Lifetimes of Heavy-Flavour Hadrons -- Whence and Whither?

A theoretical treatment for the weak decays of heavy-flavour hadrons has been developed that is genuinely based on QCD. Its methodology as it applies to total lifetimes and the underlying theoretical issues are sketched. Predictions are compared with present data. One discrepancy emerges: the beauty baryon lifetime appears to be significantly shorter than expected. The ramifications of those findings are analyzed in detail.Comment: 15 pages, no figures, LATEX, two references added and new information concerning a lower charm content in B decays incorporate

Heavy Quark Expansion and Preasymptotic Corrections to Decay Widths in the 't Hooft Model

We address nonperturbative power corrections to inclusive decay widths of heavy flavor hadrons in the context of the 't Hooft model (two-dimensional QCD at N_c->oo), with the emphasis on the spectator-dependent effects sensitive to the flavor of the spectator. The summation of exclusive widths is performed analytically using the `t Hooft equation. We show that the 1/m_Q expansion of both the Weak Annihilation and Pauli Interference widths coincides with the OPE predictions, to the computed orders. Violation of local duality in the inclusive widths is quantified, and the new example is identified where the OPE prediction and the actual effect are completely saturated by a single final state. The qualitative aspects of quark hadronization emerging from the analysis in the 't Hooft model are discussed. Certain aspects of summation of spectator-independent hadronic weak decay widths are given in more detail, which were not spelled out previously. We also give some useful details of the 1/m_Q expansion in the 't~Hooft model.Comment: 54 pages, 8 figures in the text. Version to be published in Phys. Rev. D. A number of typos are corrected and relevant references added. Clarifications in Conclusions, Appendices 2.1 and 3 are adde

Bloch-Nordsieck cancellations beyond logarithms in heavy particle decays

We investigate the one-loop radiative corrections to the semileptonic decay of a charged particle at finite gauge boson mass. Extending the Bloch-Nordsieck cancellation of infrared logarithms, the subsequent non-analytic terms are also found to vanish after eliminating the pole mass in favor of a mass defined at short distances. This observation justifies the operator product expansion for inclusive decays of heavy mesons and implies that infrared effects associated with the summation of the radiative corrections are suppressed by at least three powers of the mass of the heavy decaying particle.Comment: LATEX, 7 pages, one figure appended as uu-encoded ps-file, MPI-PhT/94-1

The Mass Definition in Hqet and a New Determination of Vcb_{\text{cb}}

Positive powers of the mass parameter in a physical quantity calculated with the help of heavy quark effective theory originate from a Wilson coefficient in the matching of QCD and HQET Green function. We show that this mass parameter enters the calculation as a well--defined running current mass. We further argue that the recently found ill--definition of the pole mass, which is the natural expansion parameter of HQET, does not affect a phenomenological analysis which uses truncated perturbative series. We reanalyse inclusive semileptonic decays of heavy mesons and obtain the $c$ quark mass $m_c^{\overline{\text{MS}}}(m_c) = (1.35\pm 0.20)\,\text{GeV}$ where the error is almost entirely due to scale--uncertainties. We also obtain $m_b^{\overline{\text{MS}}}(m_b) = (4.6\pm 0.3)\,\text{GeV}$ and $|V_{cb}|(\tau_B/1.49\,\text{ps})^{1/2} = 0.036\pm 0.005$ where the errors come from the uncertainty in the kinetic energy of the heavy quark inside the meson, in the experimental branching ratios, in QCD input parameters, and scale--uncertainties.Comment: 21 p., 5 figs, all style files incl., TUM-T31-56/R (Sec. 2 revised, phenomenological results unchanged

A Vademecum on Quark-Hadron Duality

We present an elementary introduction to the problem of quark-hadron duality and its practical limitations, in particular as it concerns local duality violation in inclusive B meson decays. We show that the accurate definition of duality violation elaborated over the recent years allows one to derive informative constraints on violations of local duality. The magnitude of duality violation is particularly restricted in the total semileptonic widths. This explains its strong suppression in concrete dynamical estimates. We analyze the origin of the suppression factors in a model-independent setting, including a fresh perspective on the Small Velocity expansion. A new potentially significant mechanism for violation of local duality in \Gamma_sl(B) is analyzed. Yet we conclude that the amount of duality violation in \Gamma_sl(B) must be safely below the half percent level, with realistic estimates being actually much smaller. Violation of local duality in \Gamma_sl(B) is thus far below the level relevant to phenomenology. We also present a cautionary note on the B->D^* decay amplitude at zero recoil and show that it is much more vulnerable to violations of quark-hadron duality than \Gamma_sl(B). A critical review of some recent literature is given. We point out that the presently limiting factor in genuinely model-independent extraction of V_cb is the precise value of the short-distance charm quark mass. We suggest a direct and precise experimental check of local quark-hadron duality in semileptonic B->X_c l\nu decays.Comment: 48 pages, 4 figures; LaTe

Infrared effects and the asymptotics of perturbation theory in weak decays of heavy particles

I discuss the interplay of infrared sensitivity in large order perturbative expansions with the presence of explicit nonperturbative corrections in the context of heavy quark expansions. The main focus is on inclusive decays and the status of the kinetic energy of the heavy quark. This talk summarizes work done with Braun and Zakharov.Comment: LATEX, world_sci.sty (appended to the file), UM-TH-94-30 (Invited talk presented at the conference ``QCD'94'', Montpellier, France, July 7 - 13, 1994) [Typo in ref. 6 corrected, pardon.

Analytical Heavy Quark Expansion in the 't Hooft Model

We present a number of exact relations for the heavy quark limit and develop an analytical 1/m_Q expansion for heavy mesons in the 't Hooft model. Among the new results are relation 3\mu_\pi^2=\bar\Lambda^2 - m_{sp}^2+\beta^2, 1/m_Q corrections to the decay constants, to the kinetic expectation values and 1/m_Q^2 nonperturbative corrections to the B->D amplitude at zero recoil. The properties of the IW functions are addressed and the small velocity sum rules are verified.Comment: 22 pages, plain LaTeX (no figures

Non-Abelian Dipole Radiation and the Heavy Quark Expansion

Dipole radiation in QCD is derived to the second order in $\alpha_s$. A power-like evolution of the spin-singlet heavy quark operators is obtained to the same accuracy. In particular, ${\cal O}(\alpha_s^2)$ relation between a short-distance low-scale running heavy quark mass and the \barMS mass is given. We discuss the properties of the effective QCD coupling \aw(E) which governs the dipole radiation. This coupling is advantageous for heavy quark physics.Comment: 12 pages, Late

B_s Mixing and B Hadron Lifetimes at CDF

We present the CDF results using 1.0 fb^{-1} of data on the mixing frequency measurement in the B_s system and the lifetime measurements of several B hadrons. We obtain \Delta m_s=17.77 +- 0.1 +- 0.07 ps^{-1} and c\tau(\Lambda_b)=473.8 +- 23.1 +- 3.5 \mu m. The later one is more than 3 sigma above the world average, but in reasonable agreement with HQE calculations.Comment: submitted to EPS2007 proceeding

Precision Studies of Duality in the 't Hooft Model

We address numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with N_c --> infinity. The primary focus of these studies is total semileptonic decay widths relevant for extracting |V_{cb}| and |V_{ub}|. We compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/m_Q expansion arising from the Operator Product Expansion. An impressive agreement sets in unexpectedly early, immediately after the threshold for the first hadronic excitation in the final state. Yet even at higher energy release it is possible to discern the seeds of duality-violating oscillations. We find the ``Small Velocity'' sum rules to be exceptionally well saturated already by the first excited state. We also obtain a convincing degree of duality in the differential distributions and in an analogue of R_{e^+e^-}(s). Finally, we discuss possible lessons for semileptonic decays of actual heavy quarks in QCD.Comment: 45 pages, 16 eps figures include