The Heavy Quark Expansion

I review the status of the modern theoretical approach to weak decays of heavy flavor hadrons based on the 1/m_Q expansion in QCD. The qualitative features are explained and the subtleties in simultaneously incorporating perturbative and power-suppressed effects are addressed. A few topical phenomenological applications are discussed in quantitative detail.Comment: 30 pages, 3 figures in the text; LaTeX. Talk given at the Symposium on Radiative Corrections (CRAD96), Cracow, 1-5 August 1996. To appear in Proceedings of "CRAD96

Comment on the Renormalization Group Improvement in Exclusive b\ra c Transitions

Using rather general consideration I argue that the numerical impact of the existing next-to-leading logarithmic summations of terms $\log{m_b/m_c}$ for perturbative factors $\eta_A$, $\eta_V$ in the exclusive zero recoil semileptonic transitions is irrelevant, and adopting corresponding corrections beyond the exact one loop result for both estimating the values of these formfactors and their theoretical uncertainty, is misleading. The central theoretical value if taken literally is then $\eta_A\simeq 0.97$.Comment: 10 pages Revised: PS file for Fig.1 corrupted my mailer is replaced by the uuencoded one. Plain LaTe

Do Higher Order Perturbative Corrections Upset |V_{cb}| and |V_{ub}| Determined from Semileptonic Widths?

It is shown that large perturbative corrections found previously for semileptonic beauty and charm decays are associated with using inappropriate pole masses. The latter, in the perturbative expansion, suffer from the 1/m_Q infrared renormalon which is absent in the widths, which leads to similar large corrections in m_Q. Pole masses are neither measured directly in experiment. If the widths are related to parameters determined in experiment, the overall impact of the calculated second order corrections becomes strongly suppressed and leads to less than 1\% change in |V_{cb}| and |V_{ub}|. Even in charm decays the perturbative corrections appear to be very moderate in the consistent OPE-compliant treatment. The updated estimate of |V_{cb}| is given, based on recent accurate determination of m_b and \alpha_s(1 GeV). The theoretical accuracy of determination of |V_{ub}| from \Gamma_{sl}(b->u) appears to be good as well.Comment: 16 pages, no figures; to appear in IJMPA. SUMMARY of CHANGES made for the journal version: 1. The Comment on the Luke's theorem is added as a footnote after Eq.(18). 2. Misprint in sign is corrected in Eq.(18) 3. Obvious misprint in the normalization of BR(b->u) in Eqs.(25), (27) is eliminated; the results of numerical analysis of b->u are formulated in a more precise way. Coefficients in Eqs.(19) and (20) changed insignificantly due to using the normalization scale 1.3GeV instead o

Perturbative corrections to semileptonic b decay distributions

We compute O(alpha_s) and O(alpha_s^n beta_0^{n-1}) (BLM) corrections to the five structure functions relevant for b->q l nu decays and apply the results to the moments of a few distributions of phenomenological importance. We present compact analytic one-loop formulae for the structure functions, with proper subtraction of the soft divergence.Comment: 23 pages, LaTex. A number of textual changes are added for clarity, a missing definition is provide

A Closer Look at Perturbative Corrections in the b->c Semileptonic Transitions

We comment on two recent calculations of the second order perturbative corrections in the heavy flavor semileptonic transitions within the Brodsky-Lepage-Mackenzie approach. It is pointed out that the results do not show significant enhancement either in the inclusive $b\rightarrow c$ decays or in the exclusive amplitudes at zero recoil provided that the expansion parameter is chosen in a way appropriate to the kinematics at hand. The values of the second-order coefficients inferred from the BLM-type calculations appear to be of order unity in the both cases. Thus, in both cases no significant uncertainty in extracting $V_{cb}$ can be attributed to perturbative effects. The theoretical accuracy is mostly determined by the existing uncertainty in $1/m_c^2$ nonperturbative corrections in the exclusive $B\rightarrow D^*$ amplitude, and, to a lesser extent, by the uncertainty in the estimated value of the kinetic energy matrix element $\mu_\pi^2$ in the case of $\Gamma_{\rm sl}(b\rightarrow c)$. The theoretical accuracy of the inclusive method of determination of $V_{cb}$ seemingly competes with and even exceeds the experimental accuracy.Comment: 9 pages, no figures, revised: One reference added and some styllistic changes mad

Operator Product Expansion, Heavy Quarks, QCD Duality and its Violations

The quark (gluon)-hadron duality constitutes a basis for the theoretical treatment of a wide range of inclusive processes -- from hadronic \tau decays and R_{e^+e^-}, to semileptonic and nonleptonic decay rates of heavy flavor hadrons. A theoretical analysis of these processes is carried out by using the operator product expansion in the Euclidean domain, with subsequent analytic continuation to the Minkowski domain. We formulate the notion of the quark (gluon)-hadron duality in quantitative terms, then classify various contributions leading to violations of duality. A prominent role in the violations of duality seems to belong to the so called exponential terms which, conceptually, may represent the (truncated) tail of the power series. A qualitative model, relying on an instanton background field, is developed, allowing one to get an estimate of the exponential terms. We then discuss a number of applications, mostly from heavy quark physics.Comment: 59 pages, 6 figures, epsf.sty required. Revised: Styllistic changes; minor clarifications added; three references corrected; minor changes in the color-related factor

Sum Rules for Heavy Flavor Transitions in the SV Limit

We show how sum rules for the weak decays of heavy flavor hadrons can be derived as the moments of spectral distributions in the small velocity (SV) limit. This systematic approach allows us to determine corrections to these sum rules, to obtain new sum rules and it provides us with a transparent physical interpretation; it also opens a new perspective on the notion of the heavy quark mass. Applying these sum rules we derive a lower bound on the deviation of the exclusive form factor $F_{B->D^*}$ from unity at zero recoil; likewise we give a field-theoretical derivation of a previously formulated inequality between the expectation value for the kinetic energy operator of the heavy quark and for the chromomagnetic operator. We analyze how the known results on nonperturbative corrections must be understood when one takes into account the normalization point dependence of the low scale parameters. Relation between the field-theoretic derivation of the sum rules and the quantum-mechanical approach is elucidated.Comment: 72 pages, 5 figures (uuencoded ps files added using figures option), Revised version. Paper is considerably extended to include some new results. New section on quantum mechanical approach is adde

On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays

In previous papers we have pointed out that there exists a QCD analog of the phenomenological concept of the so called Fermi motion for the heavy quark inside a hadron. Here we show in a more detailed way how this comes about and we analyze the limitations of this concept. Non-perturbative as well as perturbative aspects are included. We emphasize both the similarities and the differences to the well-known treatment of deep inelastic lepton-nucleon scattering. We derive a model-independent {\em lower} bound on the kinetic energy of the heavy quark inside the hadron.Comment: 34 pages, Latex, 4 figures. Some clarifying comments and postscript files of figures are adde