Renormalization Group (RG) and optimized Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic b \to u and b \to c decay rates. It is noted that the \bar{MS} scheme works favorably in the b \to u case whereas the pole mass scheme shows better convergence in the b \to c case. Upon the inclusion of the estimated three-loop contribution, we find the full perturbative decay rate to be 192π^3Γ(b\to u\barν_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2065 \pm 290{\rm GeV^5} and 192π^3Γ(b\to c\ell^-\barν_\ell)/(G_F^2|V_{cb}|^2)= 992 \pm 198 {\rm GeV^5}, respectively. The errors are inclusive of theoretical uncertainties and non-perturbative effects. Ultimately, these perturbative contributions reduce the theoretical uncertainty in the extraction of the CKM matrix elements |V_{ub}| and |V_{cb}| from their respective measured inclusive semileptonic branching ratio(s).
Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic $b \to u$ decay rate. These improved estimates of the decay rate reduce the theoretical uncertainty in the extraction of the CKM matrix element $|V_{ub}|$ from the measured inclusive semileptonic branching ratio.
The magnitude of the CKM matrix elements Vcb can be extracted from inclusive semileptonic B decays in a model independent way pioneered by Kolya Uraltsev and collaborators. I review here the present status and latest developments in this field.
We calculate the inclusive charmless semileptonic decay width of the B meson using a QCD-based approach. This approach is able to account for both dynamic and kinematic effects of nonperturbative QCD. The charmless semileptonic decay width is found to be enhanced by long-distance strong interactions by +(7\pm 5)% with respect to the free quark decay width. Using the resulting theoretical value for the charmless semileptonic decay width, an extraction of $|V_{ub}|$ is made from the measured lifetime and inclusive charmless semileptonic branching ratio of b hadrons.
In this talk, we review the QCD calculation of the lepton spectrum from inclusive semileptonic $B$ decay. We compare this prediction to that of the ACCMM model. This latter work was done in collaboration with Csaba Csaki.
This talk is a short review on the theoretical issues and uncertainties in the calculation of partial decay rates in inclusive B decays. The main emphasis is on charmless semileptonic decays, the B -> X(s) gamma photon spectrum, and the extraction of Vub using model-independent methods.
Inclusive semileptonic decays are discussed in the framework of heavy quark effective field theory by employing the short distance expansion in the effective theory. The lowest order term turns out to be the parton model; the higher order terms may be regarded as correction terms to the parton model result. The first nonvanishing corrections to the parton model result are given and the lepton energy spectrum of inclusive semileptonic decays of heavy mesons is calculated.
Some emerging difficulties in the theoretical description of exclusive semileptonic $\bar B$ decays are discussed in the context of the quark model. While there are no unambiguous problems at this time, I discuss physics beyond the valence quark model which should eventually be probed by precision measurements of $\bar B$ semileptonic decays.
Utilizing asymptotic Pade-approximant methods, we estimate the three-loop order MS-bar coefficients of alpha_s^3[\log(μ^2/m^2_b(μ)]^k terms [k = {0,1,2,3}] within the $b \to u\ell^-\barν_\ell$ decay rate. Except for the coefficient of the k = 0 term, all other coefficients may also be obtained via renormalization-group (RG) methods. The relative errors in asymptotic Pade-approximant estimates of the k = {1,2,3} terms are found to be 5.1% or less, thereby providing an estimate of the theoretical uncertainty in the asymptotic Pade-approximant estimate of the RG-inaccessible k = 0 term. By a judi…
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.
We evaluate the inclusive semileptonic B decay spectrum as a function of the final-state hadrons energy to second order in the inverse quark mass expansion and tree level in $α_{s}$. We argue that there is an energy interval below the $c$ production threshold that could be used to determine $V_{ub}$.
The renormalization-scale ($μ$) dependence of the two-loop inclusive semileptonic $b\to c\ell^-\barν_\ell$ decay rate is shown to be significant in the pole mass scheme, and the decay rate is shown to be poorly convergent in the MS-bar scheme. Three-loop contributions to the decay rate are estimated by developing Pade approximant techniques particularly suited to perturbative calculations in the pole mass scheme. An optimized Pade estimate of the three-loop contributions is obtained by comparison of the Pade estimates with the three-loop terms determined by renormalization-group invariance. Th…
We extend previous computations of the second order QCD corrections to semileptonic b \to c inclusive transitions, to the case where the charged lepton in the final state is massive. This allows accurate description of b \to c τ\bar ν_τdecays. We review techniques used in the computation of O(α_s^2) corrections to inclusive semileptonic b \to c transitions and present extensive numerical studies of O(α_s^2) QCD corrections to b \to c l \bar ν_l decays, for l =e, τ.
Starting from an Operator Product Expansion in the Heavy Quark Effective Theory up to order 1/m_b^2 we calculate the inclusive semileptonic decays of unpolarized bottom hadrons including lepton mass effects. We calculate the differential decay spectra dΓ/(dE_τ), and the total decay rate for B meson decays to final states containing a τlepton.
We present the results of a calculation of the perturbative QCD corrections for the semileptonic inclusive width of a heavy flavored meson. Within the Heavy Quark Expansion we analytically compute the QCD correction to the coefficient of power suppressed contribution of the chromo-magnetic operator in the limit of vanishing mass of the final state quark. The important phenomenological applications are decays of bottom mesons, and to the less extend, charmed mesons.
We study the inclusive charmless semileptonic decay of $Λ_b$, $Λ_b \to X_u l ν_l$, in the framework of heavy quark expansion and find that the rate is substantially enhanced by spectator effect. We obtain $Br(b \to X_u l ν_l)$ to be $1.13 \times 10^{-3}$ for $|V_{ub}| = 3.3 \times 10^{-3}$. We discuss our result in light of the recent LEP measurements of the charmless semileptonic branching ratio where such enhancement was not taken into account in extracting $|V_{ub}|$.
The determinations of |V_{cb}| and |V_{ub}| from inclusive semileptonic B decays are reviewed. A comparison of the light-cone approach with the heavy quark expansion approach is made. The perspective for further improvement of the |V_{cb}| and |V_{ub}| determinations is discussed.
We make an analysis of the hadronic invariant mass spectrum in inclusive charmless semileptonic B meson decays in a QCD-based approach. The decay width is studied as a function of the invariant mass cut. We examine their sensitivities to the parameters of the theory. The theoretical uncertainties in the determination of $|V_{ub}|$ from the hadronic invariant mass spectrum are investigated. A strategy for improving the theoretical accuracy in the value of $|V_{ub}|$ is described.
In order to study the end-point spectrum of inclusive semileptonic $b \rightarrow u$ decays, we investigate the parton model motivated by deep inelastic scattering process. The reliability of the model is carefully examined by comparing the decay rates and the lepton spectra for $b \rightarrow c$ decay with those of the heavy quark effective theory. We also compute the decay rates of the inclusive semileptonic decay into tau lepton in terms of the parton model, which give another test of the model independently. We conclude that one can make the parton model consistent with the heavy quark eff…
We present theoretical evidence that the exclusive/inclusive ratio of semileptonic $Λ_b$-decays exceeds that of semileptonic B-decays where the experimental exclusive/inclusive ratio amounts to about 66%. We start from the observation that the spectator quark model provides a lower bound on the leading order Isgur-Wise function of the $Λ_b \to Λ_c$ transition in terms of the corresponding $B \to D,D^*$ mesonic Isgur-Wise function. Using experimental data for the $B \to D,D^*$ mesonic Isgur-Wise functions this bound is established. Applying a Bethe-Salpeter model including spectator quark inter…
We present a Borel resummation method for the QCD corrections in inclusive, charmless, semileptonic B meson decay. The renormalon contributions are resummed to all orders by employing a bilocal expansion of the Borel transform that accurately accounts for the first infrared renormalons in the Borel plane. The renormalons in the pole mass and the QCD expansion are resummed separately, and a precise relation is obtained between a properly defined pole mass and the ${\bar {\rm MS}}$ mass. The inclusive decay rate is calculated to three loop order using an estimate of the yet unknown NNLO coeffici…
We re-examine the model of Altarelli, Cabibbo, Corbò, Maiani and Martinelli for inclusive semileptonic B decay, in the light of recent calculations in heavy quark effective theory. The model can be shown to have no~$1/m_b$ corrections, with a suitable definition of the b quark mass~$m_b$. However, we find that the structure of the $1/m_b^2$~terms is incompatible with the predictions of heavy quark effective theory. The numerical significance of this discrepancy is discussed.
Perturbative corrections of the order of $α_s$ to inclusive double differential lepton distribution from $b$ quark decay are considered. A perturbative correction to the charged lepton energy spectrum has been calculated for an arbitrary charged lepton mass. The perturbative contribution suppresses the partial rate but almost does not change the shape of energy distribution. Applications of our result to semileptonic B meson decays are briefly discussed.
The parton model for semileptonic B meson decays is studied with special attention to the decay distributions. We find that the spectra show dramatic variations when we introduce cuts on the hadronic energy or invariant mass of hadrons. Results for both $b\rightarrow u$ and $b\rightarrow c$ decays are presented. The detailed spectra may help to separate the two types of decays.
Recent advances in improving extractions of |Vcb| and m_b from spectra of semileptonic inclusive B decay are reported. Results of a general moment analysis of the lepton energy spectrum and the hadronic invariant mass spectrum are summarized. The calculation of the general O(α_s) structure functions for semileptonic B decay is reported, which has allowed the calculation of the O(α_s Lambda_{QCD} /m_b) terms for the hadronic invariant mass moments to be carried out. Recent theoretical advances and improvements in experimental data has allowed extractions of the CKM element |Vcb| to improve to t…
We calculate the radiative corrections to the nonleptonic inclusive B decay mode $b\to c ud$ taking into account the charm quark mass. The corrections increase the decay rate by (4--8)\%, depending on the renormalization point. Using these results, we obtain an improved theoretical prediction for the semileptonic branching ratio of B mesons. This talk relies on work done in collaboration with E. Bagan, V.M.\ Braun and P. Gosdzinsky.
We present Standard Model predictions for lepton flavour universality ratios of inclusive $B\to X_{(c)} \ell \barν_\ell$. For the $\ell=μ,e$, these ratios are very close to unity as expected. For the $τ$ mode, we update the SM prediction for the branching ratio including power-corrections in the heavy-quark expansion up to $1/m_b^3$. These inclusive ratios serve as an important cross-check of the exclusive $B\to D^{(*)}\ell\barν_\ell$ modes, in which tensions exists between the predictions and measurements in those modes.
The MSbar charm quark mass is determined to be m_c(m_c)=1224+-17+-54 MeV from a global fit to inclusive B meson decay data, where the first error is experimental, and includes the uncertainty in alpha_s, and the second is an estimate of theoretical uncertainties in the computation. We discuss the implications of the pole mass renormalon in the determination of m_c.
A selfconsistent treatment of nonperturbative effects in inclusive nonleptonic and semileptonic decays of beauty and charm hadrons is presented. It is illustrated by calculating semileptonic branching ratios, lifetime ratios, radiative decay rates and the lepton spectra in semileptonic decays.
We present a complete $O(α_s^2)$ correction to the differential width of the inclusive semileptonic decay $b\to clν_l$ at the kinematical point of vanishing invariant mass of the leptons, $q^2=0$. Together with the recently computed $O(α_s^2)$ correction at the upper boundary of the lepton invariant mass spectrum, this new information permits an estimate of the $O(α_s^2)$ effect in the total inclusive semileptonic decay width $b\to clν_l$. We argue that the non-BLM part of the $O(α_s^2)$ correction gives at most 1% correction to the inclusive semileptonic decay width $b\to clν_l$. This signifi…
We determine $|V_{cb}|$ from inclusive semileptonic B decays including resummation of supposedly large perturbative corrections, which originate from the running of the strong coupling. We argue that the low value of the BLM scale found previously for inclusive decays is a manifestation of the renormalon divergence of the perturbative series starting already in third order. A reliable determination of $|V_{cb}|$ from inclusive decays is still possible if one uses a short-distance b quark mass. We find that using the $\overline{\rm MS}$ running mass significantly reduces the perturbative coeffi…
The effects of spectator light quark in decays of heavy mesons are considered, which vanish in the limit of factorization of matrix elements of four-quark operators over the mesons. These effects include the difference of the total widths as well as of the semileptonic decay rates between the D^0 and D_s mesons and also a contribution to inclusive semileptonic decay rates of B^0 and B^\pm into the channel X_u l nu related to determination of the weak mixing parameter V_{ub}. If the observed difference of the lifetimes between D_s and D^0 mesons is attributed to non-factorizable terms, such ter…
B decay sum rules relate exclusive B semileptonic decay matrix elements to forward B-meson matrix elements of operators in HQET. At leading order the operators that occur are the b-quark kinetic energy $λ_1$ and chromomagnetic energy $λ_2$. The latter is determined by the measured $B^*-B$ mass splitting. The derivation of these sum rules is reviewed and perturbative QCD corrections are discussed. A determination of $λ_1$ and the energy of the light degrees of freedom in a B-meson, $\barΛ$, from semileptonic B decay data is presented. Future prospects for improving these sum rules are discussed…
We compute 2-loop QCD corrections to the hard coefficient functions which arise in the factorization formula for B -> X_u l nu decays in the shape-function region. Our calculation provides the last missing piece required for a NNLO analysis of inclusive semileptonic B decays, which may significantly reduce the theoretical uncertainty in the extraction of the CKM matrix element |V_ub|. Among the technical aspects, we find that the 2-loop hard coefficient functions are free of infrared singularities as predicted by the factorization framework. We perform a brief numerical analysis of the NNLO co…
An admixture of a right-handed $b \to c$ current in the semileptonic weak decays of the $B$ mesons would give a significantly different contribution to the inclusive rate of the decays $B \to l νX_c$ as compared to the exclusive decay $B \to D^* l ν$ at zero recoil. Thus a difference in the values of $|V_{cb}|$ extracted from the data on these two types of decay would measure such admixture. The present marginal mismatch in determination of $|V_{cb}|$ by the two methods can be interpreted as corresponding to $g_R/g_L \approx 0.14 \pm 0.18$.
In this talk we present theoretical evidence that the exclusive/inclusive ratio of semileptonic Lambda_b-decays exceeds that of semileptonic B-decays, where the experimental exclusive/inclusive ratio amounts to about 66%. We start from the observation that the spectator quark model provides a lower bound on the leading order Isgur-Wise function of the Lambda_b -> Lambda_c transition in terms of the corresponding B -> D,D^* mesonic Isgur-Wise function. Using experimental data for the B -> D,D^* mesonic Isgur-Wise functions this bound is established. Applying a QCD sum rule estimate of the Lambd…
We consider spin-momentum correlations between the spin of the bottom baryon $Λ_{\mathrm{b}}$ and the momenta of its decay products in its inclusive semileptonic decay. We define several polar and azimuthal spin-momentum correlation measures in different event coordinate systems. The values of the spin-momentum correlation measures are calculated up to ${\cal O}(1/m_b^2)$ using the standard OPE und HQET methods. Some of the measures turn out to be sufficiently large to make them good candidates for a determination of the polarization of the $Λ_{\mathrm{b}}$ in e.g. $\mathrm{Z}$ decays.
We reduce the perturbative uncertainty in the determination of |V_{ub}| from inclusive semileptonic B decays by calculating the rate of B -> X_u l nu events with dilepton invariant mass q^2>(M_B-M_D)^2 at subleading order in the hybrid expansion, and to next-to-leading order in renormalization-group improved perturbation theory. We also resum logarithmic corrections to the leading power-suppressed contributions. Studying the effect of different b-quark mass definitions we find that the branching ratio after the cut is Br(B -> X_u l nu)=(20.9+-4.0)|V_{ub}|^2, where the dominant error is due to …
We study logarithms of the form $\ln(m_q/m_b)$ which arise in the inclusive semileptonic decay of a bottom quark to a quark of mass $m_q$. We use the renormalization group to resum the leading radiative corrections to these terms, of the form $m_q^2α_s^n\ln^n(m_q/m_b)$, $m_q^3α_s^{n+1}\ln^n(m_q/m_b)$ and $m_q^4α_s^n\ln^{n+1}(m_q/m_b)$. The first two resummations are trivial, while the latter involves a non-trivial mixing of four-fermi operators in the $1/m_b$ expansion. We illustrate this technique in a toy model in which the semileptonic decay is mediated by a vector interaction, before treat…
We perform a complete "Michel parameter" analysis of all possible helicity structures which can appear in the process $B \to X_c \ell \barν_\ell$. We take into account the full set of operators parametrizing the effective Hamiltonian and include the complete one-loop QCD corrections as well as the non-perturbative contributions. The moments of the leptonic energy as well as the combined moments of the hadronic energy and hadronic invariant mass are calculated including the non-standard contributions.
Recent progress in calculating O(alpha_s^2) corrections to inclusive and exclusive semileptonic b-->c transitions is reviewed. The impact of these corrections on the |V_cb| determination from both inclusive and exclusive B decays is discussed.
We have quantitatively reanalyzed the inclusive charmed-baryon decays. New ingredients are the Voloshin preasymptotic effects in semileptonic decays and the Cabibbo-subleading contributions to both semileptonic and nonleptonic decays. It has been found that the Cabbibo-subleading Voloshin contribution essentially improves the theoretical semileptonic branching ratio of $Λ_c^{+}$, in agreement with experiment. The semileptonic branching ratios for $Ξ_c^{+}$ and $Ω_c^{0}$ are found to be large, i.e., of the order of 20%. The lifetimes hierarchy is in a good qualitative and even quantitative agre…
A field theoretic description for inclusive semileptonic B meson decays is formulated. We argue that large regions of the phase spaces for the decays are dominated by distances near the light cone. The light-cone dominance allows to incorporate nonperturbative QCD effects in a distribution function. A one-to-one correspondence with the heavy quark effective theory is developed, which can estimate the first two moments of the distribution function. These conditions are useful but not restrictive enough to specify the distribution function, which must still be determined from experiment. Several…
The differential decay spectrum $dΓ/dE_e dq^2$ for the semileptonic decay of an unpolarized hadron containing a b-quark, and the decay spectrum $dΓ/dE_e dq^2 d\!\cosθ$ for polarized $Λ_b$ decay are computed to second order in the $1/m_b$ expansion. Most of the $1/m_b^2$ corrections have a simple physical interpretation, which is discussed in detail. The implications of the results for the determination of $V_{ub}$ are discussed. The decay spectra for semileptonic decay of hadrons containing a c-quark are also given. There is a subtlety in the use of the equations of motion at order $1/m_b^2$ i…
In this article two-loop QED corrections to the muon decay and corrections of order $α_s^2$ to the semileptonic decay of the bottom quark are considered. We compute the imaginary part of the four-loop diagrams contributing to the corresponding fermion propagator in the limit of small external momentum. The on-shell condition is obtained with the help of a conformal mapping and Padé approximation. Via this method we confirm the existing results by an independent calculation.
We report on the determination of $|V_{cb}|$ from the comparison of the semileptonic inclusive decay rates of B-- and D--mesons using the heavy quark symmetry of QCD. While the renormalization scale ambiguity does not allow for a reliable estimate of the quark masses, it almost cancels in the prediction for $|V_{cb}|$, which reads $|V_{cb}|(τ_B/1.49\,{\rm ps})^{1/2} = 0.036\pm 0.005$, where the error stems from the uncertainty in the kinetic energy of the heavy quark inside the meson, in the experimental branching ratios, in QCD input parameters, and from scale uncertainties. This talk is base…
We estimate the sensitivity of single lepton CP violation measurements with respect to that of traditional di-lepton measurements. We find that the sensitivity of the single lepton method is better than that of the di-lepton method. The achievable sensitivity with the currently available data is already in the range relevant to standard model predictions. We also give general expressions for inclusive decay time distributions on $Υ4S$ where the other $B$ is not measured, which will be used to obtain time dependent asymmetries. The expression is of general use whenever one deals with inclusive …
We employ OPE techniques within HQET to calculate the inclusive semileptonic decays of polarized $Λ_b$ baryons. Lepton mass effects are included which enables us to also discuss rates into polarized $τ$-leptons. We present explicit results for the longitudinal polarization of the $τ$ in the $Λ_b$ rest frame as well as in the $(τ^-, \bar ν_τ)$ c.m. frame. In both cases we make use of novel calculational techniques which considerably simplify the calculations. The transverse polarization components of the $τ$ are calculated in the $(τ^-,\barν_τ)$ c.m. frame. We delineate how to measure the full …
The study of inclusive semileptonic decays of $B$ mesons is analyzed from the viewpoint of probing hadron structure and strong interactions. General formulas for the differential decay rates are given in terms of the structure functions in arbitrary frame of reference, taking into account the finite charged lepton mass. These formulas can be used for structure function measurements. The behavior of the structure functions is shown to contain information on the constitution of the $B$ meson and the dynamics of strong interactions. Measurements of the structure functions would reveal the existen…
Precision tests of the CKM mechanism and searches for new physics in the flavour sector require dedicated QCD calculations of decay widths and spectra. Significant progress has been achieved in recent years in computing inclusive B decay spectra into light energetic partons. I briefly review different theoretical approaches to this problem focusing on the determination of |V_{ub}| from inclusive semileptonic decays and show that this determination is robust. The largest uncertainty is associated with the value of the b quark mass. Finally I present new numerical results in the DGE resummation-…
We present a new theoretical framework for the study of $B\to X_u \ell ν$ decays, which includes all known perturbative and non-perturbative contributions and a description of leading and subleading Fermi motion effects. The perturbative and non-perturbative regimes are separated by a ``hard'' Wilsonian cutoff $μ\sim 1$ GeV. We bring into focus some problems related to the high $q^2$ region and to Weak Annihilation effects. We provide estimates of the CKM parameter $|V_{ub}|$ using the described framework and discuss the related theoretical uncertainty.
We review recent experimental and theoretical developments in inclusive semileptonic B -> Xc l nu decays. In particular, we discuss the determination of |Vcb| and of the heavy quark masses through fits based on the Operator Product Expansion.
The inclusive and exclusive semileptonic decay distributions for b -> c decay are computed in the Shifman-Voloshin limit. The inclusive decay distributions (computed using an operator product expansion) depend on quark masses, and the exclusive decay distributions depend on hadron masses. Nevertheless, we show explicitly how the first two terms in the 1/m expansion match between the inclusive and exclusive decays. Agreement between the inclusive and exclusive decay rates requires a minimum smearing region of size Lambda_QCD before local duality holds in QCD. The alpha_s corrections to the incl…
I identify a source of Lambda_{QCD}/m_Q corrections to the assumption of quark-hadron duality in the application of heavy quark methods to inclusive heavy quark semileptonic decays Q->q l nu_l. These corrections could substantially affect the accuracy of such methods in practical applications and in particular compromise their utility for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element V_{cb}.
We discuss the Lambda_b-polarization of the bottom baryon Lambda_b in its production and in its decay. Standard Model predictions for b-quark polarization on the Z-peak are reviewed, including beam-quark orientation effects and O(as) radiative corrections to the polarization. The b-quark polarization is expected to be handed over to the Lambda_b into which it fragments with a high degree of efficiency. We present several spin-momentum correlation measures of the spin of the Λ_b with the momenta of its decay products in its inclusive semileptonic decay. We estimate the strengths of the spin-mom…
We develop the perturbative QCD formalism for inclusive semileptonic $B$ meson decays, which includes Sudakov suppression from the resummation of large radiative corrections near the high end of charged lepton energy. Transverse degrees of freedom of partons are introduced to facilitate the factorization of $B$ meson decays. Ambiguities appearing in the quark-level analysis are then avoided. A universal distribution function, arising from the nonperturbative Fermi motion of the $b$ quark, is constructed according to the heavy quark effective field theory based operator product expansion, throu…
We calculate the hadronic tensor for inclusive semileptonic B decay to O(alpha_s). This allows O(alpha_s Lambda_{QCD}/mb) corrections to hadronic invariant mass observables to be directly evaluated with experimentally required cuts on phase space. Several moments of phenomenological interest are presented to O(alpha_s Lambda_{QCD}/mb) and O(Lambda_{QCD}^3/mb^3), allowing a consistent extraction of the HQET parameters up to O(Lambda_{QCD}^3/mb^3) and the b quark mass with theoretical error ~ 50 MeV. The hadronic invariant mass spectrum is examined with a general moment to obtain observables tha…
