the heavy quark effective theory. The integral over the $B\to X_s\,\gamma$ structure function is related to the shape function that governs the fall-off of the lepton spectrum close to the endpoint in $B\to X_u\,\ell\,\bar\nu$ decays. A measurement of the photon spectrum in rare $B$-decays can therefore help to obtain a model-independent determination of $V_{ub}$.

Abstract:
We give an introduction to the heavy-quark effective theory and the $1/m_Q$ expansion, which provide the modern framework for a systematic, model-independent description of the properties and decays of hadrons containing a heavy quark. We discuss the applications of these concepts to spectroscopy and to the weak decays of $B$ mesons.

Abstract:
We give an introduction to the heavy-quark effective theory and the $1/m_Q$ expansion, which provide the modern framework for a systematic, model-independent description of the properties and decays of hadrons containing a heavy quark. We discuss the applications of these concepts to spectroscopy and to the weak decays of $B$ mesons.

Abstract:
Using the virial theorem of the heavy-quark effective theory, we show that the mixing of the operator for the heavy-quark kinetic energy with the identity operator is forbidden at the one-loop order by Lorentz invariance. This explains why such a mixing was not observed in several one-loop calculations using regularization schemes with a Lorentz-invariant UV regulator, and why no UV renormalon singularity was found in the matrix elements of the kinetic operator in the bubble approximation (the ``invisible renormalon''). On the other hand, we show that the mixing is not protected in general by any symmetry, and it indeed occurs at the two-loop order. This implies that the parameter $\lambda_1^H$ of the heavy-quark effective theory is not directly a physical quantity, but requires a non-perturbative subtraction.

Abstract:
The decays B -> D^{**} pi, where D^{**} is a narrow p-wave charm resonance, are investigated in the context of a generalized factorization hypothesis, including the leading nonfactorizable corrections. The decay rates for these processes are related to the corresponding semileptonic rates at maximum recoil. It is pointed out that the current data on the branching ratio for the decay B^- -> D_2^{*0} pi^- may pose a problem for theory. We predict that future, more accurate measurements of this branching ratio will find a value B(B^- -> D_2^{*0} pi^-) = 4 * 10^{-4}, a factor 5 lower than the current central value.