A Few Aspects of Heavy Quark Expansion

Two topics in heavy quark expansion are discussed. The heavy quark potential in perturbation theory is reviewed in connection to the problem of the heavy quark mass. The nontrivial reason behind the failure of the "potential subtracted" mass in higher orders is elucidated. The heavy quark sum rules are the second subject. The physics behind the new exact sum rules is described and a simple quantum mechanical derivation is given. The question of saturation of sum rules is discussed. A comment on the nonstandard possibility which would affect analysis of BR_sl(B) vs. n_c is made.Comment: 21 pages, LaTeX, 7 eps figures. To appear in the Proceedings of the UK Phenomenology Workshop on Heavy Flavour and CP Violation, Durham, UK, 17-22 September 200

On Extracting Heavy Quark Parameters from Moments with Cuts

We point out that applying the photon energy cut significantly modifies the moments of energy spectrum in B->X_s+gamma decays, with a certain class of effects not accounted for in the mostly used OPE expressions. This leads to a systematic bias in the extracted values of the b quark mass and other heavy quark parameters. The apparent b quark mass increases typically by 70MeV or more, together with an even more dramatic downward shift in the kinetic expectation value. Accounting for these cut-related shifts brings different measurements into a good agreement, when the OPE-based theory employs the robust approach. These nonperturbative effects are exponential in the effective hardness severely lowered by high cuts, and do not signify a breakdown of the 1/m_b expansion itself. Similar effects in semileptonic b->c decays are briefly addressed. We stress the utility of the second moment of E_gamma once these effects are incorporated.Comment: 8 pages, LaTeX, two figure. Contributed to the Lepton-Photon Conference, 2003, FNA

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

B -> D* at zero recoil revisited

We examine the B -> D* form factor at zero recoil using a continuum QCD approach rooted in the heavy quark sum rules framework. A refined evaluation of the radiative corrections as well as the most recent estimates of higher order power terms together with more careful continuum calculation are included. An upper bound on the form factor of F(1)< 0.93 is derived, based on just the positivity of inelastic contributions. A model-independent estimate of the inelastic contributions shows they are quite significant, lowering the form factor by about 6% or more. This results in an unbiased estimate F(1) \approx 0.86 with about three percent uncertainty in the central value.Comment: 9 pages, 3 figures

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