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

Key Distributions for Charmless Semileptonic B Decay

We present theoretical predictions for a few phenomenologically interesting distributions in the semileptonic b->u decays which are affected by Fermi motion. The perturbative effects are incorporated at the one-loop level and appear to be very moderate. Our treatment of Fermi motion is based directly on QCD, being encoded in the universal distribution function F(x). The decay distributions in the charged lepton energy, invariant mass of hadrons, hadron energy, and q^2 are given. We note that typically about 90% of all decay events are expected to have M_X < M_D; this feature can be exploited in determination of |V_ub|.Comment: 9 pages, 6 figures (incorporated in the LaTeX file); plain LaTe

b -> s +\gamma : A QCD Consistent Analysis of the Photon Energy Distribution

The photon energy distribution in the inclusive b -> s+\gamma transitions is a combination of two components: the first component, soft physics, is determined by the so called primordial distribution function, while the second component, perturbative physics, is governed by the hard gluon emission. A simple ansatz is suggested for the primordial distribution function which obeys the QCD constraints known so far. We then discuss in detail how the hard gluon emission affects the energy distribution. An extension of the Sudakov approximation is worked out incorporating the Brodsky-Lepage-Mackenzie prescription and its generalizations. We explicitly calculate the marriage of nonperturbative with perturbative effects in the way required by OPE, introducing separation scale \mu. A few parameters, such as m_b and \mu_\pi^2 affect the shape of the distribution and, thus, can be determined by matching to the experimental data. The data, still scarce, while not giving precise values for these parameters, yield consistency with theory: the current values of the above parameters lie within experimental uncertainty. On the theoretical side we outline a method allowing one to go beyond the practical version of OPE.Comment: 40 pages, 5 Figures to be added as uuencoded files; plain LaTe

Calculation of 1/m^3 terms in the total semileptonic width of D mesons.

We calculate the 1/$m^3_c$ corrections in the inclusive semileptonic widths of $D$ mesons. We show that these are due to the novel penguin type operators that appear at this level in the transition operator. Taking into account the nonperturbative corrections leads to the predicted value of the semileptonic width significantly lower than the experimental value. The $1/m^3_c$ worsen the situation or at the very least, within uncertainty, give small contribution. We indicate possible ways out. It seems most probable that violations of duality are noticeable in the energy range characteristic to the inclusive decays in the charm family. Theoretically these deviations are related to divergence of the high-order terms in the power expansion in the inverse heavy quark mass.Comment: Final version accepted for publication in Physical Review D (19 pages, 5 figures appended as two PS files at the end of the LATEX file