On The Expected Photon Spectrum in B -> X_s + gamma and Its Uses

Measuring the photon energy spectrum in radiative B decays provides essential help for gaining theoretical control over semileptonic B transitions. The hadronic recoil mass distribution in B -> X_u \ell\nu promises the best environment for determining |V_ub|. The theoretical uncertainties are largest in the domain of low values of the lepton pair mass q^2. Universality relations allow to describe this domain reliably in terms of the photon spectrum in B -> X_s + \gamma. A method is proposed to incorporate 1/m_b corrections into this relation. The low-E_\gamma tail in radiative decays is important in the context of extracting |V_ub|. We argue that CLEO's recent fit to the spectrum underestimates the fraction of the photon spectrum below 2 GeV. Potentially significant uncertainties enter in the theoretical evaluation of the integrated end-point lepton spectrum or the B -> X_u \ell\nu width with a too high value of the lower cut on q^2 in alternative approaches to |V_ub|.Comment: 24 pages, 6 figures, LaTeX. Revised: Complete version. Numerical predictions are improved and the estimate for the decay fraction revised. The theoretical expectations for the decay fraction and the spectrum itself are given on the plot

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

Heavy Quark Distribution Function in QCD and the AC2^2M2^2 Model

We show that the phenomenological \ACM ansatz is consistent with QCD through order $1/m_b$ in the description of B\ra l\bar \nu_l+X_u and B\ra \gamma +X_s transitions, including their energy spectra and differential distributions. This suggests a concrete realization for the QCD distribution function, which we call the ``Roman'' function. On the other hand the \ACM model description of the end-point domain in B\ra l\bar \nu_l + X_c is incompatible with QCD: a different distribution function enters the description of b\ra c decays as compared to the transitions to the massless quarks. Both observations -- the validity of the {\ACM}-like description for heavy-to-light transitions and the emergence of the new distribution function in the b\ra c case -- are in contradiction to a recent claim in the literature. The intrinsic limitation of the \ACM model could reveal itself in different values of the effective $b$ quark mass from fits of the $\Lambda _b$ and $B$ decays.Comment: 15 pages, Latex, 2 figures are included (as 2 appended postscript files), CERN-TH.7159/94, TPI-MINN-94/2-T, UND-HEP-94-BIG02 (a few comments on the literature are added

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

On the Determination of ∣Vub∣|V_{ub}| from Inclusive Semileptonic Decay Spectra

We propose a model independent method to determine $|V_{ub}|$ from the energy spectrum of the charged lepton in inclusive semileptonic $B$ decays. The method includes perturbative QCD corrections as well as nonperturbative ones.Comment: LaTeX, 19 pages, 8 figures appended after \end{document} as uu-encoded and compressed .eps files, uses epsf, Technion-PH-94/9, CERN-TH.7308/9

Two-loop QCD corrections to semileptonic b decays at maximal recoil

We present a complete $O(\alpha_s^2)$ correction to the differential width of the inclusive semileptonic decay $b\to cl\nu_l$ at the kinematical point of vanishing invariant mass of the leptons, $q^2=0$. Together with the recently computed $O(\alpha_s^2)$ correction at the upper boundary of the lepton invariant mass spectrum, this new information permits an estimate of the $O(\alpha_s^2)$ effect in the total inclusive semileptonic decay width $b\to cl\nu_l$. We argue that the non-BLM part of the $O(\alpha_s^2)$ correction gives at most 1% correction to the inclusive semileptonic decay width $b\to cl\nu_l$. This significantly improves the credibility of extracting $|V_{cb}|$ from the inclusive semileptonic decays of the b-hadrons.Comment: 8 pages, revte

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

Second Generation of 'Miranda Procedure' for CP Violation in Dalitz Studies of B (\& D \& \tau) Decays

The `Miranda Procedure' proposed for analyzing Dalitz plots for CP asymmetries in charged B and D decays in a model-independent manner is extended and refined. The complexity of CKM CP phenomenology through order $\lambda^6$ is needed in searches for New Dynamics (ND). Detailed analyses of three-body final states other great advantages: (i) They give us more powerful tools for deciding whether an observed CP asymmetry rep- resents the manifestation of ND and its features. (ii) Many advantages can already be obtained by the `Miranda Procedure' without construction of a detailed Dalitz plot de- scription. (iii) One studies CP asymmetries independent of production asymmetries. We illustrate the power of a second generation Miranda Procedure with examples with time integrated rates for $B_d/\bar B_d$ decays to final states $K_S\pi+\pi-$ as trial runs with comments on $B^{\pm} \to K^{\pm}\pi^+\pi^-/K^{\pm}K^+K^-$.Comment: 29 pages, 7 figure

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